Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33613 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| prime radical | C17×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
662 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(18,19)(20,21)(22,23,27,32)(24,34,37,50)(25,40,41,30)(26,44,46,51)(28,47,45,33)(29,48,43,38)(31,49,36,35)(39,53,52,42);(22,24,35,40,28,39,46,48,27,37,49,30,45,52,26,38)(23,29,44,42,33,25,36,50,32,43,51,53,47,41,31,34);(19,21)(22,25)(23,30)(24,36)(26,42)(27,41)(28,43)(29,45)(31,37)(32,40)(33,38)(34,49)(35,50)(39,51)(44,52)(46,53)(47,48);(24,37)(25,41)(29,43)(30,40)(34,50)(38,48)(39,52)(42,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26601);