Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ #431 |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^1782888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#15668242, #37507279, #37507282, … |
| maximal normal subgroup of | C8×#15668242, #37507279, #37507282, … |
| maximal quotient of | #37508745, C4×(C2×D179)⋊C8, C4×Dic179⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 600);