Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#1999 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C4×C22⋊C4×C17 ◁ G | |
1052 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)(22,23,25,24)(26,27)(28,36)(29,32)(30,40)(31,35)(33,38)(34,37)(39,41);(18,19)(20,21)(22,24,25,23)(26,28,37,39,31,38,30,29)(27,32,40,33,35,41,34,36);(19,21)(23,24);(26,29,30,38,31,39,37,28)(27,33,34,32,35,36,40,41)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18399);