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×#10800 |
| 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)(24,33,36,47)(25,30)(26,31)(27,41)(28,32)(29,35,43,37)(34,46,49,53)(38,44)(39,51)(40,45)(42,48,52,50);(22,24,27,37,28,36,26,35)(23,29,31,33,32,43,41,47)(25,34,39,50,40,49,38,48)(30,42,44,46,45,52,51,53);(19,21)(22,25,26,38,28,40,27,39)(23,30,31,44,32,45,41,51)(24,34,35,48,36,49,37,50)(29,42,33,46,43,52,47,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3788);