Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #436 |
122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^c=g^1901928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #436×D191, C2×#27132738, #37581218, … |
| maximal normal subgroup of | #436×D191, C2×#27132738, #37581218, … |
| maximal quotient of | #37571402, #37571407, #37571413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 624);