Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | ΓL(1,𝔽8)×D21⋊D17 |
| unambiguous semidirect product | D51⋊(D7×ΓL(1,𝔽8)) |
| Fitting, socle, derived | C3×C72×C17 ⋊ C22×C3 |
| Hall | C3×C7×C17×ΓL(1,𝔽8) ⋊ C22 |
| Hall | C72×C17 ⋊ C2×C3×D3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ C2×D17 |
| Sylow | C72 ⋊ C3×D3×D17 |
| Sylow | C17 ⋊ D3×D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C17 | C22×C3 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 | |
184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2142 |
555 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 457);