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×#62820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7382 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)(24,30)(25,31)(26,29)(27,28)(32,36)(33,37)(34,35);(16,20)(19,21)(23,28)(24,31)(26,34)(33,36);(14,15)(16,19)(17,18)(20,21)(22,24)(23,25)(26,32)(27,31)(28,30)(29,33)(34,37)(35,36);(22,25)(23,24)(26,33)(27,30)(28,31)(29,32)(34,36)(35,37);(14,16)(15,19)(17,20)(18,21)(22,26,27,34)(23,29,28,35)(24,32,31,37)(25,33,30,36);(14,15)(16,19)(17,18)(20,21)(22,25)(23,24)(26,33)(27,30)(28,31)(29,32)(34,36)(35,37)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55808);