Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic7×GL(2,𝔽3) |
| derived | C7×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ C4×GL(2,𝔽3) |
176 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | GL(2,𝔽3)×C7⋊AGL(1,𝔽5), GL(2,𝔽3)×ΓL(1,𝔽8)⋊C4 |
| maximal normal subgroup of | GL(2,𝔽3)×ΓL(1,𝔽8)⋊C4 |
| maximal quotient of | GL(2,𝔽3)×C7⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6361);