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×#62897 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7094 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(19,21)(22,23)(24,32)(25,26)(27,29)(28,31)(30,37)(33,34)(35,36);(22,24,28,27)(23,29,31,32)(25,35,30,33)(26,34,37,36);(14,15)(16,19)(17,18)(20,21)(22,25,28,30)(23,26,31,37)(24,33,27,35)(29,36,32,34);(16,20)(19,21)(22,26)(23,30)(24,34)(25,31)(27,36)(28,37)(29,33)(32,35);(14,16)(15,19)(17,20)(18,21)(22,27,28,24)(23,29,31,32)(25,35,30,33)(26,36,37,34);(14,15)(16,19)(17,18)(20,21)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55885);