Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62843 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
7130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(22,23)(24,28)(25,32)(26,27)(29,33)(30,34)(31,37)(35,36);(14,16,17,21)(15,18,19,20)(24,30)(28,34)(31,36)(35,37);(23,27)(28,34)(29,32)(35,37);(22,23)(24,28)(25,29)(26,27)(30,34)(31,35)(32,33)(36,37);(22,24)(23,28)(25,31)(26,30)(27,34)(29,35)(32,37)(33,36);(22,25)(23,29)(24,31)(26,33)(27,32)(28,35)(30,36)(34,37)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55831);