Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11272 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #389 |
| prime radical | C24×C17 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
574 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)(18,19,21,20)(22,23,27,31,28,33,26,32)(24,34,37,45,38,48,36,29)(25,39,42,47,43,49,41,30)(35,51,52,46,53,44,40,50);(18,20,21,19)(22,24,26,36,28,38,27,37)(23,29,31,34,33,45,32,48)(25,40,41,53,43,52,42,35)(30,46,39,44,47,50,49,51);(19,20)(22,25,26,41,28,43,27,42)(23,30,31,39,33,47,32,49)(24,35,36,40,38,53,37,52)(29,44,34,50,45,51,48,46)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4260);