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×#62836 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7254 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)(15,18)(19,21)(22,23)(24,33)(25,26)(27,35)(28,29)(30,34)(31,37)(32,36);(16,20)(19,21)(23,29)(24,34)(26,31)(32,35);(14,15)(16,19)(17,18)(20,21)(22,24)(23,30)(25,35)(26,36)(27,31)(28,34)(29,33)(32,37);(22,25)(23,31)(24,35)(26,29)(27,30)(28,37)(32,34)(33,36);(14,16,17,20)(15,19,18,21)(22,26,28,31)(23,25,29,37)(24,36,34,27)(30,35,33,32);(14,15)(16,19)(17,18)(20,21)(22,27,28,36)(23,32,29,35)(24,31,34,26)(25,30,37,33)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55824);