Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #97×C191 ⋊ C2 |
| Sylow | C191 ⋊ #442 |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^190,d^b=df,g^b=g^1901922 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574418, #37574420, #442×D191, … |
| maximal normal subgroup of | #37574418, #37574420, #442×D191, … |
| maximal quotient of | #37571345, #37571386, #37571435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 662);