Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊AΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C22⋊AΓL(1,𝔽8) |
| unambiguous semidirect product | AGL(1,𝔽8)⋊(C2×A4) |
| unambiguous semidirect product | (C2×AGL(1,𝔽8))⋊A4 |
| Fitting, socle, Sylow | C26 ⋊ ΓL(1,𝔽8) |
| derived | C22×AGL(1,𝔽8) ⋊ C2×C3 |
| Hall | C23×AGL(1,𝔽8) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊AΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×AGL(1,𝔽8) | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×AGL(1,𝔽8) | |
| UCS | C1 ◁ C2 | |
226 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 42 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11689);