Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18282 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#1600 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
942 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)(21,33)(22,31)(23,29)(27,38)(30,39)(32,34)(35,42)(36,44)(43,45);(14,15,18,23)(16,21,24,34)(17,29,28,20)(19,22,25,35)(26,33,37,32)(27,36,38,45)(30,42,39,31)(40,43,41,44);(16,24)(17,30)(20,31)(21,34)(26,40)(27,38)(28,39)(29,42)(32,44)(33,43)(36,45)(37,41);(14,16,25,38)(15,21,35,45)(17,26,39,40)(18,24,19,27)(20,32,42,44)(22,36,23,34)(28,37,30,41)(29,33,31,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11270);