Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18354 |
| 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 ◁ C23×C4×C13 ◁ G | |
1022 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)(15,21)(16,25)(17,27)(18,30)(22,35)(23,31)(24,37)(26,40)(28,44)(29,32)(33,42)(36,38)(39,45)(41,43);(14,15)(16,22)(17,28)(18,31)(19,24)(20,23)(21,30)(25,38)(26,41)(27,43)(29,36)(32,44)(33,45)(34,39)(35,40)(37,42);(14,16,20,17)(15,22,23,28)(18,32,30,40)(19,25,34,27)(21,35,31,44)(24,38,39,43)(26,42,29,33)(36,45,41,37);(14,17,20,16)(15,22,23,28)(18,29,30,26)(19,27,34,25)(21,36,31,41)(24,38,39,43)(32,33,40,42)(35,45,44,37)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11342);