Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61627 |
| 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×#525 ◁ G | |
2050 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27)(28,33)(29,41)(30,35)(31,44)(32,36)(34,42)(37,52)(38,47)(39,48)(40,49)(43,50)(45,51)(46,53)(54,57)(55,56);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,37)(30,38)(31,39)(32,40)(34,46)(35,47)(36,49)(41,52)(42,53)(43,55)(44,48)(45,54)(50,56)(51,57);(26,29,32,43)(27,34,36,51)(28,37,40,55)(30,42,31,45)(33,46,49,57)(35,50,44,41)(38,53,39,54)(47,56,48,52);(20,25)(22,24)(26,30,32,31)(27,35,36,44)(28,38,40,39)(29,42,43,45)(33,47,49,48)(34,50,51,41)(37,53,55,54)(46,56,57,52);(19,23)(22,24)(26,30,32,31)(27,35,36,44)(28,39,40,38)(29,42,43,45)(33,48,49,47)(34,50,51,41)(37,54,55,53)(46,52,57,56)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54615);