Finite Group DatabasebetaFinite Group Databasebeta| order | 12224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20259346 |
| Fitting | C2×D8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 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.
1352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#20259346, #37581331, #37581345, … |
| maximal normal subgroup of | C4×#20259346, #37581331, #37581345, … |
| maximal quotient of | C2×#27132666, C2×#27132661, C2×#27132704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12224, 1334);