Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #95×C179 ⋊ C2 |
| Sylow | C179 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,179|a^2=e,b^2=f,c^2=e,b^a=bd,g^c=g^1781820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507488, #37507490, #37507514, … |
| maximal normal subgroup of | #37507488, #37507490, #37507514, … |
| maximal quotient of | #95×Dic179, #37507221, #37507226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 396);