Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21876 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| prime radical | C2×C17×#538 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C22⋊C4×C17 ◁ G | |
1254 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
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)(19,22)(20,24)(26,27)(28,31)(29,36,37,32)(30,33)(34,40,41,38)(35,39);(18,19)(20,23)(21,22)(24,25)(26,28)(27,31)(29,34)(30,35)(32,38)(33,39)(36,40)(37,41);(19,22)(23,25)(26,29)(27,32)(28,34)(30,37)(31,38)(33,36)(35,41)(39,40);(18,20,21,24)(19,23,22,25)(28,35)(31,39)(34,41)(38,40)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14864);