Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20857 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
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)(24,32)(25,29)(26,38)(27,30)(28,34)(31,41)(33,49)(35,46)(36,47)(37,44)(39,43)(40,45)(42,50)(48,51)(52,53);(18,20,21,19)(22,24)(23,28)(25,33)(26,39)(27,35)(29,42)(30,43)(31,46)(32,38)(34,41)(36,52)(37,51)(40,50)(44,53)(45,48)(47,49);(22,25,27,37)(23,29,30,44)(24,33,35,51)(26,40,41,36)(28,42,43,53)(31,47,38,45)(32,48,46,49)(34,52,39,50);(23,30)(28,43)(29,44)(31,38)(32,46)(42,53)(45,47)(48,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13845);