Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C292 ⋊ C2×C3 |
| Hall | C7×C292⋊C3 ⋊ C2 |
| Hall | C7⋊(C29⋊D29) ⋊ C3 |
| Hall | C292⋊C3 ⋊ D7 |
| Sylow | C292 ⋊ C3×D7 |
| Sylow | C7 ⋊ (C29⋊D29)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C292 | C2×C3 |
| LCS | G ▷ C7×C292 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 94 |
| transitive degree | μt(G) = 609 |
A minimal faithful permutation representation — 2 generators on 94 points:
(2,3)(4,5)(6,7)(8,9,11)(10,25,26,14,15,37)(12,38,40,19,20,63)(13,18,48,23,24,36)(16,55,56,29,30,82)(17,62,51,32,33,27)(21,73,75,42,43,93)(22,49,78,45,46,80)(28,64,65,54,34,87)(31,44,84,59,60,77)(35,90,57,67,68,53)(39,41,89,47,66,71)(50,83,91,70,72,86)(52,69,94,58,81,88)(61,79,92,85,74,76);(1,2,4,6,7,5,3)(8,10,16,31,61,71,78,90,33,63,86,75,94,87,36,48,65,88,93,91,40,62,68,80,89,85,59,29,14)(9,12,21,30,57,54,74,39,13,22,44,58,51,25,50,70,15,27,52,60,45,23,47,79,28,53,55,42,19)(11,17,34,66,84,43,72,82,46,18,35,26,38,69,76,92,81,20,37,67,24,49,56,83,73,77,41,64,32)Polycyclic presentation:
2,3,7,29^2|c^a=c^6,d^a=d^28,e^a=e^28,d^b=d^8e,e^b=d^14e^20995 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 71);