Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61681 |
| 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 ◁ C13×#532 ◁ G | |
2036 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)(24,30)(25,36)(26,31)(27,40)(28,34)(29,38)(32,39)(33,48)(35,43)(37,47)(41,45)(42,52)(44,50)(46,51)(49,53);(14,16)(15,18)(17,21)(19,20)(22,24)(23,28)(25,33)(26,34)(27,35)(29,42)(30,31)(32,43)(36,53)(37,49)(38,50)(39,51)(40,46)(41,52)(44,45)(47,48);(22,25,26,37)(23,29,31,45)(24,33,34,49)(27,41,39,38)(28,42,30,44)(32,47,40,36)(35,52,51,50)(43,48,46,53);(16,21)(18,20)(22,24)(23,30)(25,33)(26,34)(27,35)(28,31)(29,44)(32,46)(36,48)(37,49)(38,50)(39,51)(40,43)(41,52)(42,45)(47,53);(15,19)(18,20)(23,31)(24,34)(29,45)(32,40)(33,49)(35,51)(36,47)(50,52)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54669);