# Properties

 Label 30T42 Degree $30$ Order $180$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no Group: $S_3\times D_{15}$

Show commands: Magma

magma: G := TransitiveGroup(30, 42);

## Group action invariants

 Degree $n$: $30$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $42$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $S_3\times D_{15}$ 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: (16,18,17)(19,21,20)(22,24,23)(25,27,26)(28,30,29), (2,3)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(16,28)(17,30)(18,29)(19,27)(20,26)(21,25)(22,23), (1,17,6,19,7,23,12,25,13,28)(2,18,4,20,8,24,10,26,14,29)(3,16,5,21,9,22,11,27,15,30) magma: Generators(G);

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$ x 2
$10$:  $D_{5}$
$12$:  $D_{6}$ x 2
$20$:  $D_{10}$
$30$:  $D_{15}$
$36$:  $S_3^2$
$60$:  $D_5\times S_3$, $D_{30}$

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: $C_2$

Degree 3: None

Degree 5: $D_{5}$

Degree 6: $S_3^2$

Degree 10: $D_{10}$

Degree 15: None

## Low degree siblings

45T13

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 $2^{15}$ $3$ $2$ $15$ $( 1,24)( 2,22)( 3,23)( 4,27)( 5,25)( 6,26)( 7,29)( 8,30)( 9,28)(10,16)(11,17)(12,18)(13,20)(14,21)(15,19)$ 2B $2^{15}$ $15$ $2$ $15$ $( 1,24)( 2,23)( 3,22)( 4,19)( 5,21)( 6,20)( 7,18)( 8,17)( 9,16)(10,28)(11,30)(12,29)(13,26)(14,25)(15,27)$ 2C $2^{14},1^{2}$ $45$ $2$ $14$ $( 1, 3)( 4,14)( 5,13)( 6,15)( 7,11)( 8,10)( 9,12)(16,29)(17,28)(18,30)(19,25)(20,27)(21,26)(22,24)$ 3A $3^{10}$ $2$ $3$ $20$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)$ 3B $3^{10}$ $2$ $3$ $20$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27)(28,29,30)$ 3C $3^{5},1^{15}$ $4$ $3$ $10$ $(16,18,17)(19,21,20)(22,24,23)(25,27,26)(28,30,29)$ 5A1 $5^{6}$ $2$ $5$ $24$ $( 1,12, 6,13, 7)( 2,10, 4,14, 8)( 3,11, 5,15, 9)(16,27,21,30,22)(17,25,19,28,23)(18,26,20,29,24)$ 5A2 $5^{6}$ $2$ $5$ $24$ $( 1, 6, 7,12,13)( 2, 4, 8,10,14)( 3, 5, 9,11,15)(16,21,22,27,30)(17,19,23,25,28)(18,20,24,26,29)$ 6A $6^{5}$ $6$ $6$ $25$ $( 1,22, 3,24, 2,23)( 4,25, 6,27, 5,26)( 7,30, 9,29, 8,28)(10,17,12,16,11,18)(13,21,15,20,14,19)$ 6B $6^{5}$ $30$ $6$ $25$ $( 1,23, 3,24, 2,22)( 4,21, 6,19, 5,20)( 7,17, 9,18, 8,16)(10,30,12,28,11,29)(13,25,15,26,14,27)$ 10A1 $10^{3}$ $6$ $10$ $27$ $( 1,18, 6,20, 7,24,12,26,13,29)( 2,16, 4,21, 8,22,10,27,14,30)( 3,17, 5,19, 9,23,11,25,15,28)$ 10A3 $10^{3}$ $6$ $10$ $27$ $( 1,26, 7,18,13,24, 6,29,12,20)( 2,27, 8,16,14,22, 4,30,10,21)( 3,25, 9,17,15,23, 5,28,11,19)$ 15A1 $15^{2}$ $2$ $15$ $28$ $( 1, 8,15, 6,10, 3, 7,14, 5,12, 2, 9,13, 4,11)(16,23,29,21,25,18,22,28,20,27,17,24,30,19,26)$ 15A2 $15^{2}$ $2$ $15$ $28$ $( 1,10, 5,13, 8, 3,12, 4,15, 7, 2,11, 6,14, 9)(16,25,20,30,23,18,27,19,29,22,17,26,21,28,24)$ 15A4 $15^{2}$ $2$ $15$ $28$ $( 1,14,11, 7, 4, 3,13,10, 9, 6, 2,15,12, 8, 5)(16,28,26,22,19,18,30,25,24,21,17,29,27,23,20)$ 15A7 $15^{2}$ $2$ $15$ $28$ $( 1, 4, 9,12,14, 3, 6, 8,11,13, 2, 5, 7,10,15)(16,19,24,27,28,18,21,23,26,30,17,20,22,25,29)$ 15B1 $15,5^{3}$ $4$ $15$ $26$ $( 1, 7,13, 6,12)( 2, 8,14, 4,10)( 3, 9,15, 5,11)(16,24,28,21,26,17,22,29,19,27,18,23,30,20,25)$ 15B2 $15,5^{3}$ $4$ $15$ $26$ $( 1,12, 6,13, 7)( 2,10, 4,14, 8)( 3,11, 5,15, 9)(16,26,19,30,24,17,27,20,28,22,18,25,21,29,23)$ 15C1 $15^{2}$ $4$ $15$ $28$ $( 1, 5, 8,12,15, 2, 6, 9,10,13, 3, 4, 7,11,14)(16,19,24,27,28,18,21,23,26,30,17,20,22,25,29)$ 15C2 $15,5^{3}$ $4$ $15$ $26$ $( 1, 6, 7,12,13)( 2, 4, 8,10,14)( 3, 5, 9,11,15)(16,20,23,27,29,17,21,24,25,30,18,19,22,26,28)$ 15C4 $15^{2}$ $4$ $15$ $28$ $( 1,11, 4,13, 9, 2,12, 5,14, 7, 3,10, 6,15, 8)(16,25,20,30,23,18,27,19,29,22,17,26,21,28,24)$ 15C7 $15,5^{3}$ $4$ $15$ $26$ $( 1,13,12, 7, 6)( 2,14,10, 8, 4)( 3,15,11, 9, 5)(16,29,25,22,20,17,30,26,23,21,18,28,27,24,19)$ 30A1 $30$ $6$ $30$ $29$ $( 1,27, 9,18,14,23, 6,30,11,20, 2,25, 7,16,15,24, 4,28,12,21, 3,26, 8,17,13,22, 5,29,10,19)$ 30A7 $30$ $6$ $30$ $29$ $( 1,30,15,26,10,23, 7,21, 5,18, 2,28,13,27,11,24, 8,19, 6,16, 3,29,14,25,12,22, 9,20, 4,17)$ 30A11 $30$ $6$ $30$ $29$ $( 1,21,11,29, 4,23,13,16, 9,26, 2,19,12,30, 5,24,14,17, 7,27, 3,20,10,28, 6,22,15,18, 8,25)$ 30A13 $30$ $6$ $30$ $29$ $( 1,16, 5,20, 8,23,12,27,15,29, 2,17, 6,21, 9,24,10,25,13,30, 3,18, 4,19, 7,22,11,26,14,28)$

magma: ConjugacyClasses(G);

Malle's constant $a(G)$:     $1/10$

## Group invariants

 Order: $180=2^{2} \cdot 3^{2} \cdot 5$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: yes magma: IsSolvable(G); Nilpotency class: not nilpotent Label: 180.29 magma: IdentifyGroup(G); Character table:

