Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C13 · Schur multiplier (H2) = C2 |
| direct product | C3×C13×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4×C13 | C22 |
| commutator | C2 | C3×C42×C13 |
| Frattini, cosocle | C2×C4 | C22×C3×C13 |
| socle, prime radical | C22×C3×C13 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4×C13 ◁ G | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1248 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(21,22,23,26,24,25,27,28);(17,18,19,20)(22,25)(26,28)780 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 264);