Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#547 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
624 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)(19,22)(20,24)(23,25)(26,27,31,29)(28,34,38,41)(30,39,40,33)(32,36,35,37);(26,28,31,38)(27,32,29,35)(30,36,40,37)(33,41,39,34);(18,19,21,23)(20,25,24,22)(26,29,31,27)(28,35,38,32)(30,39,40,33)(34,37,41,36);(28,36)(30,40)(32,41)(33,39)(34,35)(37,38)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12796);