Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C179 ⋊ C2 |
| Sylow | C179 ⋊ #453 |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^178,d^b=df,e^b=ef,d^c=df1529 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37510982, #37510994, #37511004, … |
| maximal normal subgroup of | #37510982, #37510994, #37511004, … |
| maximal quotient of | #37507918, #37507923, #37507946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 717);