Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #474 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,191|a^2=d,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^190,e^c=ef1349 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #474×D191, C2×#27132941, #37582304, … |
| maximal normal subgroup of | #474×D191, C2×#27132941, #37582304, … |
| maximal quotient of | #37572518, #37572765, #37572769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 827);