Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C23×C13 | H(5,𝔽2) |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
714 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,18)(16,20,21,19)(22,23,27,32,29,25,28,33)(24,34,37,40,39,35,38,30)(26,42,43,41,45,47,44,31)(36,46,50,49,52,53,51,48);(15,18)(19,20)(22,24,29,39)(23,30,25,40)(26,36,45,52)(27,38,28,37)(31,46,41,53)(32,35,33,34)(42,48,47,49)(43,51,44,50);(22,25,29,23)(24,35,39,34)(26,41,45,31)(27,32,28,33)(30,37,40,38)(36,49,52,48)(42,44,47,43)(46,51,53,50);(14,16,17,21)(15,19,18,20)(22,26)(23,31)(24,36)(25,41)(27,44)(28,43)(29,45)(30,46)(32,47)(33,42)(34,48)(35,49)(37,51)(38,50)(39,52)(40,53)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19913);