Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61477 |
| 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 | |
1772 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)(26,27,32,36)(28,33,39,48)(29,41,43,49)(30,35,31,44)(34,45,50,42)(37,51,53,56)(38,47,40,54)(46,55,57,52);(18,19)(20,23)(21,22)(24,25)(26,28,32,39)(27,33,36,48)(29,37,43,53)(30,38,31,40)(34,46,50,57)(35,47,44,54)(41,51,49,56)(42,52,45,55);(26,29)(27,34)(28,37)(30,42)(31,45)(32,43)(33,46)(35,49)(36,50)(38,52)(39,53)(40,55)(41,44)(47,56)(48,57)(51,54);(19,22)(23,25)(26,30,32,31)(27,35,36,44)(28,38,39,40)(29,42,43,45)(33,47,48,54)(34,49,50,41)(37,52,53,55)(46,56,57,51);(18,20,21,24)(19,23,22,25)(28,39)(33,48)(37,53)(38,40)(46,57)(47,54)(51,56)(52,55)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54465);