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×#33612 |
| 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 | |
694 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)(23,28)(25,29)(26,36)(30,38)(31,39)(32,46)(34,42)(35,48)(37,43)(40,41)(44,53)(45,51)(47,52)(49,50);(22,23,29,41,26,32,37,39,27,31,43,46,36,40,25,28)(24,30,42,50,35,44,47,51,33,45,52,53,48,49,34,38);(19,21)(22,24)(23,30)(25,34)(26,35)(27,33)(28,38)(29,42)(31,45)(32,44)(36,48)(37,47)(39,51)(40,49)(41,50)(43,52)(46,53);(23,31)(24,33)(28,39)(32,40)(34,47)(35,48)(41,46)(42,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26600);