Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #327 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C2×C42 |
| direct product | C13×#8013 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C23×C13 | C2×C22⋊C4 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19)(20,22)(21,24)(23,25)(26,27)(28,34)(29,32)(30,33)(31,36)(35,40)(37,39)(38,41);(19,22,24,23)(26,28)(27,31,33,34)(29,35)(30,36)(32,38,39,40)(37,41);(26,29,30,37)(27,32,33,39)(28,35,36,41)(31,38,34,40)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1001);