Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#19897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#550 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
638 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)(18,19,21,24)(20,22,25,23)(26,27,31,29)(28,34,35,41)(30,38,40,33)(32,39,37,36);(26,28,31,35)(27,32,29,37)(30,39,40,36)(33,41,38,34);(19,22)(20,25)(23,24)(28,35)(32,37)(34,41)(36,39);(26,29,31,27)(28,34,35,41)(30,33,40,38)(32,39,37,36)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12885);