Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13032 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1879 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
476 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)(14,15,20,26,28,31,19,24,22,27,37,30,21,16,18,25)(17,32,34,23,40,41,33,29,36,45,38,43,35,44,39,42);(14,16,28,27,22,31,21,15)(17,29,35,43,36,42,40,23)(18,25,20,30,19,24,37,26)(32,34,41,39,45,38,44,33);(14,17)(15,23)(16,29)(18,34)(19,38)(20,39)(21,40)(22,36)(24,44)(25,41)(26,32)(27,43)(28,35)(30,45)(31,42)(33,37)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6020);