Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #470 |
110 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 110 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|a^2=f,b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^1901346 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #470×D191, C2×#27132919, #37582124, … |
| maximal normal subgroup of | #470×D191, C2×#27132919, #37582124, … |
| maximal quotient of | #37572007, #37572012, #37572041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 805);