Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10597315 |
| Sylow | C19 ⋊ C2×C4⋊Q8 |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#11926289, C2×#11926291, C2×#11926292, … |
| maximal normal subgroup of | C2×#11926289, C2×#11926291, C2×#11926292, … |
| maximal quotient of | C2×#11926414, C2×#11926442, C2×#11926450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1093);