Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61502 |
| 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 | |
1788 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)(19,22)(23,25)(26,27)(28,37)(29,41)(30,35)(31,36)(32,46)(33,40)(34,43)(38,54)(39,50)(42,57)(44,52)(45,49)(47,53)(48,55)(51,56);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,42)(30,45)(31,40)(32,39)(34,51)(35,50)(36,37)(38,44)(41,54)(43,55)(46,49)(47,56)(48,53)(52,57);(26,29,31,44)(27,34,36,53)(28,38,40,42)(30,43,32,47)(33,48,37,51)(35,52,46,41)(39,55,45,56)(49,57,50,54);(19,22)(23,25)(26,30,31,32)(27,35,36,46)(28,39,40,45)(29,43,44,47)(33,49,37,50)(34,52,53,41)(38,55,42,56)(48,57,51,54);(18,20,21,24)(19,23,22,25)(28,40)(33,37)(38,42)(39,45)(48,51)(49,50)(54,57)(55,56)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54490);