Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13072 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #466 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
458 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)(18,19)(20,21)(22,23,27,32,29,25,28,39)(24,33,36,50,37,49,45,51)(26,40,42,38,44,53,43,31)(30,46,47,35,34,52,48,41);(22,24,26,41,28,36,43,46,29,37,44,35,27,45,42,52)(23,30,38,33,32,48,53,51,25,34,31,49,39,47,40,50);(19,21)(22,25)(23,29)(24,34)(26,31)(27,32)(28,39)(30,37)(33,35)(36,47)(38,44)(40,43)(41,49)(42,53)(45,48)(46,50)(51,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6060);