Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60773 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C13×#41 ◁ G | |
2118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 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)(22,23,27,31)(24,32,33,45)(25,29,36,43)(26,38,40,30)(28,39,41,35)(34,46,47,53)(37,50,49,44)(42,51,52,48);(14,16)(15,18)(17,21)(19,20)(24,33)(28,41)(32,45)(34,47)(35,39)(42,52)(46,53)(48,51);(16,21)(18,20)(22,24,27,33)(23,28,31,41)(25,34,36,47)(26,39,40,35)(29,42,43,52)(30,45,38,32)(37,51,49,48)(44,53,50,46);(15,19)(18,20)(22,25)(23,29)(24,34)(26,37)(27,36)(28,42)(30,44)(31,43)(32,46)(33,47)(35,48)(38,50)(39,51)(40,49)(41,52)(45,53);(25,36)(29,43)(34,47)(37,49)(42,52)(44,50)(46,53)(48,51)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53761);