Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D8×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C4⋊C4×C17 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,25,24)(26,27)(28,35)(29,33)(30,32)(31,36)(34,38)(37,39)(40,41);(18,20,21,19)(23,24)(26,28,29,36)(27,31,33,35)(30,37,38,41)(32,40,34,39);(27,32)(28,36)(30,38)(31,39)(33,34)(35,40);(22,24,25,23)(28,36)(31,35)(37,41)(39,40)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15993);