Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4⋊Q8×C191 ⋊ C2 |
| Sylow | C191 ⋊ #536 |
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^190,c^b=ce,g^d=g^1901352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37574208, #37574213, #37581885, … |
| maximal normal subgroup of | #37574208, #37574213, #37581885, … |
| maximal quotient of | #37575103, #37575111, #37575141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1124);