LMFDB - Galois group: 30T79

Show commands: Magma

magma:G := TransitiveGroup(30, 79);

Group invariants

Abstract group:	$C_{15}:D_{10}$	magma:IdentifyGroup(G);
Order:	$300=2^{2} \cdot 3 \cdot 5^{2}$	magma:Order(G);
Cyclic:	no	magma:IsCyclic(G);
Abelian:	no	magma:IsAbelian(G);
Solvable:	yes	magma:IsSolvable(G);
Nilpotency class:	not nilpotent	magma:NilpotencyClass(G);

Group action invariants

Degree $n$:	$30$	magma:t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$79$	magma:t, n := TransitiveGroupIdentification(G); t;
Parity:	$-1$	magma:IsEven(G);
Primitive:	no	magma:IsPrimitive(G);
$\card{\Aut(F/K)}$:	$3$	magma:Order(Centralizer(SymmetricGroup(n), G));
Generators:	$(1,3,2)(4,10,5,11,6,12)(7,27,8,25,9,26)(13,19,14,20,15,21)(16,28,17,29,18,30)(22,24,23)$, $(1,24,19,12,8,28,26,18,15,5)(2,23,20,11,9,30,27,17,13,4)(3,22,21,10,7,29,25,16,14,6)$	magma:Generators(G);

Low degree resolvents

$\card{(G/N)}$ Galois groups for stem field(s)
$2$: $C_2$ x 3
$4$: $C_2^2$
$6$: $S_3$
$10$: $D_{5}$ x 2
$12$: $D_{6}$
$20$: $D_{10}$ x 2
$60$: $D_5\times S_3$ x 2
$100$: $D_5^2$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$
$6$:	$S_3$
$10$:	$D_{5}$ x 2
$12$:	$D_{6}$
$20$:	$D_{10}$ x 2
$60$:	$D_5\times S_3$ x 2
$100$:	$D_5^2$

Subfields

Degree 2: $C_2$
Degree 3: $S_3$
Degree 5: None
Degree 6: $S_3$
Degree 10: $D_5^2$
Degree 15: None

