Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D19 |
| Fitting | C4×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D19×Q8⋊C8, #14562028, #14562062, … |
| maximal normal subgroup of | D19×Q8⋊C8, #14562028, #14562062, … |
| maximal quotient of | C4×C4⋊C4×D19, C4×#10597333, C4×Q8×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1012);