Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D7×D17×C7⋊C9 |
| derived, Hall | C72×C17 ⋊ C22×C9 |
| Hall | C7×C17×C7⋊C9 ⋊ C22 |
| Hall | C7×D7×D17 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ C2×D17 |
| Sylow | C72 ⋊ C2×C9×D17 |
| Sylow | C17 ⋊ C2×D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D7×ΓL(1,𝔽8)×D17 |
| commutator, hypocenter | C72×C17 | C22×C9 |
| Fitting, socle, cosocle | C3×C72×C17 | C22×C3 |
| prime radical | C3×C7×D7×D17 | C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2142 |
750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 191);