Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of #64525 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#64527 |
| Fitting | C4×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14562432, C8×#64527, #14562445, … |
| maximal normal subgroup of | #14562432, C8×#64527, #14562445, … |
| maximal quotient of | C8×#64527, #14562469, #14562478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 637);