Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#21556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×#41×C17 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 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)(22,23,28,33)(24,34,36,45)(25,39,41,47)(26,32,27,31)(29,38,44,37)(30,42,46,40)(35,49,50,43)(48,52,53,51);(22,24,26,37,28,36,27,38)(23,29,31,34,33,44,32,45)(25,35,40,51,41,50,42,52)(30,43,39,48,46,49,47,53);(22,25)(23,30)(24,35)(26,40)(27,42)(28,41)(29,43)(31,39)(32,47)(33,46)(34,48)(36,50)(37,51)(38,52)(44,49)(45,53);(18,20,21,19)(24,36)(29,44)(34,45)(35,50)(37,38)(43,49)(48,53)(51,52)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14544);