LMFDB - Galois group: 45T48

Show commands: Magma

magma: G := TransitiveGroup(45, 48);

Group action invariants

Degree $n$:	$45$	magma: t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$:	$48$	magma: t, n := TransitiveGroupIdentification(G); t;
Group:	$C_3:S_3\times F_5$
Parity:	$-1$	magma: IsEven(G);
Primitive:	no	magma: IsPrimitive(G);
magma: NilpotencyClass(G);
$\card{\Aut(F/K)}$:	$1$	magma: Order(Centralizer(SymmetricGroup(n), G));
Generators:	(1,22)(2,24)(3,23)(4,20)(5,19)(6,21)(7,18)(8,17)(9,16)(10,14)(11,13)(12,15)(25,45)(26,44)(27,43)(28,40)(29,42)(30,41)(31,37)(32,39)(33,38)(34,36), (1,9,41,19,16,22,10,35,31,37,27,5)(2,7,40,21,17,23,12,34,32,38,26,4)(3,8,42,20,18,24,11,36,33,39,25,6)(13,29,45)(14,30,43)(15,28,44), (1,15,34,37,33,45,19,24,17,30,6,7)(2,14,36,38,31,44,21,22,18,29,5,8)(3,13,35,39,32,43,20,23,16,28,4,9)(10,42,26)(11,40,27)(12,41,25)	magma: Generators(G);

Low degree resolvents

|G/N| Galois groups for stem field(s)
$2$: $C_2$ x 3
$4$: $C_4$ x 2, $C_2^2$
$6$: $S_3$ x 4
$8$: $C_4\times C_2$
$12$: $D_{6}$ x 4
$18$: $C_3^2:C_2$
$20$: $F_5$
$24$: $S_3 \times C_4$ x 4
$36$: 18T12
$40$: $F_{5}\times C_2$
$72$: 36T41
$120$: $F_5 \times S_3$ x 4

Resolvents shown for degrees $\leq 47$

\|G/N\|	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_4$ x 2, $C_2^2$
$6$:	$S_3$ x 4
$8$:	$C_4\times C_2$
$12$:	$D_{6}$ x 4
$18$:	$C_3^2:C_2$
$20$:	$F_5$
$24$:	$S_3 \times C_4$ x 4
$36$:	18T12
$40$:	$F_{5}\times C_2$
$72$:	36T41
$120$:	$F_5 \times S_3$ x 4

Subfields

Degree 3: $S_3$ x 4
Degree 5: $F_5$
Degree 9: $C_3^2:C_2$
Degree 15: $F_5 \times S_3$ x 4

