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×#62918 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7386 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)(24,29)(25,35)(26,36)(27,30)(28,34)(31,37)(32,33);(22,24)(23,28)(25,32)(26,33)(27,34)(29,30)(31,36)(35,37);(14,15)(16,19)(17,18)(20,21)(22,25)(23,26)(24,31)(27,36)(28,37)(29,33)(30,35)(32,34);(16,20)(19,21)(22,25)(23,26)(24,32)(27,36)(28,33)(29,37)(30,35)(31,34);(14,16,17,20)(15,19,18,21)(22,24)(23,29)(25,31)(26,33)(27,34)(28,30)(32,36)(35,37);(14,15)(16,19)(17,18)(20,21)(22,26)(23,25)(24,33)(27,35)(28,32)(29,31)(30,36)(34,37)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55906);