Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24987 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#24987 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2420 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
638 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)(17,28)(18,30)(22,37)(23,33)(26,27)(29,41)(31,35)(34,42)(38,39)(44,45);(14,15,18,20,19,23,30,33)(16,21,24,35,27,36,26,31)(17,22,28,32,29,37,41,43)(25,34,38,44,40,45,39,42);(14,16)(15,21)(17,25)(18,26)(19,27)(20,31)(22,34)(23,36)(24,30)(28,39)(29,40)(32,42)(33,35)(37,45)(38,41)(43,44);(14,17,18,28,19,29,30,41)(15,22,20,32,23,37,33,43)(16,25,26,39,27,40,24,38)(21,34,31,42,36,45,35,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17975);