Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D4×C191⋊C8 |
| Sylow | C191 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
1940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37571312, D8×C191⋊C8, SD16×C191⋊C8, … |
| maximal normal subgroup of | #37571312, D8×C191⋊C8, SD16×C191⋊C8, … |
| maximal quotient of | D8×C191⋊C8, SD16×C191⋊C8, Q16×C191⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 615);