Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33770 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
576 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)(16,20)(17,19)(18,21)(22,23,26,32)(24,35,37,29)(25,34,28,31)(27,42,41,45)(30,48,49,38)(33,40,51,44)(36,46,39,50)(43,52,53,47);(14,16)(15,18)(17,21)(19,20)(22,24,26,37)(23,29,32,35)(25,39,28,36)(27,38,41,48)(30,42,49,45)(31,50,34,46)(33,47,51,52)(40,53,44,43);(16,21)(18,20)(22,24)(23,30)(25,36)(26,37)(27,43)(28,39)(29,45)(31,47)(32,49)(33,50)(34,52)(35,42)(38,44)(40,48)(41,53)(46,51);(15,19)(18,20)(22,25,26,28)(23,31,32,34)(24,36,37,39)(27,40,41,44)(29,46,35,50)(30,47,49,52)(33,45,51,42)(38,43,48,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26758);