Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×C13×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C13 | C22 |
| commutator | C2 | C22×C3×C4×C13 |
| Frattini, cosocle | C4 | C23×C3×C13 |
| socle | C22×C3×C13 | C2×C4 |
| prime radical | C23×C3×C13 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C13 ◁ G | |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26);(3,4,5,6,7,8,9,10);(4,8)(6,10)780 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1144);