Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3515 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1756 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)(28,33,40,50)(29,42,45,53)(30,37,31,35)(34,46,52,44)(38,54,43,57)(39,49,41,48)(47,56,51,55);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,43)(30,39)(31,41)(32,40)(34,51)(35,48)(36,50)(37,49)(38,45)(42,57)(44,56)(46,55)(47,52)(53,54);(26,29)(27,34)(28,38)(30,44)(31,46)(32,45)(33,47)(35,42)(36,52)(37,53)(39,55)(40,43)(41,56)(48,54)(49,57)(50,51);(19,22)(23,25)(26,30,32,31)(27,35,36,37)(28,39,40,41)(29,44,45,46)(33,48,50,49)(34,42,52,53)(38,55,43,56)(47,54,51,57);(18,20,21,24)(19,23,22,25)(27,36)(28,40)(34,52)(35,37)(38,43)(39,41)(42,53)(55,56)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54540);