Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C7⋊#10597479 |
| unambiguous semidirect product | C7⋊(C7×#10597479) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived | C32×C7×C17 ⋊ C4×C7 |
| Hall | C72×C17 ⋊ #157 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #10597479 |
| Sylow | C17 ⋊ C7×C7⋊#157 |
| Sylow | C32 ⋊ C7×C7⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#10597479 |
| commutator, hypocenter | C32×C7×C17 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C72×C3⋊D51 | C2 |
| cosocle | C7×C3⋊D51 | C2×C7 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 ◁ C7 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
1932 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 555);