Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D7⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C22×Dic7⋊A4 |
| derived | C22×C7 ⋊ C22×C3×C4 |
| Hall | C24×Dic7 ⋊ C3 |
| Sylow | C7 ⋊ C22×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D7⋊A4 |
| commutator, hypocenter | C22×C7 | C22×C3×C4 |
| Frattini | C2 | C22×D7⋊A4 |
| Fitting, socle | C25×C7 | C2×C3 |
| prime radical | C23×C22⋊ΓL(1,𝔽8) | C2 |
| cosocle | C23×C7 | C23×C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C23 | |
634 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11490);