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×#62835 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7148 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)(22,23,28,26)(24,31,29,25)(27,34,35,30)(32,33,36,37);(16,20)(19,21)(23,26)(24,29)(30,34)(32,36);(14,15)(16,19)(17,18)(20,21)(22,24)(23,25)(26,31)(27,32)(28,29)(30,33)(34,37)(35,36);(22,25,28,31)(23,29,26,24)(27,33,35,37)(30,36,34,32);(14,16,17,20)(15,19,18,21)(22,26,28,23)(24,31,29,25)(27,34,35,30)(32,37,36,33);(14,15)(16,19)(17,18)(20,21)(22,27)(23,30)(24,32)(25,33)(26,34)(28,35)(29,36)(31,37)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55823);