Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10422 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
452 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19,22,25)(20,23,21,24)(26,27)(28,29)(30,32)(31,33);(14,15)(16,17)(18,20,22,21)(19,23,25,24)(26,28,31,32)(27,29,33,30);(14,16,17,15)(19,24)(20,21)(23,25)(27,28)(29,30)(32,33)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3410);