Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C22×C32 |
| Hall | C13⋊C3×C19⋊C3 ⋊ C22 |
| Hall | D13×D19 ⋊ C32 |
| Sylow | C19 ⋊ C2×C3×D13⋊C3 |
| Sylow | C13 ⋊ C2×C3×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C22×C32 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×AGL(1,𝔽19), D19⋊C3×AGL(1,𝔽13) |
| maximal normal subgroup of | D13⋊C3×AGL(1,𝔽19), D19⋊C3×AGL(1,𝔽13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 146);