Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #10620796 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#10620796 |
| Fitting | C25×C7 ⋊ C2×C3 |
| derived | C24×C7 ⋊ C22×C3 |
| Hall | C2×#6516 ⋊ C3 |
| Sylow | C7 ⋊ C2×#120⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620796 |
| commutator, cosocle, hypocenter | C24×C7 | C22×C3 |
| Frattini | C22 | C2×A4×D7 |
| Fitting | C25×C7 | C2×C3 |
| socle | C23×C7 | C2×A4 |
| LCS | G ▷ C24×C7 | |
| UCS | C1 ◁ C2 | |
284 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214606, C2×D7×#120⋊C3, #72277737, … |
| maximal normal subgroup of | C2×#72214606, C2×D7×#120⋊C3, #72277737, … |
| maximal quotient of | #72277737 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6918);