Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C37 ⋊ C3×D3 |
| derived | C37×#3862 ⋊ C2×C3 |
| Hall | #30654589 ⋊ C2 |
| Sylow | C72 ⋊ D3×C37⋊C3 |
| Sylow | C37 ⋊ #64418⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×#3862 | C2×C3 |
| Fitting, socle | C72×C37 | C3×D3 |
| LCS | G ▷ C37×#3862 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 518 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,10,8,4,7,9)(2,3,13,6,11,14)(5,12)(16,17,19)(18,21,26)(20,24,23)(22,28,35)(25,30,32)(27,33,29)(31,38,42)(34,40,39)(36,43,37)(41,46,47)(44,48,45)(49,51,50);(3,7,6)(4,9,11)(5,10,13)(8,14,12)(15,16,18,22,28,36,44,49,48,33,19,23,29,37,38,21,27,34,41,43,26,32,39,45,46,30,17,20,25,31,35,42,47,50,51,40,24)Polycyclic presentation:
2,3^2,37,7^2|c^a=c^2,e^a=f^3,f^a=e^5,d^b=d^26,e^b=e^2,f^b=f^2,e^c=e^4,f^c=f^2260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 167);