Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#25189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,28,32,29,33,27,43)(24,34,36,30,25,37,39,46)(26,40,41,31,42,47,44,48)(35,45,51,52,38,53,50,49);(18,19)(20,21)(22,24,28,36,29,25,27,39)(23,30,32,37,33,46,43,34)(26,35,41,51,42,38,44,50)(31,45,47,52,48,53,40,49);(19,21)(22,25)(23,30)(24,29)(26,38)(27,39)(28,36)(31,45)(32,34)(33,46)(35,42)(37,43)(40,52)(41,51)(44,50)(47,49)(48,53);(22,26,29,42)(23,31,33,48)(24,35,25,38)(27,44,28,41)(30,45,46,53)(32,47,43,40)(34,49,37,52)(36,51,39,50)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18177);