Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61197 |
| 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 | |
2046 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)(18,19,21,23)(20,24,25,22)(26,27)(28,33)(29,42)(30,35)(31,36)(32,37)(34,43)(38,52)(39,47)(40,51)(41,48)(44,49)(45,50)(46,53)(54,57)(55,56);(18,20)(19,22)(21,25)(23,24)(26,28,32,41)(27,33,37,48)(29,38,44,55)(30,39,31,40)(34,46,50,57)(35,47,36,51)(42,52,49,56)(43,53,45,54);(26,29)(27,34)(28,38)(30,43)(31,45)(32,44)(33,46)(35,49)(36,42)(37,50)(39,53)(40,54)(41,55)(47,56)(48,57)(51,52);(20,25)(22,24)(26,30,32,31)(27,35,37,36)(28,39,41,40)(29,43,44,45)(33,47,48,51)(34,49,50,42)(38,53,55,54)(46,56,57,52);(26,30,32,31)(27,36,37,35)(28,40,41,39)(29,43,44,45)(33,47,48,51)(34,42,50,49)(38,54,55,53)(46,56,57,52)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54185);