Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C19⋊C8) |
| Sylow | C19 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14561469, #14561470, #14561475, … |
| maximal normal subgroup of | #14561469, #14561470, #14561475, … |
| maximal quotient of | C2×#11926295, C2×#11926297, #14562383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 570);