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×#62905 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7326 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)(15,17)(19,20)(22,23)(24,29)(25,27)(26,33)(28,32)(30,34)(31,35)(36,37);(14,15,18,17)(16,20,21,19)(22,24)(23,28)(25,29)(26,31)(27,32)(30,35)(33,36)(34,37);(14,16,18,21)(15,19,17,20)(22,23,27,25)(24,29,32,28)(26,30,34,33)(31,36,37,35);(14,17,18,15)(16,20,21,19)(22,25,27,23)(24,29,32,28)(26,33,34,30)(31,36,37,35);(22,24)(23,29)(25,28)(26,31)(27,32)(30,36)(33,35)(34,37);(22,26)(23,30)(24,31)(25,33)(27,34)(28,35)(29,36)(32,37)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55893);