Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27×C4 |
| direct product | C13×#60797 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C22×C13 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#117 ◁ G | |
2062 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)(24,29)(25,37)(26,31)(27,40)(28,32)(30,38)(33,47)(34,43)(35,44)(36,50)(39,45)(41,46)(42,49)(48,53)(51,52);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,33)(26,35)(27,36)(28,34)(30,42)(31,44)(32,43)(37,47)(38,49)(39,48)(40,50)(41,51)(45,53)(46,52);(16,21)(18,20)(22,25)(23,30)(24,33)(26,38)(27,41)(28,39)(29,42)(31,45)(32,46)(34,48)(35,49)(36,51)(37,40)(43,52)(44,53)(47,50);(15,19)(18,20)(24,34)(29,43)(33,48)(35,36)(42,52)(44,50)(47,53)(49,51);(22,26,28,27)(23,31,32,40)(24,35,34,36)(25,38,39,41)(29,44,43,50)(30,45,46,37)(33,49,48,51)(42,53,52,47)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53785);