Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#62160 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 65 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 65 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,25)(20,26,27,23)(21,29,30,24)(28,31,33,32)(34,35)(36,41)(37,49)(38,43)(39,52)(40,44)(42,50)(45,59)(46,55)(47,56)(48,62)(51,57)(53,58)(54,60)(61,64)(63,65);(18,20)(19,23)(21,28)(22,27)(24,31)(25,26)(29,32)(30,33)(34,36,40,47)(35,41,44,56)(37,45,51,61)(38,46,39,48)(42,54,58,65)(43,55,52,62)(49,59,57,64)(50,60,53,63);(34,37)(35,42)(36,45)(38,50)(39,53)(40,51)(41,54)(43,57)(44,58)(46,60)(47,61)(48,63)(49,52)(55,64)(56,65)(59,62);(20,27)(23,26)(28,33)(31,32)(34,38,40,39)(35,43,44,52)(36,46,47,48)(37,50,51,53)(41,55,56,62)(42,57,58,49)(45,60,61,63)(54,64,65,59);(18,21,22,30)(19,24,25,29)(20,28,27,33)(23,31,26,32)(36,47)(41,56)(45,61)(46,48)(54,65)(55,62)(59,64)(60,63)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55148);