Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21100 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
1030 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
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)(22,23,27,31,28,32,26,42)(24,33,37,44,35,47,36,29)(25,38,41,45,39,52,40,30)(34,48,50,53,51,43,49,46);(22,24)(23,29,32,44)(25,34)(26,36)(27,37)(28,35)(30,43,45,48)(31,33,42,47)(38,46,52,53)(39,51)(40,49)(41,50);(19,21)(22,25,26,40,28,39,27,41)(23,30,31,38,32,45,42,52)(24,34,36,49,35,51,37,50)(29,43,33,46,44,48,47,53);(24,35)(25,39)(29,44)(30,45)(33,47)(36,37)(38,52)(40,41)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14088);