Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C179 ⋊ #339 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^178,g^b=g^1781808 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #339×D179, C2×#26038200, #37508708, … |
| maximal normal subgroup of | #339×D179, C2×#26038200, #37508708, … |
| maximal quotient of | #37506832, #37506838, #37506839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 310);