Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33676 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
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)(16,19)(17,18)(20,21)(22,23,28,33)(24,29,37,45)(25,31,27,41)(26,30,40,47)(32,38,46,39)(34,43,36,51)(35,42,50,53)(44,48,52,49);(15,18)(19,21)(22,24,28,37)(23,29,33,45)(25,34,27,36)(26,35,40,50)(30,42,47,53)(31,43,41,51)(32,44,46,52)(38,48,39,49);(23,30)(25,27)(26,39)(29,42)(31,32)(33,47)(34,36)(35,49)(38,40)(41,46)(43,44)(45,53)(48,50)(51,52);(14,16,17,20)(15,19,18,21)(22,25,28,27)(23,31,33,41)(24,34,37,36)(26,38,40,39)(29,43,45,51)(30,46,47,32)(35,48,50,49)(42,52,53,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26664);