Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33692 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#405 ◁ G | |
536 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)(16,24)(17,28)(18,32)(20,33)(22,37)(23,36)(25,30)(26,41)(27,42)(29,43)(31,44)(34,45)(35,40)(38,39);(14,15,19,21)(16,20,26,35)(17,29,31,22)(18,23,32,36)(24,40,41,33)(25,39,27,34)(28,43,44,37)(30,45,42,38);(14,16)(15,20)(17,30)(18,25)(19,26)(21,35)(22,38)(23,39)(24,28)(27,32)(29,45)(31,42)(33,37)(34,36)(40,43)(41,44);(15,21)(16,25,26,27)(17,31)(20,34,35,39)(23,36)(24,30,41,42)(28,44)(33,45,40,38)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26680);