Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33785 |
| 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×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
594 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)(24,34)(25,33)(26,29)(27,40)(28,31)(30,37)(32,42)(35,51)(36,50)(38,45)(39,47)(41,49)(43,48)(44,52)(46,53);(14,16,17,21)(15,18,19,20)(23,29)(30,44)(31,33)(32,45)(34,50)(40,47)(46,49)(48,51);(16,21)(18,20)(22,24)(23,30)(25,35)(26,36)(27,41)(28,43)(29,44)(31,46)(32,48)(33,49)(34,40)(37,42)(38,52)(39,53)(45,51)(47,50);(15,19)(18,20)(22,25,26,28)(23,31,29,33)(24,35,36,43)(27,38,39,42)(30,46,44,49)(32,47,45,40)(34,48,50,51)(37,41,52,53)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26773);