Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #460 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,e^c=ef,g^c=g^1901349 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571577, #37571578, #37571582, … |
| maximal normal subgroup of | #37571577, #37571578, #37571582, … |
| maximal quotient of | #37571865, #37571877, #37571887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 746);