Finite Group DatabasebetaFinite Group Databasebeta| order | 32718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊#11716328 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19×C41 | C2×C3 |
| LCS | G ▷ C7×C19×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 5453 |
A minimal faithful permutation representation — 2 generators on 67 points:
(2,5,6,3,4,7)(9,13,14,10,11,15)(12,20,21,16,17,25)(18,26,24,23,22,19)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67);(1,2,4,7,6,5,3)(8,9,12,17,22,25,24,14,13,18,23,11,15,19,21,26,20,16,10)(27,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29)Polycyclic presentation:
2,3,7,19,41|c^a=c^6,d^a=d^18,e^a=e^40,c^b=c^2,d^b=d^11968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32718, 48);