Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25183 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1000 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,24,30)(20,31,35,46)(21,37,22,27)(23,41,25,29)(26,36,43,34)(28,39,45,40)(32,44,48,47)(33,42,38,49);(14,16,17,15)(18,20,24,35)(19,26,30,43)(21,38,22,33)(23,36,25,34)(27,44,37,47)(28,42,45,49)(29,46,41,31)(32,40,48,39);(15,16)(18,21,24,22)(19,27,30,37)(20,32,35,48)(23,39,25,40)(26,42,43,49)(28,29,45,41)(31,47,46,44)(33,34,38,36);(18,22,24,21)(19,28,30,45)(20,33,35,38)(23,39,25,40)(26,42,43,49)(27,29,37,41)(31,44,46,47)(32,34,48,36)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18171);