Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C191 ⋊ C2 |
| Sylow | C191 ⋊ #430 |
102 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,c^b=cf,g^c=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574733, #37574736, #37574738, … |
| maximal normal subgroup of | #37574733, #37574736, #37574738, … |
| maximal quotient of | #37571269, #37571271, #37571284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 596);