Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18462 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1030 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)(17,29)(21,34)(22,32)(23,30)(25,28)(27,42)(31,41)(33,38)(35,45)(36,44)(37,43)(39,40);(14,15)(16,21)(17,30)(18,23)(19,22)(20,29)(24,38)(25,35)(26,36)(27,43)(28,37)(31,44)(32,41)(33,40)(34,42)(39,45);(16,25)(17,31)(20,32)(21,35)(24,28)(27,39)(29,41)(30,44)(33,34)(37,38)(40,42)(43,45);(14,16,26,24)(15,21,36,38)(17,27,41,39)(18,25,19,28)(20,33,44,34)(22,37,23,35)(29,40,31,42)(30,43,32,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11450);