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×#33610 |
| 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 ◁ C2×#41×C17 ◁ C2×C17×#131 ◁ G | |
674 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)(24,33)(25,30)(26,41)(27,39)(28,32)(29,36)(31,34)(35,46)(37,52)(38,48)(40,45)(42,53)(43,50)(44,51)(47,49);(22,24,34,49,27,37,42,51,28,38,40,50,25,35,26,36)(23,29,41,46,30,43,45,48,32,44,53,52,39,47,31,33);(19,21)(22,23)(24,29)(25,39)(26,31)(27,30)(28,32)(33,36)(34,41)(35,47)(37,43)(38,44)(40,53)(42,45)(46,49)(48,51)(50,52);(22,25,28,27)(23,30,32,39)(24,35,38,37)(26,40,42,34)(29,43,44,47)(31,41,45,53)(33,46,48,52)(36,50,51,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26598);