Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61549 |
| 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 | |
1774 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)(28,32)(29,39)(30,43)(31,34)(33,41)(35,45)(36,52)(37,47)(38,55)(40,57)(42,51)(44,50)(46,53)(48,54)(49,56);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,40)(30,38)(31,37)(33,49)(34,47)(35,48)(36,42)(39,57)(41,56)(43,55)(44,53)(45,54)(46,50)(51,52);(26,29,31,42)(27,33,34,50)(28,36,37,40)(30,44,45,41)(32,46,47,49)(35,51,43,39)(38,56,54,53)(48,57,55,52);(19,22)(23,25)(27,34)(32,47)(33,50)(35,43)(39,51)(46,49)(48,55)(52,57);(18,20,21,24)(19,23,22,25)(27,34)(28,37)(33,50)(35,43)(36,40)(38,54)(39,51)(53,56)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54537);