Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C179 ⋊ #362 |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=f,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 | #362×D179, C2×#26038256, #37510746, … |
| maximal normal subgroup of | #362×D179, C2×#26038256, #37510746, … |
| maximal quotient of | #37506971, #37507019, #37507050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 366);