Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C179 ⋊ C2 |
| Sylow | C179 ⋊ #472 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^178,e^c=ef,g^c=g^1781262 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37510958, #37510960, #37510965, … |
| maximal normal subgroup of | #37510958, #37510960, #37510965, … |
| maximal quotient of | #37508356, #37508361, #37508400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 820);