Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62903 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23)(16,24,25,20)(17,28,30,22)(19,21,31,36)(26,33,38,37)(27,32,39,34)(29,41,42,35)(40,44,45,43);(14,16,19,27)(15,20,21,34)(17,26,29,40)(18,25,31,39)(22,33,35,44)(23,24,36,32)(28,37,41,43)(30,38,42,45);(15,21)(16,25)(20,32)(22,35)(23,36)(24,34)(26,38)(27,39)(28,41)(33,43)(37,44)(40,45);(14,17,18,30)(15,22,23,28)(16,26,25,38)(19,29,31,42)(20,33,24,37)(21,35,36,41)(27,40,39,45)(32,43,34,44);(17,29)(22,35)(26,40)(28,41)(30,42)(33,44)(37,43)(38,45);(15,21)(20,34)(22,35)(23,36)(24,32)(28,41)(33,44)(37,43)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55891);