Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#22675 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C4⋊C4×C17 ◁ G | |
898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
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)(19,21)(22,23,24,25)(27,32)(30,39)(33,34)(35,40)(36,38)(37,41);(26,27,31,35)(28,33,29,37)(30,40,39,32)(34,36,41,38);(18,19,20,21)(26,28,31,29)(27,33,35,37)(30,36,39,38)(32,34,40,41);(26,29,31,28)(27,34,35,41)(30,36,39,38)(32,33,40,37)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 15663);