Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#17596 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C42×C13 ◁ G | |
994 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,23,26,20)(17,21)(18,27)(19,22)(24,29,25,28)(30,31)(32,38)(33,41)(34,36)(35,39)(37,43)(40,45)(42,44);(14,16,19,26)(15,20,22,23)(17,24,18,25)(21,28,27,29)(30,32,34,40)(31,35,36,44)(33,42,43,39)(37,45,41,38);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,28,23,29)(31,36)(35,44)(37,41)(38,45);(14,18,19,17)(15,21,22,27)(16,25,26,24)(20,28,23,29)(31,36)(35,44)(37,41)(38,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10584);