Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #459 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
476 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)(22,23,28,35,48,49,47,33,30,37,27,34,29,36,26,46)(24,38,41,31,45,32,39,52,43,53,40,51,42,50,25,44);(22,24,29,45,30,43,48,42)(23,31,49,44,37,51,36,52)(25,26,41,27,39,47,40,28)(32,35,38,33,50,34,53,46);(19,21)(22,25)(23,32)(24,26)(27,45)(28,42)(29,41)(30,39)(31,35)(33,44)(34,51)(36,53)(37,50)(38,49)(40,48)(43,47)(46,52)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6016);