Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #478 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^190,e^c=ef,g^c=g^1901919 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #478×D191, C2×#27132964, #37582307, … |
| maximal normal subgroup of | #478×D191, C2×#27132964, #37582307, … |
| maximal quotient of | #37572531, #37572770, #37572784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 850);