Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33531 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33531 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1122 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)(17,27)(18,30)(21,35)(22,34)(23,38)(25,40)(26,39)(28,32)(29,43)(31,44)(33,36)(37,45)(41,42);(14,15)(16,21)(17,28)(18,32)(19,22)(20,27)(23,30)(24,36)(25,41)(26,42)(29,45)(31,38)(33,43)(34,44)(35,40)(37,39);(14,16)(15,21)(17,29)(18,26)(19,24)(20,33)(22,36)(23,37)(25,31)(27,43)(28,45)(30,39)(32,42)(34,35)(38,41)(40,44);(16,24)(21,36)(25,29)(26,39)(33,35)(37,42)(40,43)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26519);