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×#18347 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3490 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1072 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)(14,15,18,23)(16,24,25,38)(17,28,31,22)(19,21,32,37)(20,29,35,26)(27,39,41,40)(30,43,45,36)(33,42,34,44);(14,16)(15,20)(17,29)(18,25)(19,27)(21,34)(22,38)(23,35)(24,28)(26,31)(30,44)(32,41)(33,37)(36,40)(39,43)(42,45);(17,30)(22,36)(24,39)(26,42)(28,43)(29,44)(31,45)(38,40);(15,21)(16,25)(20,33)(22,36)(23,37)(24,40)(26,29)(27,41)(28,43)(34,35)(38,39)(42,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11335);