Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61449 |
| 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 ◁ C4×C13×#41 ◁ G | |
1958 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)(19,21)(22,23)(24,28)(25,32)(26,35)(27,30)(29,31)(33,37)(34,36);(14,15)(16,19)(17,18)(20,21)(22,24,27,26)(23,28,30,35)(25,33,34,31)(29,32,37,36);(22,25)(23,29)(24,31)(26,33)(27,34)(28,36)(30,37)(32,35);(15,18)(19,21)(22,24,27,26)(23,28,30,35)(25,31,34,33)(29,36,37,32);(14,16,17,20)(15,19,18,21)(22,24,27,26)(23,28,30,35)(25,31,34,33)(29,36,37,32)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54437);