Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×Dic191 |
| Sylow | C191 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×Dic191, #103×Dic191, #37572352, … |
| maximal normal subgroup of | #101×Dic191, #103×Dic191, #37572352, … |
| maximal quotient of | C2×C4⋊C4×Dic191, C4×Q8×Dic191, C2×#27132549, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1015);