Low degree siblings

There are no siblings with degree $\leq 47$

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

Conjugacy classes

Label	Cycle Type	Size	Order	Representative
	$ 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$2$	$( 4,13)( 5,14)( 6,15)( 7,26)( 8,25)( 9,27)(10,37)(11,39)(12,38)(19,30)(20,28) (21,29)(22,41)(23,40)(24,42)(34,45)(35,43)(36,44)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$4$	$( 4,23,13,40)( 5,22,14,41)( 6,24,15,42)( 7,45,26,34)( 8,44,25,36)( 9,43,27,35) (10,19,37,30)(11,20,39,28)(12,21,38,29)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$5$	$4$	$( 4,40,13,23)( 5,41,14,22)( 6,42,15,24)( 7,34,26,45)( 8,36,25,44)( 9,35,27,43) (10,30,37,19)(11,28,39,20)(12,29,38,21)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 1 $	$45$	$4$	$( 2, 3)( 4, 8,13,25)( 5, 9,14,27)( 6, 7,15,26)(10,19,37,30)(11,21,39,29) (12,20,38,28)(16,31)(17,33)(18,32)(22,43,41,35)(23,44,40,36)(24,45,42,34)$
	$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 1 $	$45$	$4$	$( 2, 3)( 4,25,13, 8)( 5,27,14, 9)( 6,26,15, 7)(10,30,37,19)(11,29,39,21) (12,28,38,20)(16,31)(17,33)(18,32)(22,35,41,43)(23,36,40,44)(24,34,42,45)$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1 $	$9$	$2$	$( 2, 3)( 4,36)( 5,35)( 6,34)( 7,24)( 8,23)( 9,22)(11,12)(13,44)(14,43)(15,45) (16,31)(17,33)(18,32)(20,21)(25,40)(26,42)(27,41)(28,29)(38,39)$
	$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $	$45$	$2$	$( 2, 3)( 4,44)( 5,43)( 6,45)( 7,42)( 8,40)( 9,41)(10,37)(11,38)(12,39)(13,36) (14,35)(15,34)(16,31)(17,33)(18,32)(19,30)(20,29)(21,28)(22,27)(23,25)(24,26)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$2$	$3$	$( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,12,11)(13,15,14)(16,17,18)(19,21,20) (22,23,24)(25,27,26)(28,30,29)(31,32,33)(34,36,35)(37,38,39)(40,42,41) (43,45,44)$
	$ 6, 6, 6, 6, 6, 6, 3, 3, 3 $	$10$	$6$	$( 1, 2, 3)( 4,15, 5,13, 6,14)( 7,25, 9,26, 8,27)(10,38,11,37,12,39)(16,17,18) (19,29,20,30,21,28)(22,40,24,41,23,42)(31,32,33)(34,44,35,45,36,43)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 2, 3)( 4,24,14,40, 6,22,13,42, 5,23,15,41)( 7,44,27,34, 8,43,26,36, 9,45, 25,35)(10,21,39,30,12,20,37,29,11,19,38,28)(16,17,18)(31,32,33)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 2, 3)( 4,42,14,23, 6,41,13,24, 5,40,15,22)( 7,36,27,45, 8,35,26,44, 9,34, 25,43)(10,29,39,19,12,28,37,21,11,30,38,20)(16,17,18)(31,32,33)$
	$ 10, 10, 10, 10, 5 $	$36$	$10$	$( 1, 4,37,40,30,32,19,23,10,13)( 2, 5,38,41,29,31,21,22,12,14)( 3, 6,39,42,28, 33,20,24,11,15)( 7,27,45,16,34, 9,26,43,17,35)( 8,25,44,18,36)$
	$ 15, 15, 15 $	$8$	$15$	$( 1, 4, 8,10,13,18,19,23,25,30,32,36,37,40,44)( 2, 6, 9,12,15,16,21,24,27,29, 33,35,38,42,43)( 3, 5, 7,11,14,17,20,22,26,28,31,34,39,41,45)$
