Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #97×C191 ⋊ C2 |
| Sylow | C191 ⋊ #433 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^190,c^b=cf,g^b=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #433×D191, C2×#27132725, #37581154, … |
| maximal normal subgroup of | #433×D191, C2×#27132725, #37581154, … |
| maximal quotient of | #37572273, #37572289, #37572380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 611);