Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63041 |
| 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)(22,23)(24,31)(25,34)(26,32)(27,28)(29,35)(30,36)(33,37);(15,18)(19,20)(23,28)(25,36)(29,31)(32,33);(14,15)(16,19)(17,18)(20,21)(22,24)(23,29)(25,33)(26,34)(27,35)(28,31)(30,37)(32,36);(14,16)(15,19)(17,21)(18,20)(22,25)(23,30)(24,33)(26,31)(27,36)(28,34)(29,37)(32,35);(22,24)(23,31)(25,33)(26,30)(27,35)(28,29)(32,36)(34,37);(22,26)(23,32)(24,34)(25,31)(27,37)(28,33)(29,36)(30,35)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56029);