Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,21)(16,25)(17,19)(18,32)(22,38)(23,33)(24,30)(26,41)(27,34)(28,43)(29,42)(31,35)(36,40)(39,44);(14,15)(16,26)(17,30)(18,33)(19,21)(20,24)(22,28)(23,35)(25,40)(27,39)(29,36)(31,37)(32,45)(34,41)(38,42)(43,44);(14,16)(15,22,24,26)(17,29)(18,34)(19,27)(20,28)(21,36,30,39)(23,41,33,38)(25,32)(31,43)(35,42)(37,40,45,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6392);