	$ 6, 6, 6, 6, 6, 6, 3, 3, 3 $	$10$	$6$	$( 1, 4,18,19,32,36)( 2, 6,16,21,33,35)( 3, 5,17,20,31,34)( 7,28,22,45,39,14) ( 8,30,23,44,37,13)( 9,29,24,43,38,15)(10,40,25)(11,41,26)(12,42,27)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 4,25,37,32,36,10,23,18,19,40, 8)( 2, 6,27,38,33,35,12,24,16,21,42, 9) ( 3, 5,26,39,31,34,11,22,17,20,41, 7)(13,44,30)(14,45,28)(15,43,29)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 4,44,10,32,36,30,40,18,19,13,25)( 2, 6,43,12,33,35,29,42,16,21,15,27) ( 3, 5,45,11,31,34,28,41,17,20,14,26)( 7,39,22)( 8,37,23)( 9,38,24)$
	$ 15, 15, 15 $	$8$	$15$	$( 1, 5, 9,10,14,16,19,22,27,30,31,35,37,41,43)( 2, 4, 7,12,13,17,21,23,26,29, 32,34,38,40,45)( 3, 6, 8,11,15,18,20,24,25,28,33,36,39,42,44)$
	$ 6, 6, 6, 6, 6, 6, 3, 3, 3 $	$10$	$6$	$( 1, 5,16,19,31,35)( 2, 4,17,21,32,34)( 3, 6,18,20,33,36)( 7,29,23,45,38,13) ( 8,28,24,44,39,15)( 9,30,22,43,37,14)(10,41,27)(11,42,25)(12,40,26)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 5,27,37,31,35,10,22,16,19,41, 9)( 2, 4,26,38,32,34,12,23,17,21,40, 7) ( 3, 6,25,39,33,36,11,24,18,20,42, 8)(13,45,29)(14,43,30)(15,44,28)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 5,43,10,31,35,30,41,16,19,14,27)( 2, 4,45,12,32,34,29,40,17,21,13,26) ( 3, 6,44,11,33,36,28,42,18,20,15,25)( 7,38,23)( 8,39,24)( 9,37,22)$
	$ 15, 15, 15 $	$8$	$15$	$( 1, 6, 7,10,15,17,19,24,26,30,33,34,37,42,45)( 2, 5, 8,12,14,18,21,22,25,29, 31,36,38,41,44)( 3, 4, 9,11,13,16,20,23,27,28,32,35,39,40,43)$
	$ 6, 6, 6, 6, 6, 6, 3, 3, 3 $	$10$	$6$	$( 1, 6,17,19,33,34)( 2, 5,18,21,31,36)( 3, 4,16,20,32,35)( 7,30,24,45,37,15) ( 8,29,22,44,38,14)( 9,28,23,43,39,13)(10,42,26)(11,40,27)(12,41,25)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 6,26,37,33,34,10,24,17,19,42, 7)( 2, 5,25,38,31,36,12,22,18,21,41, 8) ( 3, 4,27,39,32,35,11,23,16,20,40, 9)(13,43,28)(14,44,29)(15,45,30)$
	$ 12, 12, 12, 3, 3, 3 $	$10$	$12$	$( 1, 6,45,10,33,34,30,42,17,19,15,26)( 2, 5,44,12,31,36,29,41,18,21,14,25) ( 3, 4,43,11,32,35,28,40,16,20,13,27)( 7,37,24)( 8,38,22)( 9,39,23)$
	$ 5, 5, 5, 5, 5, 5, 5, 5, 5 $	$4$	$5$	$( 1,10,19,30,37)( 2,12,21,29,38)( 3,11,20,28,39)( 4,13,23,32,40) ( 5,14,22,31,41)( 6,15,24,33,42)( 7,17,26,34,45)( 8,18,25,36,44) ( 9,16,27,35,43)$
	$ 15, 15, 15 $	$8$	$15$	$( 1,11,21,30,39, 2,10,20,29,37, 3,12,19,28,38)( 4,14,24,32,41, 6,13,22,33,40, 5,15,23,31,42)( 7,16,25,34,43, 8,17,27,36,45, 9,18,26,35,44)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$2$	$3$	$( 1,16,31)( 2,17,32)( 3,18,33)( 4,21,34)( 5,19,35)( 6,20,36)( 7,23,38) ( 8,24,39)( 9,22,37)(10,27,41)(11,25,42)(12,26,40)(13,29,45)(14,30,43) (15,28,44)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$2$	$3$	$( 1,17,33)( 2,18,31)( 3,16,32)( 4,20,35)( 5,21,36)( 6,19,34)( 7,24,37) ( 8,22,38)( 9,23,39)(10,26,42)(11,27,40)(12,25,41)(13,28,43)(14,29,44) (15,30,45)$
	$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $	$2$	$3$	$( 1,18,32)( 2,16,33)( 3,17,31)( 4,19,36)( 5,20,34)( 6,21,35)( 7,22,39) ( 8,23,37)( 9,24,38)(10,25,40)(11,26,41)(12,27,42)(13,30,44)(14,28,45) (15,29,43)$

