Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C3×C7 |
| direct product | C17×C7⋊(C7⋊#157) |
| unambiguous semidirect product | C7⋊(C17×C7⋊#157) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived, Hall | C32×C72 ⋊ C4×C17 |
| Hall | C72×C17 ⋊ #157 |
| Hall | C32×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C17×#157 |
| Sylow | C32 ⋊ C17×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C7⋊(C7⋊#157) |
| commutator, hypocenter | C32×C72 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C72×C17×C3⋊D3 | C2 |
| cosocle | C72×C3⋊D3 | C2×C17 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 ◁ C17 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
2550 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 557);