Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13402 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
404 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,21)(16,26)(17,19)(18,32)(22,37)(23,40)(24,25)(27,45)(28,33)(29,43)(30,44)(31,34)(35,38)(39,41);(14,15)(16,27)(17,24)(18,23)(19,21)(20,25)(22,28)(26,41)(29,39)(30,35)(31,42)(32,36)(33,45)(34,40)(37,44)(38,43);(14,16)(15,22,25,39)(17,29)(18,33)(19,28)(20,30)(21,35,24,27)(23,41,40,37)(26,32)(31,44)(34,43)(36,38,42,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6390);