magma: ConjugacyClasses(G);

Group invariants

Order:	$360=2^{3} \cdot 3^{2} \cdot 5$	magma: Order(G);
Cyclic:	no	magma: IsCyclic(G);
Abelian:	no	magma: IsAbelian(G);
Solvable:	yes	magma: IsSolvable(G);
Nilpotency class:	not nilpotent
Label:	360.127	magma: IdentifyGroup(G);
Character table:

		1A	2A	2B	2C	3A	3B	3C	3D	4A1	4A-1	4B1	4B-1	5A	6A	6B	6C	6D	10A	12A1	12A-1	12B1	12B-1	12C1	12C-1	12D1	12D-1	15A	15B	15C	15D
	Size	1	5	9	45	2	2	2	2	5	5	45	45	4	10	10	10	10	36	10	10	10	10	10	10	10	10	8	8	8	8
	2 P	1A	1A	1A	1A	3A	3B	3C	3D	2A	2A	2A	2A	5A	3A	3B	3C	3D	5A	6C	6A	6B	6D	6A	6C	6D	6B	15A	15B	15C	15D
	3 P	1A	2A	2B	2C	1A	1A	1A	1A	4A-1	4A1	4B-1	4B1	5A	2A	2A	2A	2A	10A	4A-1	4A1	4A-1	4A-1	4A-1	4A1	4A1	4A1	5A	5A	5A	5A
	5 P	1A	2A	2B	2C	3A	3B	3C	3D	4A1	4A-1	4B1	4B-1	1A	6A	6B	6C	6D	2B	12C1	12A1	12B1	12D1	12A-1	12C-1	12D-1	12B-1	3A	3B	3D	3C
	Type
360.127.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
360.127.1b	R	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$
360.127.1c	R	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
360.127.1d	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$
360.127.1e1	C	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$- i$	$i$	$i$	$- i$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$i$	$- i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$1$	$1$	$1$	$1$
360.127.1e2	C	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$i$	$- i$	$- i$	$i$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- i$	$i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$1$	$1$	$1$	$1$
360.127.1f1	C	$1$	$- 1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$- i$	$i$	$- i$	$i$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$i$	$- i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$1$	$1$	$1$	$1$
360.127.1f2	C	$1$	$- 1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$i$	$- i$	$i$	$- i$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$- i$	$i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$1$	$1$	$1$	$1$
360.127.2a	R	$2$	$2$	$0$	$0$	$- 1$	$- 1$	$- 1$	$2$	$2$	$2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$2$	$0$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$2$	$2$	$- 1$	$- 1$	$2$	$- 1$
360.127.2b	R	$2$	$2$	$0$	$0$	$- 1$	$- 1$	$2$	$- 1$	$2$	$2$	$0$	$0$	$2$	$- 1$	$- 1$	$2$	$- 1$	$0$	$- 1$	$- 1$	$- 1$	$- 1$	$2$	$2$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$2$
360.127.2c	R	$2$	$2$	$0$	$0$	$- 1$	$2$	$- 1$	$- 1$	$2$	$2$	$0$	$0$	$2$	$- 1$	$2$	$- 1$	$- 1$	$0$	$- 1$	$- 1$	$2$	$2$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$2$	$- 1$	$- 1$
360.127.2d	R	$2$	$2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$2$	$2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$2$	$- 1$	$- 1$	$- 1$
360.127.2e	R	$2$	$2$	$0$	$0$	$- 1$	$- 1$	$- 1$	$2$	$- 2$	$- 2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$2$	$0$	$1$	$1$	$1$	$1$	$1$	$1$	$- 2$	$- 2$	$- 1$	$- 1$	$2$	$- 1$
360.127.2f	R	$2$	$2$	$0$	$0$	$- 1$	$- 1$	$2$	$- 1$	$- 2$	$- 2$	$0$	$0$	$2$	$- 1$	$- 1$	$2$	$- 1$	$0$	$1$	$1$	$1$	$1$	$- 2$	$- 2$	$1$	$1$	$- 1$	$- 1$	$- 1$	$2$
