Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24775 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
850 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)(15,16)(18,19,23,28,22,27,24,29)(20,30,33,45,32,25,39,41)(21,34,37,43,36,44,38,26)(31,47,35,40,48,42,49,46);(14,15,17,16)(18,20,22,32)(19,25,27,30)(21,35,36,49)(23,33,24,39)(26,42,43,47)(28,41,29,45)(31,37,48,38)(34,46,44,40);(18,21,22,36)(19,26,27,43)(20,31,32,48)(23,38,24,37)(25,40,30,46)(28,44,29,34)(33,49,39,35)(41,47,45,42);(14,16,17,15)(19,27)(25,30)(26,43)(28,29)(34,44)(40,46)(41,45)(42,47)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17763);