Low degree siblings

30T79
Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{30}$	$1$	$1$	$0$	$()$
2A	$2^{15}$	$15$	$2$	$15$	$( 1,11)( 2,10)( 3,12)( 4,26)( 5,25)( 6,27)( 7,18)( 8,17)( 9,16)(13,22)(14,24)(15,23)(19,30)(20,29)(21,28)$
2B	$2^{15}$	$15$	$2$	$15$	$( 1,28)( 2,30)( 3,29)( 4,27)( 5,26)( 6,25)( 7,22)( 8,24)( 9,23)(10,21)(11,20)(12,19)(13,17)(14,16)(15,18)$
2C	$2^{12},1^{6}$	$25$	$2$	$12$	$( 4,30)( 5,28)( 6,29)( 7,25)( 8,26)( 9,27)(10,22)(11,23)(12,24)(13,20)(14,21)(15,19)$
3A	$3^{10}$	$2$	$3$	$20$	$( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)$
5A1	$5^{6}$	$2$	$5$	$24$	$( 1, 8,15,19,26)( 2, 9,13,20,27)( 3, 7,14,21,25)( 4,30,23,17,11)( 5,28,24,18,12)( 6,29,22,16,10)$
5A2	$5^{6}$	$2$	$5$	$24$	$( 1,15,26, 8,19)( 2,13,27, 9,20)( 3,14,25, 7,21)( 4,23,11,30,17)( 5,24,12,28,18)( 6,22,10,29,16)$
5B1	$5^{6}$	$2$	$5$	$24$	$( 1,26,19,15, 8)( 2,27,20,13, 9)( 3,25,21,14, 7)( 4,30,23,17,11)( 5,28,24,18,12)( 6,29,22,16,10)$
5B2	$5^{6}$	$2$	$5$	$24$	$( 1,19, 8,26,15)( 2,20, 9,27,13)( 3,21, 7,25,14)( 4,23,11,30,17)( 5,24,12,28,18)( 6,22,10,29,16)$
5C1	$5^{3},1^{15}$	$4$	$5$	$12$	$( 4,23,11,30,17)( 5,24,12,28,18)( 6,22,10,29,16)$
5C2	$5^{3},1^{15}$	$4$	$5$	$12$	$( 4,11,17,23,30)( 5,12,18,24,28)( 6,10,16,22,29)$
5D1	$5^{6}$	$4$	$5$	$24$	$( 1, 8,15,19,26)( 2, 9,13,20,27)( 3, 7,14,21,25)( 4,17,30,11,23)( 5,18,28,12,24)( 6,16,29,10,22)$
5D2	$5^{6}$	$4$	$5$	$24$	$( 1,15,26, 8,19)( 2,13,27, 9,20)( 3,14,25, 7,21)( 4,30,23,17,11)( 5,28,24,18,12)( 6,29,22,16,10)$
6A	$6^{4},3^{2}$	$50$	$6$	$24$	$( 1, 2, 3)( 4,28, 6,30, 5,29)( 7,26, 9,25, 8,27)(10,23,12,22,11,24)(13,21,15,20,14,19)(16,17,18)$
10A1	$10^{3}$	$30$	$10$	$27$	$( 1,23,26,17,19,11,15, 4, 8,30)( 2,22,27,16,20,10,13, 6, 9,29)( 3,24,25,18,21,12,14, 5, 7,28)$
10A3	$10^{3}$	$30$	$10$	$27$	$( 1,17,15,30,26,11, 8,23,19, 4)( 2,16,13,29,27,10, 9,22,20, 6)( 3,18,14,28,25,12, 7,24,21, 5)$
