Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×Dic19 |
| Sylow | C19 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #101×Dic19, #103×Dic19, #14563467, … |
| maximal normal subgroup of | #101×Dic19, #103×Dic19, #14563467, … |
| maximal quotient of | C2×C4⋊C4×Dic19, C4×Q8×Dic19, C2×#11926430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1015);