Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9781 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #390 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,21)(17,18)(22,23)(24,26,28,29)(25,27);(14,15,17,20,19,21,18,16)(22,24)(23,26,27,29)(25,28);(14,16,18,21,19,20,17,15)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2769);