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×#62824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7330 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)(16,17)(18,19)(20,21)(23,27)(25,32)(28,33)(31,36);(15,19)(17,20)(24,30)(28,33)(31,36)(35,37);(14,15,18,19)(16,20,21,17)(22,23,26,27)(24,28,30,33)(25,29,32,34)(31,35,36,37);(14,16)(15,20)(17,19)(18,21);(14,17,18,20)(15,16,19,21)(22,24)(23,28)(25,31)(26,30)(27,33)(29,35)(32,36)(34,37);(14,16)(15,20)(17,19)(18,21)(22,25)(23,29)(24,31)(26,32)(27,34)(28,35)(30,36)(33,37)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55812);