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×#62900 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7428 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)(14,15)(16,20)(17,18)(19,21)(23,28)(24,30)(26,34)(33,36);(15,18)(19,20)(22,23,27,28)(24,25,30,29)(26,31,34,35)(32,33,37,36);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,28)(26,32)(27,30)(31,36)(33,35)(34,37);(14,16)(15,19)(17,21)(18,20)(22,24)(23,25)(26,32)(27,30)(28,29)(31,33)(34,37)(35,36);(22,25)(23,30)(24,28)(26,33)(27,29)(31,37)(32,35)(34,36);(22,26)(23,31)(24,32)(25,33)(27,34)(28,35)(29,36)(30,37)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55888);