Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#10608 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #396 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C23×C13 | C22⋊Q8 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
322 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)(14,15,18,19,17,21,16,20)(22,23,28,31)(24,26,30,27)(25,32,35,36)(29,33,37,34);(22,24,26,31,28,30,27,23)(25,32,33,29,35,36,34,37);(15,19)(16,18)(20,21)(22,25,28,35)(23,29,31,37)(24,32,30,36)(26,34,27,33)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3596);