Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #441 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #441×D191, C2×#27132768, #37581315, … |
| maximal normal subgroup of | #441×D191, C2×#27132768, #37581315, … |
| maximal quotient of | #37571337, #37571389, #37571391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 654);