Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18376 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#1595 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
984 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)(21,35)(22,33)(23,30)(25,39)(26,42)(27,28)(31,44)(34,41)(36,40)(37,45)(38,43);(14,15)(16,25)(17,30)(18,23)(19,22)(20,29)(21,27)(24,36)(26,34)(28,41)(31,45)(32,37)(33,44)(35,38)(39,42)(40,43);(17,31)(20,33)(26,42)(29,44)(30,45)(34,39)(35,40)(38,43);(14,16,19,28)(15,21,22,36)(17,26,31,42)(18,27,32,24)(20,34,33,39)(23,25,37,41)(29,43,44,38)(30,40,45,35)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11374);