Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#24675 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
764 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)(16,20)(17,18)(19,21)(22,23,27,32,26,31,28,33)(24,34,37,49,36,29,43,45)(25,38,41,47,40,48,42,30)(35,51,39,44,52,46,53,50);(15,18)(19,20)(22,24)(23,29)(25,39)(26,36)(27,37)(28,43)(30,46)(31,34)(32,45)(33,49)(35,42)(38,50)(40,53)(41,52)(44,48)(47,51);(22,25,26,40)(23,30,31,47)(24,35,36,52)(27,42,28,41)(29,44,34,50)(32,48,33,38)(37,53,43,39)(45,51,49,46);(14,16,17,21)(15,19,18,20)(23,31)(29,34)(30,47)(32,33)(38,48)(44,50)(45,49)(46,51)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17663);