Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#12909 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#107 |
| prime radical | C23×C17 | C2×Q16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(19,21)(22,23,26,31,28,32,27,42)(24,33,36,48,38,49,37,52)(25,39,40,46,41,53,34,30)(29,43,44,51,45,50,47,35);(22,24,34,50,27,37,41,51,28,38,40,43,26,36,25,35)(23,29,39,48,31,44,46,49,32,45,53,52,42,47,30,33);(18,19,20,21)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5897);