Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,25,30)(20,31,35,47)(21,22,27,40)(23,29,24,28)(26,42,46,34)(32,33,36,49)(37,43,41,39)(38,48,44,45);(18,20,25,35)(19,26,30,46)(21,36,27,32)(22,38,40,44)(23,34,24,42)(28,31,29,47)(33,43,49,39)(37,48,41,45);(15,17)(18,21,25,27)(19,22,30,40)(20,32,35,36)(23,41,24,37)(26,44,46,38)(28,43,29,39)(31,33,47,49)(34,48,42,45);(18,22)(19,27)(20,33)(21,30)(23,39)(24,43)(25,40)(26,45)(28,41)(29,37)(31,36)(32,47)(34,44)(35,49)(38,42)(46,48);(18,23,25,24)(19,28,30,29)(20,34,35,42)(21,37,27,41)(22,39,40,43)(26,31,46,47)(32,45,36,48)(33,44,49,38)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54079);