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×#25191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
1010 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)(22,23,27,34,29,35,28,33)(24,36,40,50,41,49,39,30)(25,42,45,32,26,46,44,31)(37,47,38,48,53,52,43,51);(18,19)(20,21)(22,24,27,40,29,41,28,39)(23,30,34,36,35,50,33,49)(25,43,45,37,26,38,44,53)(31,51,42,47,32,48,46,52);(19,21)(22,25,29,26)(23,31,35,32)(24,37,41,53)(27,44,28,45)(30,47,50,52)(33,42,34,46)(36,51,49,48)(38,40,43,39);(22,26,29,25)(23,32,35,31)(24,38,41,43)(27,44,28,45)(30,48,50,51)(33,42,34,46)(36,52,49,47)(37,40,53,39)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 18179);