Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D19)⋊C8 |
| Fitting | C19×C22⋊C8 ⋊ C2 |
| Sylow | C19 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^18220 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D4×D19, C2×(C22⋊D19)⋊C8, #14572325, … |
| maximal normal subgroup of | C8×D4×D19, C2×(C22⋊D19)⋊C8, #14572325, … |
| maximal quotient of | #14562427, #14562432, #14562438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 612);