Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#10947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
914 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,32,35,28)(25,36)(26,39)(27,30)(29,38)(31,41)(33,47,48,53)(34,43,40,45)(37,50)(42,49,46,52)(44,51);(18,19,20,21)(22,24)(23,28)(25,33)(26,40)(27,35)(29,42)(30,32)(31,45)(34,41)(36,47)(37,48)(38,52)(39,43)(44,46)(49,51)(50,53);(22,25,26,38,27,37,41,51)(23,29,31,36,30,44,39,50)(24,33,40,52,35,48,34,49)(28,42,45,47,32,46,43,53)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3935);