Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1178 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)(22,23,27,33,28,31,26,32)(24,29,36,43,35,44,41,47)(25,37,39,30,40,46,38,45)(34,48,50,52,49,53,51,42);(19,21)(22,24)(23,29,31,44)(25,34)(26,36)(27,41)(28,35)(30,42,45,52)(32,43,33,47)(37,48,46,53)(38,50)(39,51)(40,49);(22,25,28,40)(23,30,31,45)(24,34,35,49)(26,39,27,38)(29,42,44,52)(32,46,33,37)(36,51,41,50)(43,53,47,48)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3774);