Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C4×Dic382 |
| Sylow | C191 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
3080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37570843, #37570863, C2×#27132393, … |
| maximal normal subgroup of | #37570843, #37570863, C2×#27132393, … |
| maximal quotient of | C2×C4×C4⋊Dic191, C2×C4×Dic191⋊C4, C42×Dic382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1014);