Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33611 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,33)(25,30)(26,40)(27,39)(28,32)(29,36)(31,41)(34,46)(35,47)(37,53)(38,49)(42,43)(44,50)(45,52)(48,51);(22,24,34,50,27,37,26,36,28,38,41,51,25,35,42,52)(23,29,43,53,30,44,31,33,32,45,40,47,39,48,46,49);(19,21)(22,23)(24,29)(25,39)(26,31)(27,30)(28,32)(33,36)(34,43)(35,48)(37,44)(38,45)(40,41)(42,46)(47,51)(49,52)(50,53);(22,25,28,27)(23,30,32,39)(24,35,38,37)(26,34,42,41)(29,44,45,48)(31,40,46,43)(33,47,49,53)(36,50,52,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26599);