Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,c^b=ce,g^b=g^1781808 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D179, C2×#26038166, #37507380, … |
| maximal normal subgroup of | D4⋊C8×D179, C2×#26038166, #37507380, … |
| maximal quotient of | #37506820, #37506824, #37506839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 276);