# Properties

 Label 30T16 Degree $30$ Order $90$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no Group: $C_3\times D_{15}$

Show commands: Magma

magma: G := TransitiveGroup(30, 16);

## Group action invariants

 Degree $n$: $30$ magma: t, n := TransitiveGroupIdentification(G); n; Transitive number $t$: $16$ magma: t, n := TransitiveGroupIdentification(G); t; Group: $C_3\times D_{15}$ Parity: $-1$ magma: IsEven(G); Primitive: no magma: IsPrimitive(G); magma: NilpotencyClass(G); $\card{\Aut(F/K)}$: $15$ magma: Order(Centralizer(SymmetricGroup(n), G)); Generators: (1,15,12,9,5,3,14,11,8,4,2,13,10,7,6)(16,29,25,22,20,17,30,26,23,21,18,28,27,24,19), (1,21,2,19,3,20)(4,16,5,17,6,18)(7,28,8,29,9,30)(10,27,11,25,12,26)(13,24,14,22,15,23) magma: Generators(G);

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$10$:  $D_{5}$
$18$:  $S_3\times C_3$
$30$:  $D_{15}$, $D_5\times C_3$

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 2: $C_2$

Degree 3: None

Degree 5: $D_{5}$

Degree 6: $S_3\times C_3$

Degree 10: $D_5$

Degree 15: None

## Low degree siblings

45T5

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

magma: ConjugacyClasses(G);

Malle's constant $a(G)$:     $1/10$

## Group invariants

 Order: $90=2 \cdot 3^{2} \cdot 5$ magma: Order(G); Cyclic: no magma: IsCyclic(G); Abelian: no magma: IsAbelian(G); Solvable: yes magma: IsSolvable(G); Nilpotency class: not nilpotent Label: 90.7 magma: IdentifyGroup(G); Character table:

