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×#61204 |
| 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×#532 ◁ G | |
2032 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)(18,19,21,23)(20,24,25,22)(26,27,30,35)(28,34,38,32)(29,40,41,51)(31,44,43,36)(33,45,49,42)(37,52,53,57)(39,47,55,50)(46,54,48,56);(18,20)(19,22)(21,25)(23,24)(26,28,30,38)(27,32,35,34)(29,37,41,53)(31,39,43,55)(33,46,49,48)(36,47,44,50)(40,57,51,52)(42,54,45,56);(26,29,30,41)(27,33,35,49)(28,37,38,53)(31,45,43,42)(32,46,34,48)(36,51,44,40)(39,56,55,54)(47,52,50,57);(20,25)(22,24)(26,28)(27,34)(29,37)(30,38)(31,39)(32,35)(33,48)(36,50)(40,52)(41,53)(42,54)(43,55)(44,47)(45,56)(46,49)(51,57);(28,38)(32,34)(37,53)(39,55)(46,48)(47,50)(52,57)(54,56)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54192);