Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62864 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6666 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)(16,24)(17,28)(18,22)(19,23)(20,27)(21,30)(25,40)(26,39)(29,43)(31,36)(32,38)(33,44)(34,42)(35,41)(37,45);(14,16,18,27)(15,20,22,24)(17,29,31,25)(19,26,32,42)(21,35,37,33)(23,34,38,39)(28,40,36,43)(30,44,45,41);(14,17,18,31)(15,21,22,37)(16,25,27,29)(19,30,32,45)(20,33,24,35)(23,28,38,36)(26,41,42,44)(34,43,39,40);(15,22)(17,30)(20,24)(21,36)(23,38)(25,41)(28,37)(29,44)(31,45)(33,40)(34,39)(35,43);(16,26)(20,34)(24,39)(25,41)(27,42)(29,44)(33,43)(35,40);(15,23)(20,34)(21,28)(22,38)(24,39)(33,43)(35,40)(36,37)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55852);