Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10799 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C42 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #376 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
650 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)(18,19)(20,21)(22,23)(24,32,35,45)(25,29)(26,30)(27,31)(28,34,40,48)(33,44,47,52)(36,41)(37,42)(38,43)(39,46,50,53)(49,51);(22,24)(23,28,31,40)(25,33)(26,34)(27,35)(29,39,42,50)(30,32,43,45)(36,46)(37,47)(38,48)(41,44,51,52)(49,53);(19,21)(22,25,26,36,27,37,38,49)(23,29,30,41,31,42,43,51)(24,33,34,46,35,47,48,53)(28,39,32,44,40,50,45,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3787);