Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#33607 |
| 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 | |
714 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)(31,46)(32,41)(34,42)(35,48)(37,43)(39,40)(44,49)(45,53)(47,52)(50,51);(22,23,29,40,26,31,37,41,27,32,43,46,36,39,25,28)(24,30,42,51,35,45,47,49,33,44,52,53,48,50,34,38);(19,21)(22,24)(23,30)(25,34)(26,35)(27,33)(28,38)(29,42)(31,45)(32,44)(36,48)(37,47)(39,50)(40,51)(41,49)(43,52)(46,53);(24,33)(30,44)(34,47)(35,48)(38,49)(42,52)(45,50)(51,53)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26595);