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×#62946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,20)(23,27)(28,34)(29,35)(36,37);(14,15,18,17)(16,20,21,19);(14,16,18,21)(15,19,17,20)(22,23)(24,28)(25,29)(26,27)(30,36)(31,34)(32,37)(33,35);(14,17,18,15)(16,20,21,19)(22,24,26,31)(23,28,27,34)(25,32,33,30)(29,37,35,36);(22,25,26,33)(23,29,27,35)(24,30,31,32)(28,36,34,37);(22,23)(24,28)(25,29)(26,27)(30,36)(31,34)(32,37)(33,35)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55934);