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 |
| Sylow | C292 ⋊ AGL(1,𝔽7) |
| 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:
(2,5,6,3,4,7)(8,9,11)(10,25,26,14,15,40)(12,38,39,19,20,63)(13,18,44,22,23,36)(16,55,56,29,30,76)(17,61,52,32,33,27)(21,71,72,41,42,60)(24,37,77,46,47,69)(28,70,74,48,54,90)(31,53,35,59,43,67)(34,89,57,64,65,58)(45,87,49,62,75,79)(50,51,92,81,73,68)(66,94,82,83,91,84)(78,86,80,88,93,85);(1,2,4,7,6,5,3)(8,10,16,31,60,86,92,44,74,89,33,63,87,91,77,69,94,75,39,61,65,90,36,68,93,72,59,29,14)(9,12,13,21,24,43,48,52,25,49,50,80,82,30,57,58,55,84,85,81,79,15,27,28,53,46,41,22,19)(11,17,34,26,38,70,56,62,18,35,66,51,71,47,78,88,37,42,73,83,67,23,45,76,54,20,40,64,32)Polycyclic presentation:
2,3,7,29^2|c^a=c^6,d^a=d^28,e^a=e^28,c^b=c^2,d^b=d^10e^20,e^b=d^22e^18987 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 62);