 1A 2A 3A1 3A-1 3B 3C1 3C-1 5A1 5A2 6A1 6A-1 15A1 15A2 15A4 15A7 15B1 15B-1 15B2 15B-2 15C1 15C-1 15C2 15C-2 15C4 15C-4 15C7 15C-7 Size 1 15 1 1 2 2 2 2 2 15 15 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 P 1A 1A 3A-1 3A1 3C1 3B 3C-1 5A2 5A1 3A-1 3A1 15C-2 15C4 15B2 15A1 15A4 15C2 15A2 15B-2 15C7 15A7 15B-1 15C-7 15C1 15C-1 15C-4 15B1 3 P 1A 2A 1A 1A 1A 1A 1A 5A2 5A1 2A 2A 5A1 5A2 5A2 5A2 5A2 5A1 5A1 5A2 5A1 5A1 5A1 5A1 5A2 5A2 5A2 5A1 5 P 1A 2A 3A-1 3A1 3C1 3B 3C-1 1A 1A 6A-1 6A1 3C-1 3C-1 3A1 3B 3B 3C1 3B 3A-1 3C-1 3B 3A1 3C1 3C-1 3C1 3C1 3A-1 Type 90.7.1a R $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ 90.7.1b R $1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $−1$ $−1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ 90.7.1c1 C $1$ $1$ $ζ3−1$ $ζ3$ $1$ $ζ3−1$ $ζ3$ $1$ $1$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $1$ $1$ $1$ $1$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $ζ3$ $ζ3−1$ 90.7.1c2 C $1$ $1$ $ζ3$ $ζ3−1$ $1$ $ζ3$ $ζ3−1$ $1$ $1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $1$ $1$ $1$ $1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $ζ3−1$ $ζ3$ 90.7.1d1 C $1$ $−1$ $ζ3−1$ $ζ3$ $1$ $ζ3−1$ $ζ3$ $1$ $1$ $−ζ3$ $−ζ3−1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $1$ $1$ $1$ $1$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $ζ3$ $ζ3−1$ 90.7.1d2 C $1$ $−1$ $ζ3$ $ζ3−1$ $1$ $ζ3$ $ζ3−1$ $1$ $1$ $−ζ3−1$ $−ζ3$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $1$ $1$ $1$ $1$ $ζ3−1$ $ζ3$ $ζ3$ $ζ3−1$ $ζ3−1$ $ζ3$ $ζ3−1$ $ζ3$ 90.7.2a R $2$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $2$ $2$ $0$ $0$ $2$ $2$ $2$ $2$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ $−1$ 90.7.2b1 R $2$ $0$ $2$ $2$ $2$ $2$ $2$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $0$ $0$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ 90.7.2b2 R $2$ $0$ $2$ $2$ $2$ $2$ $2$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $0$ $0$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ $ζ5−1+ζ5$ $ζ5−1+ζ5$ $ζ5−2+ζ52$ $ζ5−2+ζ52$ 90.7.2c1 C $2$ $0$ $2ζ3−1$ $2ζ3$ $−1$ $−ζ3−1$ $−ζ3$ $2$ $2$ $0$ $0$ $2ζ3−1$ $2ζ3$ $2ζ3$ $2ζ3−1$ $−1$ $−1$ $−1$ $−1$ $−ζ3$ $−ζ3−1$ $−ζ3−1$ $−ζ3$ $−ζ3$ $−ζ3−1$ $−ζ3$ $−ζ3−1$ 90.7.2c2 C $2$ $0$ $2ζ3$ $2ζ3−1$ $−1$ $−ζ3$ $−ζ3−1$ $2$ $2$ $0$ $0$ $2ζ3$ $2ζ3−1$ $2ζ3−1$ $2ζ3$ $−1$ $−1$ $−1$ $−1$ $−ζ3−1$ $−ζ3$ $−ζ3$ $−ζ3−1$ $−ζ3−1$ $−ζ3$ $−ζ3−1$ $−ζ3$ 90.7.2d1 R $2$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $ζ15−3+ζ153$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−6+ζ156$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−1+ζ15$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−7+ζ157$ 90.7.2d2 R $2$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $ζ15−3+ζ153$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−6+ζ156$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−4+ζ154$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−2+ζ152$ 90.7.2d3 R $2$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $ζ15−6+ζ156$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−3+ζ153$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−2+ζ152$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−1+ζ15$ 90.7.2d4 R $2$ $0$ $2$ $2$ $−1$ $−1$ $−1$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $ζ15−6+ζ156$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−3+ζ153$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−7+ζ157$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−4+ζ154$ 90.7.2e1 C $2$ $0$ $2ζ15−5$ $2ζ155$ $2$ $2ζ15−5$ $2ζ155$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ 90.7.2e2 C $2$ $0$ $2ζ155$ $2ζ15−5$ $2$ $2ζ155$ $2ζ15−5$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ 90.7.2e3 C $2$ $0$ $2ζ15−5$ $2ζ155$ $2$ $2ζ15−5$ $2ζ155$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ 90.7.2e4 C $2$ $0$ $2ζ155$ $2ζ15−5$ $2$ $2ζ155$ $2ζ15−5$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ 90.7.2f1 C $2$ $0$ $2ζ15−5$ $2ζ155$ $−1$ $−ζ15−5$ $−ζ155$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ154+ζ156$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $ζ153+ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ152+ζ153$ 90.7.2f2 C $2$ $0$ $2ζ155$ $2ζ15−5$ $−1$ $−ζ155$ $−ζ15−5$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $ζ154+ζ156$ $ζ153+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $ζ152+ζ153$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ 90.7.2f3 C $2$ $0$ $2ζ15−5$ $2ζ155$ $−1$ $−ζ15−5$ $−ζ155$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $ζ152+ζ153$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ154+ζ156$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $ζ153+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ 90.7.2f4 C $2$ $0$ $2ζ155$ $2ζ15−5$ $−1$ $−ζ155$ $−ζ15−5$ $ζ15−6+ζ156$ $ζ15−3+ζ153$ $0$ $0$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ152+ζ153$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $ζ154+ζ156$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $ζ153+ζ157$ 90.7.2f5 C $2$ $0$ $2ζ15−5$ $2ζ155$ $−1$ $−ζ15−5$ $−ζ155$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ153+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ152+ζ153$ $ζ154+ζ156$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ 90.7.2f6 C $2$ $0$ $2ζ155$ $2ζ15−5$ $−1$ $−ζ155$ $−ζ15−5$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $ζ153+ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $ζ152+ζ153$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $ζ154+ζ156$ 90.7.2f7 C $2$ $0$ $2ζ15−5$ $2ζ155$ $−1$ $−ζ15−5$ $−ζ155$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $ζ15+ζ154$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $1−ζ15−ζ154+ζ155$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ152+ζ153$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $ζ154+ζ156$ $ζ153+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ 90.7.2f8 C $2$ $0$ $2ζ155$ $2ζ15−5$ $−1$ $−ζ155$ $−ζ15−5$ $ζ15−3+ζ153$ $ζ15−6+ζ156$ $0$ $0$ $1−ζ15−ζ152+ζ153−ζ154−ζ157$ $ζ15+ζ154$ $1−ζ15−ζ154+ζ155$ $−1+ζ15+ζ152−ζ153+ζ154−ζ155+ζ157$ $ζ15−2+ζ152$ $ζ15−4+ζ154$ $ζ15−7+ζ157$ $ζ15−1+ζ15$ $ζ152+ζ153$ $1−ζ15−ζ152−ζ154+ζ155−2ζ157$ $ζ154+ζ156$ $−1−ζ15+ζ152−ζ153−2ζ156+ζ157$ $−1+ζ15−ζ152−ζ153+ζ154−ζ155$ $ζ153+ζ157$ $1−ζ152+ζ153−ζ154+2ζ156−ζ157$ $−1+ζ15+ζ152−ζ153−ζ156+ζ157$

magma: CharacterTable(G);