Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10895 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,28)(21,24)(22,26)(23,27)(25,29)(30,32)(31,33);(19,24,27,26)(25,32,33,28);(14,16,17,15)(18,20)(19,25)(21,29)(22,31)(23,30)(24,32)(26,28)(27,33)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3883);