Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D19 |
| Fitting | C22×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | #14563557, #14563568, D19×#391, … |
| maximal normal subgroup of | #14563557, #14563568, D19×#391, … |
| maximal quotient of | C22×C4⋊C4×D19, C2×C4×Q8×D19, C22×#10597333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1372);