Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #125×C181 ⋊ C2 |
| Sylow | C181 ⋊ #488 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^180,g^b=g^180,g^c=g^1801282 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #488×D181, C2×#26041636, #37544042, … |
| maximal normal subgroup of | #488×D181, C2×#26041636, #37544042, … |
| maximal quotient of | #37533851, #37534396, #37534403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 906);