Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61690 |
| 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 | |
2110 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)(14,15)(16,20)(17,19)(18,21)(23,29)(24,31)(26,28)(30,32)(33,35)(36,37);(14,16)(15,18)(17,21)(19,20)(22,23,27,29)(24,30,33,36)(25,26,34,28)(31,37,35,32);(22,24)(23,30)(25,32)(26,31)(27,33)(28,35)(29,36)(34,37);(16,21)(18,20)(22,25)(23,26)(24,32)(27,34)(28,29)(30,31)(33,37)(35,36);(15,19)(18,20)(22,26,27,28)(23,25,29,34)(24,31,33,35)(30,32,36,37)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54678);