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×#63045 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7484 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)(14,15,18,20)(16,17,21,19)(22,23,27,31)(24,32,35,28)(25,26,30,29)(33,36,37,34);(14,16,18,21)(15,19,20,17)(22,24,27,35)(23,28,31,32)(25,33,30,37)(26,34,29,36);(14,16)(15,17)(18,21)(19,20)(22,25)(23,29)(24,33)(26,31)(27,30)(28,36)(32,34)(35,37);(14,17)(15,16)(18,19)(20,21)(22,24)(23,28)(25,33)(26,34)(27,35)(29,36)(30,37)(31,32);(22,25)(23,26)(24,33)(27,30)(28,34)(29,31)(32,36)(35,37);(22,26)(23,30)(24,34)(25,31)(27,29)(28,37)(32,33)(35,36)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56033);