Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#21550 |
| 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 | C17×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
914 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)(24,33,37,43,34,48,36,29)(25,30,40,46,41,47,39,53)(35,49,51,45,38,52,50,44);(22,24,26,36,28,34,27,37)(23,29,31,33,32,43,42,48)(25,38,39,51,41,35,40,50)(30,45,46,52,47,44,53,49);(19,21)(24,34)(29,43)(33,48)(35,38)(36,37)(44,45)(49,52)(50,51);(22,25,27,40,28,41,26,39)(23,30,31,46,32,47,42,53)(24,35,37,51,34,38,36,50)(29,44,33,49,43,45,48,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14538);