Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ D4×Q8 |
280 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 115 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,b^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^d=g^1901355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37584027, #37584028, #37584034, … |
| maximal normal subgroup of | #37584027, #37584028, #37584034, … |
| maximal quotient of | #37575352, #37575354, #37575416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1212);