Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23406 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#120 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
2022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,28)(21,30)(22,25)(23,26)(24,27)(29,32)(31,33);(14,15)(16,17)(18,20)(19,21)(22,29)(23,30)(24,31)(25,28)(26,33)(27,32);(15,17)(18,21)(19,20)(22,28)(23,33)(24,32)(25,29)(26,30)(27,31);(18,22,24,23)(19,25,27,26)(20,29,31,30)(21,28,32,33)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16394);