Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C179 ⋊ C2 |
| Sylow | C179 ⋊ #349 |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1781802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #349×D179, C2×#26038220, #37510619, … |
| maximal normal subgroup of | #349×D179, C2×#26038220, #37510619, … |
| maximal quotient of | #37506923, #37506939, #37506957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 330);