Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #463 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,191|b^2=df,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 | #463×D191, C2×#27132876, #37581968, … |
| maximal normal subgroup of | #463×D191, C2×#27132876, #37581968, … |
| maximal quotient of | #37571927, #37571941, #37571955, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 762);