Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#547 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
2098 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(26,27,31,35)(28,36,37,41)(29,34,30,33)(32,39,40,38);(18,20)(19,22)(21,25)(23,24)(28,37)(32,40)(36,41)(38,39);(26,28)(27,32)(29,38)(30,39)(31,37)(33,36)(34,41)(35,40);(20,25)(22,24)(26,29,31,30)(27,33,35,34)(28,38,37,39)(32,36,40,41);(19,23)(22,24)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54574);