Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12563 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #106 |
| commutator | C8 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×#106 |
| prime radical | C24×C13 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
570 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)(20,31,34,44)(21,27)(22,39)(23,40)(24,41)(25,30)(26,33,43,35)(28,38)(29,37)(32,45,36,49)(42,47,46,48);(15,17)(18,20,23,35,24,36,37,47,25,34,22,33,21,32,38,48)(19,26,29,44,27,42,40,49,30,43,28,31,41,46,39,45);(18,21,25,24)(19,27,30,41)(20,32,34,36)(22,37,23,38)(26,42,43,46)(28,39,29,40)(31,45,44,49)(33,47,35,48)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5551);