Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #476 |
| 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 | |
414 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)(19,21)(22,23)(24,34)(25,38,40,45)(26,42)(27,29)(28,33)(30,36,48,52)(31,35)(32,37)(39,51,41,50)(43,47,53,49)(44,46);(18,19,20,21)(22,24,35,44,28,37,26,27)(23,29,42,32,33,46,31,34)(25,36,41,53,40,52,39,43)(30,45,49,50,48,38,47,51);(22,25)(23,30)(24,36)(26,39)(27,43)(28,40)(29,45)(31,47)(32,50)(33,48)(34,51)(35,41)(37,52)(38,46)(42,49)(44,53)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5812);