Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61511 |
| 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×#529 ◁ G | |
1760 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(19,21)(22,23)(24,28)(25,35)(26,38)(27,30)(29,36)(31,40)(32,46)(33,42)(34,50)(37,45)(39,44)(41,48)(43,49)(47,53)(51,52);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,32)(26,34)(27,33)(29,41)(30,42)(31,43)(35,46)(36,48)(37,47)(38,50)(39,51)(40,49)(44,52)(45,53);(22,25,27,37)(23,29,30,44)(24,32,33,47)(26,39,40,36)(28,41,42,52)(31,45,38,35)(34,51,49,48)(43,53,50,46);(15,18)(19,21)(23,30)(28,42)(29,44)(31,38)(35,45)(41,52)(43,50)(46,53);(14,16,17,20)(15,19,18,21)(24,33)(28,42)(32,47)(34,49)(41,52)(43,50)(46,53)(48,51)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54499);