Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C7×SL(2,𝔽3) ⋊ C2×C4 |
| Sylow | C7 ⋊ C4×GL(2,𝔽3) |
176 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^3,3,7,2^3|a^2=c,b^2=c,f^2=h,g^2=h,e^a=e^6,d^b=d^2,f^b=fg,g^b=gh,f^d=g,g^d=fgh,g^f=gh80 conjugacy classes — view the full character table.
| maximal subgroup of | #72218842, #72218845 |
| maximal normal subgroup of | #72218845 |
| maximal quotient of | #72218842 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6362);