Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61635 |
| 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 | |
2070 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)(20,24)(21,23)(22,25)(26,27)(28,33)(29,40)(30,35)(31,44)(32,36)(34,41)(37,52)(38,47)(39,48)(42,50)(43,49)(45,51)(46,55)(53,56)(54,57);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,37)(30,43)(31,38)(32,39)(34,46)(35,49)(36,48)(40,52)(41,55)(42,54)(44,47)(45,53)(50,57)(51,56);(26,29)(27,34)(28,37)(30,41)(31,45)(32,42)(33,46)(35,50)(36,51)(38,53)(39,54)(40,44)(43,55)(47,52)(48,56)(49,57);(20,25)(22,24)(26,30,32,31)(27,35,36,44)(28,38,39,43)(29,41,42,45)(33,47,48,49)(34,50,51,40)(37,53,54,55)(46,52,56,57);(19,23)(22,24)(28,39)(33,48)(37,54)(38,43)(46,56)(47,49)(52,57)(53,55)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54623);