Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#10597278 |
| Fitting | C22×C8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#102 |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14563449, C4×#10597278, #14563459, … |
| maximal normal subgroup of | #14563449, C4×#10597278, #14563459, … |
| maximal quotient of | C2×#11926273, #14562035, #14562061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 537);