 1A 2A 2B 2C 3A 3B 3C 5A1 5A2 6A 6B 10A1 10A3 15A1 15A2 15A4 15A7 15B1 15B2 15C1 15C2 15C4 15C7 30A1 30A7 30A11 30A13 Size 1 3 15 45 2 2 4 2 2 6 30 6 6 2 2 2 2 4 4 4 4 4 4 6 6 6 6 2 P 1A 1A 1A 1A 3A 3B 3C 5A2 5A1 3B 3A 5A2 5A1 15A7 15A2 15A4 15A1 15C1 15C4 15B1 15C2 15B2 15C7 15A1 15A7 15A4 15A2 3 P 1A 2A 2B 2C 1A 1A 1A 5A2 5A1 2A 2B 10A3 10A1 5A2 5A2 5A1 5A1 5A2 5A2 5A1 5A1 5A2 5A1 10A1 10A3 10A1 10A3 5 P 1A 2A 2B 2C 3A 3B 3C 1A 1A 6A 6B 2A 2A 3B 3B 3B 3B 3C 3C 3A 3C 3A 3C 6A 6A 6A 6A Type 180.29.1a R $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ 180.29.1b R $1$ $−1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $−1$ $−1$ $−1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $−1$ $−1$ $−1$ $−1$ 180.29.1c R $1$ $−1$ $1$ $−1$ $1$ $1$ $1$ $1$ $1$ $−1$ $1$ $−1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $−1$ $−1$ $−1$ $−1$ 180.29.1d R $1$ $1$ $−1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ 180.29.2a R $2$ $0$ $2$ $0$ $−1$ $2$ $−1$ $2$ $2$ $0$ $−1$ $0$ $0$ $2$ $2$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $0$ $0$ $0$ $0$ 180.29.2b R $2$ $2$ $0$ $0$ $2$ $−1$ $−1$ $2$ $2$ $−1$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ 180.29.2c R $2$ $−2$ $0$ $0$ $2$ $−1$ $−1$ $2$ $2$ $1$ $0$ $−2$ $−2$ $−1$ $−1$ $−1$ $−1$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $1$ $1$ $1$ $1$ 180.29.2d R $2$ $0$ $−2$ $0$ $−1$ $2$ $−1$ $2$ $2$ $0$ $1$ $0$ $0$ $2$ $2$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $0$ $0$ $0$ $0$ 180.29.2e1 R $2$ $2$ $0$ $0$ $2$ $2$ $2$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $2$ $0$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ 180.29.2e2 R $2$ $2$ $0$ $0$ $2$ $2$ $2$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $2$ $0$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ 180.29.2f1 R $2$ $−2$ $0$ $0$ $2$ $2$ $2$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $−2$ $0$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ 180.29.2f2 R $2$ $−2$ $0$ $0$ $2$ $2$ $2$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $−2$ $0$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ 180.29.2g1 R $2$ $2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $−1$ $0$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−4+ζ154$ $ζ15−2+ζ152$ $ζ15−1+ζ15$ $ζ15−7+ζ157$ 180.29.2g2 R $2$ $2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $−1$ $0$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−1+ζ15$ $ζ15−7+ζ157$ $ζ15−4+ζ154$ $ζ15−2+ζ152$ 180.29.2g3 R $2$ $2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $−1$ $0$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−2+ζ152$ $ζ15−1+ζ15$ $ζ15−7+ζ157$ $ζ15−4+ζ154$ 180.29.2g4 R $2$ $2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $−1$ $0$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−7+ζ157$ $ζ15−4+ζ154$ $ζ15−2+ζ152$ $ζ15−1+ζ15$ 180.29.2h1 R $2$ $−2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $1$ $0$ $−ζ15−3−ζ153$ $−ζ15−6−ζ156$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $−ζ15−4−ζ154$ $−ζ15−2−ζ152$ $−ζ15−1−ζ15$ $−ζ15−7−ζ157$ 180.29.2h2 R $2$ $−2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $1$ $0$ $−ζ15−3−ζ153$ $−ζ15−6−ζ156$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $−ζ15−1−ζ15$ $−ζ15−7−ζ157$ $−ζ15−4−ζ154$ $−ζ15−2−ζ152$ 180.29.2h3 R $2$ $−2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $1$ $0$ $−ζ15−6−ζ156$ $−ζ15−3−ζ153$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $−ζ15−2−ζ152$ $−ζ15−1−ζ15$ $−ζ15−7−ζ157$ $−ζ15−4−ζ154$ 180.29.2h4 R $2$ $−2$ $0$ $0$ $2$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $1$ $0$ $−ζ15−6−ζ156$ $−ζ15−3−ζ153$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $−ζ15−7−ζ157$ $−ζ15−4−ζ154$ $−ζ15−2−ζ152$ $−ζ15−1−ζ15$ 180.29.4a R $4$ $0$ $0$ $0$ $−2$ $−2$ $1$ $4$ $4$ $0$ $0$ $0$ $0$ $−2$ $−2$ $−2$ $−2$ $−2$ $−2$ $1$ $1$ $1$ $1$ $0$ $0$ $0$ $0$ 180.29.4b1 R $4$ $0$ $0$ $0$ $−2$ $4$ $−2$ $2ζ5−2+2ζ52$ $2ζ5−1+2ζ5$ $0$ $0$ $0$ $0$ $2ζ5−1+2ζ5$ $2ζ5−2+2ζ52$ $2ζ5−1+2ζ5$ $2ζ5−2+2ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $0$ $0$ $0$ $0$ 180.29.4b2 R $4$ $0$ $0$ $0$ $−2$ $4$ $−2$ $2ζ5−1+2ζ5$ $2ζ5−2+2ζ52$ $0$ $0$ $0$ $0$ $2ζ5−2+2ζ52$ $2ζ5−1+2ζ5$ $2ζ5−2+2ζ52$ $2ζ5−1+2ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $−ζ5−2−ζ52$ $−ζ5−1−ζ5$ $0$ $0$ $0$ $0$ 180.29.4c1 R $4$ $0$ $0$ $0$ $−2$ $−2$ $1$ $2ζ15−6+2ζ156$ $2ζ15−3+2ζ153$ $0$ $0$ $0$ $0$ $2ζ15−7+2ζ157$ $2ζ15−1+2ζ15$ $2ζ15−2+2ζ152$ $2ζ15−4+2ζ154$ $−ζ15−3−ζ153$ $−ζ15−6−ζ156$ $−ζ15−2−ζ152$ $−ζ15−4−ζ154$ $−ζ15−7−ζ157$ $−ζ15−1−ζ15$ $0$ $0$ $0$ $0$ 180.29.4c2 R $4$ $0$ $0$ $0$ $−2$ $−2$ $1$ $2ζ15−6+2ζ156$ $2ζ15−3+2ζ153$ $0$ $0$ $0$ $0$ $2ζ15−2+2ζ152$ $2ζ15−4+2ζ154$ $2ζ15−7+2ζ157$ $2ζ15−1+2ζ15$ $−ζ15−3−ζ153$ $−ζ15−6−ζ156$ $−ζ15−7−ζ157$ $−ζ15−1−ζ15$ $−ζ15−2−ζ152$ $−ζ15−4−ζ154$ $0$ $0$ $0$ $0$ 180.29.4c3 R $4$ $0$ $0$ $0$ $−2$ $−2$ $1$ $2ζ15−3+2ζ153$ $2ζ15−6+2ζ156$ $0$ $0$ $0$ $0$ $2ζ15−4+2ζ154$ $2ζ15−7+2ζ157$ $2ζ15−1+2ζ15$ $2ζ15−2+2ζ152$ $−ζ15−6−ζ156$ $−ζ15−3−ζ153$ $−ζ15−1−ζ15$ $−ζ15−2−ζ152$ $−ζ15−4−ζ154$ $−ζ15−7−ζ157$ $0$ $0$ $0$ $0$ 180.29.4c4 R $4$ $0$ $0$ $0$ $−2$ $−2$ $1$ $2ζ15−3+2ζ153$ $2ζ15−6+2ζ156$ $0$ $0$ $0$ $0$ $2ζ15−1+2ζ15$ $2ζ15−2+2ζ152$ $2ζ15−4+2ζ154$ $2ζ15−7+2ζ157$ $−ζ15−6−ζ156$ $−ζ15−3−ζ153$ $−ζ15−4−ζ154$ $−ζ15−7−ζ157$ $−ζ15−1−ζ15$ $−ζ15−2−ζ152$ $0$ $0$ $0$ $0$

magma: CharacterTable(G);