Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ #480 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^178,e^c=ef,g^c=g^1781799 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507987, #37507988, #37507999, … |
| maximal normal subgroup of | #37507987, #37507988, #37507999, … |
| maximal quotient of | #37509087, #37509190, #37509315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 863);