Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#33834 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×D4×C17 ◁ C8×D4×C17 ◁ G | |
702 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)(18,19)(20,21)(22,23)(24,32)(25,31)(26,40)(28,29)(30,35)(33,45)(34,46)(36,49)(38,39)(41,43)(44,48)(47,53)(50,52);(22,24,29,34)(23,30,28,43)(25,33,39,47)(26,41,40,35)(27,32,42,46)(31,44,38,52)(36,50,49,48)(37,45,51,53);(19,21)(22,25,29,39)(23,31,28,38)(24,33,34,47)(26,36,40,49)(27,37,42,51)(30,44,43,52)(32,45,46,53)(35,48,41,50);(22,26)(23,27)(24,34)(25,36)(28,42)(29,40)(31,37)(32,41)(33,47)(35,46)(38,51)(39,49)(45,50)(48,53)731 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26822);