Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#10914 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | C4×C22⋊C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
698 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)(22,23,26,30,27,31,38,44)(24,32,35,46,34,28,39,41)(25,29,36,42,37,43,49,52)(33,45,48,53,47,40,50,51);(22,24)(23,28,31,32)(25,33)(26,35)(27,34)(29,40,43,45)(30,41,44,46)(36,48)(37,47)(38,39)(42,51,52,53)(49,50);(19,21)(22,25,26,36,27,37,38,49)(23,29,30,42,31,43,44,52)(24,33,35,48,34,47,39,50)(28,40,41,51,32,45,46,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3902);