Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62033 |
| 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 | |
1896 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(24,32)(25,26)(28,35)(29,31)(33,34)(36,37);(14,15)(16,19)(17,18)(20,21)(22,23,27,30)(24,28,33,36)(25,29,26,31)(32,35,34,37);(22,24)(23,28)(25,32)(26,34)(27,33)(29,35)(30,36)(31,37);(15,18)(19,21)(22,25,27,26)(23,29,30,31)(24,32,33,34)(28,35,36,37);(14,16,17,20)(15,19,18,21)(23,30)(28,36)(29,31)(35,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55021);