Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10597372 |
| Sylow | C19 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14563331, #14563333, C2×#11926300, … |
| maximal normal subgroup of | #14563331, #14563333, C2×#11926300, … |
| maximal quotient of | C2×#11926390, C2×C4×C22⋊Dic19, C2×C4×C4⋊Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1005);