Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| isoclinism | isoclinic class of Dic38 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×D76 |
| Fitting | C4×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14561589, #14561591, C8×#64525, … |
| maximal normal subgroup of | #14561589, #14561591, C8×#64525, … |
| maximal quotient of | C8×D152, C8×#64516, C8×Dic76, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 616);