Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20)(16,18,21,19)(23,28)(24,31)(25,26)(29,32)(30,35)(33,34);(22,23,27,30)(24,32,34,29)(25,35,26,28)(31,37,33,36);(15,18)(16,21)(19,20)(22,24,25,33,27,34,26,31)(23,29,28,36,30,32,35,37)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3442);