Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62686 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| socle | C22×C13 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C13 ◁ G | |
7226 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)(16,19)(17,18)(20,21)(22,23)(24,27)(25,29)(26,28)(30,33)(31,34)(32,35)(36,37);(15,18)(19,21)(22,24)(23,27)(25,31)(26,30)(28,33)(29,34)(32,36)(35,37);(23,28)(24,30)(29,35)(31,36);(23,28)(27,33)(29,35)(34,37);(22,25,26,32)(23,29,28,35)(24,31,30,36)(27,34,33,37);(14,16,17,20)(15,19,18,21)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55674);