Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17852 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C4 | C23×C8×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C2×C13×AGL(1,ℤ/8) | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C13×#431 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20,18,16,19,21)(22,23)(24,28)(25,27)(26,30)(29,33)(31,35)(32,34)(36,37);(23,27)(25,33)(28,34)(29,30)(32,37)(35,36);(14,16,17,21,18,15,19,20)(22,24)(23,28)(25,32)(26,31)(27,34)(29,36)(30,35)(33,37);(24,31)(28,35)(32,37)(34,36)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10840);