Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| 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 ◁ C17×#405 ◁ G | |
402 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)(18,19,21,20)(22,23,27,33)(24,35,38,51)(25,29,43,32)(26,44,40,31)(28,45,42,34)(30,41,49,37)(36,50,53,52)(39,48,46,47);(18,20,21,19)(23,29)(25,40)(26,43)(28,42)(30,47)(31,34)(32,33)(35,50)(36,37)(39,46)(41,53)(44,45)(48,49)(51,52);(22,24)(23,30)(25,41)(26,36)(27,38)(28,46)(29,47)(31,51)(32,48)(33,49)(34,52)(35,44)(37,43)(39,42)(40,53)(45,50)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5934);