Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11651 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13002 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#102 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,23,28,24,29,36,46,25,30,22,38,21,27,37,44)(20,31,34,42,32,45,40,43,35,48,33,47,41,49,39,26);(18,20)(19,26,30,43)(21,32)(22,39)(23,40)(24,41)(25,35)(27,42,29,47)(28,45,38,49)(31,44,48,46)(33,37)(34,36);(15,17)(18,21,25,24)(19,27,30,29)(20,32,35,41)(22,36,23,37)(26,42,43,47)(28,44,38,46)(31,45,48,49)(33,39,34,40)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5990);