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×#20561 |
| 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 | |
990 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)(26,27,30,29,31,33,38,37)(28,32,36,34,35,39,41,40);(14,15,16,17)(18,20)(19,22)(21,25)(23,24)(26,28)(27,32)(29,34)(30,36)(31,35)(33,39)(37,40)(38,41);(20,25)(22,24)(26,29,30,33,31,37,38,27)(28,34,36,39,35,40,41,32);(19,23)(22,24)(28,35)(32,39)(34,40)(36,41)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13549);