Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1004 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,24)(17,29)(21,34)(22,32)(23,30)(25,40)(27,43)(28,39)(31,42)(33,36)(35,45)(37,41)(38,44);(14,15,18,23)(16,25,28,21)(17,30,29,20)(19,22,26,35)(24,37,39,36)(27,33,44,41)(31,45,42,32)(34,43,40,38);(17,31)(20,32)(27,38)(29,42)(30,45)(33,34)(40,41)(43,44);(14,16,26,39)(15,21,35,37)(17,27,42,43)(18,28,19,24)(20,33,45,40)(22,36,23,25)(29,44,31,38)(30,41,32,34)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11347);