Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20259322 |
| Sylow | C191 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
3068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#27132408, C2×#27132410, C2×#27132411, … |
| maximal normal subgroup of | C2×#27132408, C2×#27132410, C2×#27132411, … |
| maximal quotient of | C2×#27132533, C2×#27132561, C2×#27132569, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1093);