Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9929 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
610 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)(22,23,27,30)(24,31,33,36)(25,29,26,34)(28,35,37,32)(38,39)(40,43)(41,44)(42,45)(46,49)(47,50)(48,52)(51,53);(22,24,27,33)(23,28,30,37)(25,32,26,35)(29,36,34,31)(38,40,42,47)(39,43,45,50)(41,46,48,53)(44,51,52,49);(19,21)(22,25,27,26)(23,29,30,34)(24,32,33,35)(28,36,37,31)(38,41)(39,44)(40,46)(42,48)(43,49)(45,52)(47,53)(50,51)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2917);