360.127.2g	R	$2$	$2$	$0$	$0$	$- 1$	$2$	$- 1$	$- 1$	$- 2$	$- 2$	$0$	$0$	$2$	$- 1$	$2$	$- 1$	$- 1$	$0$	$1$	$1$	$- 2$	$- 2$	$1$	$1$	$1$	$1$	$- 1$	$2$	$- 1$	$- 1$
360.127.2h	R	$2$	$2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$- 2$	$- 2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$- 2$	$- 2$	$1$	$1$	$1$	$1$	$1$	$1$	$2$	$- 1$	$- 1$	$- 1$
360.127.2i1	C	$2$	$- 2$	$0$	$0$	$- 1$	$- 1$	$- 1$	$2$	$- 2 i$	$2 i$	$0$	$0$	$2$	$1$	$1$	$1$	$- 2$	$0$	$- i$	$i$	$i$	$- i$	$i$	$- i$	$- 2 i$	$2 i$	$- 1$	$- 1$	$2$	$- 1$
360.127.2i2	C	$2$	$- 2$	$0$	$0$	$- 1$	$- 1$	$- 1$	$2$	$2 i$	$- 2 i$	$0$	$0$	$2$	$1$	$1$	$1$	$- 2$	$0$	$i$	$- i$	$- i$	$i$	$- i$	$i$	$2 i$	$- 2 i$	$- 1$	$- 1$	$2$	$- 1$
360.127.2j1	C	$2$	$- 2$	$0$	$0$	$- 1$	$- 1$	$2$	$- 1$	$- 2 i$	$2 i$	$0$	$0$	$2$	$1$	$1$	$- 2$	$1$	$0$	$- i$	$i$	$i$	$- i$	$- 2 i$	$2 i$	$i$	$- i$	$- 1$	$- 1$	$- 1$	$2$
360.127.2j2	C	$2$	$- 2$	$0$	$0$	$- 1$	$- 1$	$2$	$- 1$	$2 i$	$- 2 i$	$0$	$0$	$2$	$1$	$1$	$- 2$	$1$	$0$	$i$	$- i$	$- i$	$i$	$2 i$	$- 2 i$	$- i$	$i$	$- 1$	$- 1$	$- 1$	$2$
360.127.2k1	C	$2$	$- 2$	$0$	$0$	$- 1$	$2$	$- 1$	$- 1$	$- 2 i$	$2 i$	$0$	$0$	$2$	$1$	$- 2$	$1$	$1$	$0$	$- i$	$i$	$- 2 i$	$2 i$	$i$	$- i$	$i$	$- i$	$- 1$	$2$	$- 1$	$- 1$
360.127.2k2	C	$2$	$- 2$	$0$	$0$	$- 1$	$2$	$- 1$	$- 1$	$2 i$	$- 2 i$	$0$	$0$	$2$	$1$	$- 2$	$1$	$1$	$0$	$i$	$- i$	$2 i$	$- 2 i$	$- i$	$i$	$- i$	$i$	$- 1$	$2$	$- 1$	$- 1$
360.127.2l1	C	$2$	$- 2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$- 2 i$	$2 i$	$0$	$0$	$2$	$- 2$	$1$	$1$	$1$	$0$	$2 i$	$- 2 i$	$i$	$- i$	$i$	$- i$	$i$	$- i$	$2$	$- 1$	$- 1$	$- 1$
360.127.2l2	C	$2$	$- 2$	$0$	$0$	$2$	$- 1$	$- 1$	$- 1$	$2 i$	$- 2 i$	$0$	$0$	$2$	$- 2$	$1$	$1$	$1$	$0$	$- 2 i$	$2 i$	$- i$	$i$	$- i$	$i$	$- i$	$i$	$2$	$- 1$	$- 1$	$- 1$
360.127.4a	R	$4$	$0$	$4$	$0$	$4$	$4$	$4$	$4$	$0$	$0$	$0$	$0$	$- 1$	$0$	$0$	$0$	$0$	$- 1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$- 1$	$- 1$
360.127.4b	R	$4$	$0$	$- 4$	$0$	$4$	$4$	$4$	$4$	$0$	$0$	$0$	$0$	$- 1$	$0$	$0$	$0$	$0$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$- 1$	$- 1$
360.127.8a	R	$8$	$0$	$0$	$0$	$- 4$	$- 4$	$- 4$	$8$	$0$	$0$	$0$	$0$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$- 2$	$1$
360.127.8b	R	$8$	$0$	$0$	$0$	$- 4$	$- 4$	$8$	$- 4$	$0$	$0$	$0$	$0$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$1$	$1$	$- 2$
360.127.8c	R	$8$	$0$	$0$	$0$	$- 4$	$8$	$- 4$	$- 4$	$0$	$0$	$0$	$0$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$1$	$- 2$	$1$	$1$
360.127.8d	R	$8$	$0$	$0$	$0$	$8$	$- 4$	$- 4$	$- 4$	$0$	$0$	$0$	$0$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$- 2$	$1$	$1$	$1$

magma: CharacterTable(G);

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

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Group action invariants

Low degree resolvents

Subfields

Low degree siblings

Conjugacy classes

Group invariants

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	45T48
Degree	$45$
Order	$360$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$-group	no
Group:	$C_3:S_3\times F_5$