10B1	$10^{3}$	$30$	$10$	$27$	$( 1,12, 8, 5,15,28,19,24,26,18)( 2,11, 9, 4,13,30,20,23,27,17)( 3,10, 7, 6,14,29,21,22,25,16)$
10B3	$10^{3}$	$30$	$10$	$27$	$( 1, 5,19,18, 8,28,26,12,15,24)( 2, 4,20,17, 9,30,27,11,13,23)( 3, 6,21,16, 7,29,25,10,14,22)$
15A1	$15^{2}$	$4$	$15$	$28$	$( 1,14,27, 8,21, 2,15,25, 9,19, 3,13,26, 7,20)( 4,22,12,30,16, 5,23,10,28,17, 6,24,11,29,18)$
15A2	$15^{2}$	$4$	$15$	$28$	$( 1,27,21,15, 9, 3,26,20,14, 8, 2,25,19,13, 7)( 4,12,16,23,28, 6,11,18,22,30, 5,10,17,24,29)$
15B1	$15^{2}$	$4$	$15$	$28$	$( 1,20, 7,26,13, 3,19, 9,25,15, 2,21, 8,27,14)( 4,24,10,30,18, 6,23,12,29,17, 5,22,11,28,16)$
15B2	$15^{2}$	$4$	$15$	$28$	$( 1, 9,14,19,27, 3, 8,13,21,26, 2, 7,15,20,25)( 4,12,16,23,28, 6,11,18,22,30, 5,10,17,24,29)$
15C1	$15,3^{5}$	$4$	$15$	$24$	$( 1, 3, 2)( 4,10,18,23,29, 5,11,16,24,30, 6,12,17,22,28)( 7, 9, 8)(13,15,14)(19,21,20)(25,27,26)$
15C-1	$15,3^{5}$	$4$	$15$	$24$	$( 1,25,20,15, 7, 2,26,21,13, 8, 3,27,19,14, 9)( 4, 6, 5)(10,12,11)(16,18,17)(22,24,23)(28,30,29)$
15C2	$15,3^{5}$	$4$	$15$	$24$	$( 1, 2, 3)( 4,18,29,11,24, 6,17,28,10,23, 5,16,30,12,22)( 7, 8, 9)(13,14,15)(19,20,21)(25,26,27)$
15C-2	$15,3^{5}$	$4$	$15$	$24$	$( 1,20, 7,26,13, 3,19, 9,25,15, 2,21, 8,27,14)( 4, 5, 6)(10,11,12)(16,17,18)(22,23,24)(28,29,30)$
15D1	$15^{2}$	$4$	$15$	$28$	$( 1,13,25, 8,20, 3,15,27, 7,19, 2,14,26, 9,21)( 4,28,22,17,12, 6,30,24,16,11, 5,29,23,18,10)$
15D-1	$15^{2}$	$4$	$15$	$28$	$( 1, 9,14,19,27, 3, 8,13,21,26, 2, 7,15,20,25)( 4,24,10,30,18, 6,23,12,29,17, 5,22,11,28,16)$
15D2	$15^{2}$	$4$	$15$	$28$	$( 1, 7,13,19,25, 2, 8,14,20,26, 3, 9,15,21,27)( 4,16,28,11,22, 5,17,29,12,23, 6,18,30,10,24)$
15D-2	$15^{2}$	$4$	$15$	$28$	$( 1,21, 9,26,14, 2,19, 7,27,15, 3,20, 8,25,13)( 4,29,24,17,10, 5,30,22,18,11, 6,28,23,16,12)$

