Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1864 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
384 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)(15,20,23,22)(16,25,26,44)(17,28)(18,32)(21,36)(24,41,33,29)(27,30,34,45)(31,43)(35,37)(38,40);(14,15,18,33,19,23,32,24)(16,21,34,39,26,36,27,42)(17,29,28,20,31,41,43,22)(25,40,30,38,44,35,45,37);(14,16)(15,21)(17,30)(18,34)(19,26)(20,35)(22,40)(23,36)(24,42)(25,43)(27,32)(28,44)(29,38)(31,45)(33,39)(37,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5940);