Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13309 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13466 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #2065 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
314 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)(14,15,22,27)(16,28)(17,34)(18,25,39,45)(19,24,20,42)(21,29,41,26)(23,36)(30,38)(31,44)(32,35)(33,43)(37,40);(14,16,18,30,21,32,19,40,22,33,39,34,41,23,20,31)(15,17,24,28,26,37,25,36,27,38,42,43,29,44,45,35);(14,17)(15,23)(16,29)(18,36)(19,28)(20,43)(21,44)(22,38)(24,30)(25,31)(26,33)(27,32)(34,42)(35,39)(37,41)(40,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6454);