Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1062 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)(14,15,19,24)(16,26,29,42)(17,23,18,33)(20,25,36,41)(21,34,39,27)(22,35,31,32)(28,37,30,44)(38,43,40,45);(14,16)(15,21)(17,27)(18,34)(19,29)(20,30)(22,37)(23,42)(24,39)(25,40)(26,33)(28,36)(31,44)(32,43)(35,45)(38,41);(14,15)(16,21)(17,31)(18,22)(19,24)(20,25)(23,35)(26,43)(27,44)(28,38)(29,39)(30,40)(32,33)(34,37)(36,41)(42,45);(14,17,19,18)(15,22,24,31)(16,27,29,34)(20,32,36,35)(21,37,39,44)(23,41,33,25)(26,40,42,38)(28,45,30,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11407);