Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C179 ⋊ C2 |
| Sylow | C179 ⋊ #361 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^178,c^b=cef,d^b=df,e^b=ef,g^b=g^1781796 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #361×D179, C2×#26038253, #37510748, … |
| maximal normal subgroup of | #361×D179, C2×#26038253, #37510748, … |
| maximal quotient of | #37506968, #37507016, #37507047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 363);