Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7338 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
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)(24,33)(25,36)(26,27)(28,29)(30,34)(31,35)(32,37);(16,20)(19,21)(23,29)(24,34)(26,32)(31,36);(14,15)(16,19)(17,18)(20,21)(22,24)(23,30)(25,32)(26,35)(27,36)(28,34)(29,33)(31,37);(22,25,28,35)(23,31,29,36)(24,32,34,26)(27,30,37,33);(14,16)(15,19)(17,20)(18,21)(22,26,28,32)(23,27,29,37)(24,35,34,25)(30,36,33,31);(14,15)(16,19)(17,18)(20,21)(22,27)(23,32)(24,36)(25,30)(26,29)(28,37)(31,34)(33,35)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55809);