Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C23 |
| direct product | C22×C13×C3⋊C8 |
| derived, Sylow | C3 ⋊ C22×C8×C13 |
| Hall | C3×C13 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C13 | D3 |
| commutator, hypocenter | C3 | C22×C8×C13 |
| Frattini | C4 | C22×D3×C13 |
| Fitting | C22×C3×C4×C13 | C2 |
| socle, prime radical | C23×C3×C13 | C4 |
| cosocle | C3×C4 | C23×C13 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C4×C13 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1248 |
624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1008);