Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60831 |
| 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 ◁ C4×#41×C17 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(28,37)(29,41)(30,36)(31,33)(32,45)(34,39)(35,43)(38,53)(40,49)(42,51)(44,50)(46,47)(48,54)(52,55)(56,57);(18,20,21,25)(19,22,23,24)(27,33)(34,47)(35,41)(36,45)(37,49)(48,57)(50,51)(52,53);(20,25)(22,24)(26,28,31,40)(27,34,33,47)(29,38,43,55)(30,39,32,46)(35,48,41,57)(36,49,45,37)(42,54,44,56)(50,52,51,53);(19,23)(22,24)(26,29)(27,35)(28,38)(30,44)(31,43)(32,42)(33,41)(34,48)(36,51)(37,52)(39,56)(40,55)(45,50)(46,54)(47,57)(49,53);(26,30,31,32)(27,36,33,45)(28,39,40,46)(29,42,43,44)(34,49,47,37)(35,50,41,51)(38,54,55,56)(48,52,57,53)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53819);