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×#62955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7310 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
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)(22,23)(24,31)(25,28)(26,29)(27,33)(30,35)(32,36)(34,37);(15,19)(16,20)(22,24,28,26)(23,29,25,31)(27,32,35,34)(30,36,33,37);(14,16,18,20)(15,17,19,21)(22,23,28,25)(24,31,26,29)(27,30,35,33)(32,37,34,36);(14,17)(15,20)(16,19)(18,21)(22,25,28,23)(24,31,26,29)(27,33,35,30)(32,37,34,36);(22,26,28,24)(23,29,25,31)(27,34,35,32)(30,36,33,37);(22,27)(23,30)(24,32)(25,33)(26,34)(28,35)(29,36)(31,37)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55943);