Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61473 |
| 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 | |
1770 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)(26,27,31,35)(28,32,37,46)(29,39,41,49)(30,42,44,34)(33,43,48,40)(36,50,51,57)(38,54,53,47)(45,55,56,52);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,36)(30,38)(31,37)(33,45)(34,47)(35,46)(39,50)(40,52)(41,51)(42,54)(43,55)(44,53)(48,56)(49,57);(26,29,31,41)(27,33,35,48)(28,36,37,51)(30,43,44,40)(32,45,46,56)(34,49,42,39)(38,55,53,52)(47,57,54,50);(19,22)(23,25);(18,20,21,24)(19,23,22,25)(28,37)(32,46)(36,51)(38,53)(45,56)(47,54)(50,57)(52,55)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54461);