Malle's constant $a(G)$: $1/12$

magma:ConjugacyClasses(G);

Character table

		1A	2A	2B	2C	3A	5A1	5A2	5B1	5B2	5C1	5C2	5D1	5D2	6A	10A1	10A3	10B1	10B3	15A1	15A2	15B1	15B2	15C1	15C-1	15C2	15C-2	15D1	15D-1	15D2	15D-2
	Size	1	15	15	25	2	2	2	2	2	4	4	4	4	50	30	30	30	30	4	4	4	4	4	4	4	4	4	4	4	4
	2 P	1A	1A	1A	1A	3A	5A2	5A1	5B2	5B1	5C2	5C1	5D2	5D1	3A	5B1	5B2	5A1	5A2	15A2	15A1	15B2	15B1	15C2	15C-2	15C1	15C-1	15D2	15D-2	15D1	15D-1
	3 P	1A	2A	2B	2C	1A	5A2	5A1	5B2	5B1	5C2	5C1	5D2	5D1	2C	10A3	10A1	10B3	10B1	5A1	5A2	5B1	5B2	5C1	5C1	5C2	5C2	5D1	5D1	5D2	5D2
	5 P	1A	2A	2B	2C	3A	1A	1A	1A	1A	1A	1A	1A	1A	6A	2A	2A	2B	2B	3A	3A	3A	3A	3A	3A	3A	3A	3A	3A	3A	3A
	Type
300.40.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
300.40.1b	R	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
300.40.1c	R	$1$	$- 1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
300.40.1d	R	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
300.40.2a	R	$2$	$0$	$0$	$2$	$- 1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$- 1$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
300.40.2b	R	$2$	$0$	$0$	$- 2$	$- 1$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$2$	$1$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
300.40.2c1	R	$2$	$0$	$2$	$0$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$0$	$0$	$0$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$
300.40.2c2	R	$2$	$0$	$2$	$0$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$0$	$0$	$0$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$
300.40.2d1	R	$2$	$2$	$0$	$0$	$2$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$0$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$0$	$0$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$
300.40.2d2	R	$2$	$2$	$0$	$0$	$2$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$0$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$0$	$0$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$
300.40.2e1	R	$2$	$- 2$	$0$	$0$	$2$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$0$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$0$	$0$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$
300.40.2e2	R	$2$	$- 2$	$0$	$0$	$2$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$0$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$0$	$0$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$
300.40.2f1	R	$2$	$0$	$- 2$	$0$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$0$	$0$	$0$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$
300.40.2f2	R	$2$	$0$	$- 2$	$0$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$0$	$0$	$0$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$ζ_{5}^{- 2} + ζ_{5}^{2}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$2$	$ζ_{5}^{- 1} + ζ_{5}$	$ζ_{5}^{- 1} + ζ_{5}$
300.40.4a1	R	$4$	$0$	$0$	$0$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$- 1$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$- 1$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- 1$	$- 1$	$- 1$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$
300.40.4a2	R	$4$	$0$	$0$	$0$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$- 1$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$- 1$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- 1$	$- 1$	$- 1$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$
300.40.4b1	R	$4$	$0$	$0$	$0$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- 1$	$- 1$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$0$	$0$	$0$	$0$	$0$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- 1$	$- 1$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$- 1$	$- 1$
300.40.4b2	R	$4$	$0$	$0$	$0$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- 1$	$- 1$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$0$	$0$	$0$	$0$	$0$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- 1$	$- 1$	$ζ_{5}^{- 2} + 2 + ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$- ζ_{5}^{- 2} + 1 - ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$- 1$	$- 1$
300.40.4c1	R	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$0$	$0$	$0$	$0$	$0$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- 2$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- 2$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$
300.40.4c2	R	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$0$	$0$	$0$	$0$	$0$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- 2$	$- ζ_{5}^{- 1} - ζ_{5}$	$- 2$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$
300.40.4d1	R	$4$	$0$	$0$	$0$	$- 2$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$0$	$0$	$0$	$0$	$0$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- 2$	$- ζ_{5}^{- 1} - ζ_{5}$	$- 2$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$
300.40.4d2	R	$4$	$0$	$0$	$0$	$- 2$	$4$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$4$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 1} + 2 ζ_{5}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$2 ζ_{5}^{- 2} + 2 ζ_{5}^{2}$	$0$	$0$	$0$	$0$	$0$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- 2$	$- ζ_{5}^{- 2} - ζ_{5}^{2}$	$- 2$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$	$- ζ_{5}^{- 1} - ζ_{5}$
300.40.4e1	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$- 1$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$
300.40.4e2	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$- 1$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$
300.40.4e3	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$- 1$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$
300.40.4e4	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$- 1$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$- 1$	$0$	$0$	$0$	$0$	$0$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$
300.40.4f1	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$- 1$	$- 1$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$0$	$0$	$0$	$0$	$0$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$
300.40.4f2	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$- 1$	$- 1$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$0$	$0$	$0$	$0$	$0$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$
300.40.4f3	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$- 1$	$- 1$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$0$	$0$	$0$	$0$	$0$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$
300.40.4f4	C	$4$	$0$	$0$	$0$	$- 2$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 6} + 2 ζ_{15}^{6}$	$2 ζ_{15}^{- 3} + 2 ζ_{15}^{3}$	$2 - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{7}$	$- 1$	$- 1$	$1 + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{7}$	$0$	$0$	$0$	$0$	$0$	$ζ_{15} + ζ_{15}^{4} + 2 ζ_{15}^{5}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$- 1 - ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - ζ_{15}^{4} - 2 ζ_{15}^{5} - ζ_{15}^{7}$	$1 - ζ_{15} - ζ_{15}^{4} + 3 ζ_{15}^{5}$	$- 3 + ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + ζ_{15}^{4} - 3 ζ_{15}^{5} + ζ_{15}^{7}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 3} - ζ_{15}^{3}$	$- ζ_{15}^{- 6} - ζ_{15}^{6}$	$- 1 + 2 ζ_{15} + ζ_{15}^{2} - ζ_{15}^{3} + 2 ζ_{15}^{4} - ζ_{15}^{5} + ζ_{15}^{7}$	$2 - 2 ζ_{15} - ζ_{15}^{2} + ζ_{15}^{3} - 2 ζ_{15}^{4} + ζ_{15}^{5} - ζ_{15}^{7}$

magma:CharacterTable(G);

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	30T79

Degree	$30$
Order	$300$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$-group	no
Group:	$C_{15}:D_{10}$