Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#16809726⋊C3 |
| unambiguous semidirect product | #16809726⋊C32 |
| unambiguous semidirect product | (C3×#16809726)⋊C3 |
| Fitting, socle | C3×C72×C17 ⋊ C3×C4 |
| derived, Hall | C72×C17 ⋊ C32×C4 |
| Hall | C3×C17×#3861 ⋊ C4 |
| Hall | #16809726 ⋊ C32 |
| Hall | C3×#3861 ⋊ Dic17 |
| Sylow | C72 ⋊ C32×Dic17 |
| Sylow | C17 ⋊ C3×#5997⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809726⋊C3 |
| commutator, hypocenter | C72×C17 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C3×C4 |
| prime radical | C3×C17×#64424 | C2 |
| cosocle | C17×C7⋊D7 | C2×C32 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 376);