Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13175 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13175 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1943 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
256 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)(16,25,28,41)(17,19)(18,32)(22,36,38,39)(23,33)(24,30)(26,37,43,45)(27,42,29,40)(31,34);(14,15)(16,26,28,43)(17,30)(18,33)(19,21)(20,24)(22,29,38,27)(23,34)(25,39,41,36)(31,35)(32,44)(37,40,45,42);(14,16,18,25,19,29,32,42,20,28,34,41,17,27,31,40)(15,22,23,37,21,26,35,36,24,38,33,45,30,43,44,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6163);