Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#20560 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C23×C13 | C23×C4 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19)(20,24)(21,23)(22,25)(26,27,29,33,30,32,36,39)(28,31,35,38,34,37,40,41);(14,15,16,17)(18,20)(19,22)(21,25)(23,24)(28,34)(31,37)(35,40)(38,41);(20,25)(22,24)(26,28,29,35,30,34,36,40)(27,31,33,38,32,37,39,41);(19,23)(22,24)(27,32)(31,37)(33,39)(38,41)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13548);