Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C3⋊(#5997⋊C3) |
| unambiguous semidirect product | C3⋊(C17×#5997⋊C3) |
| unambiguous semidirect product | (C3⋊#5997)⋊(C3×C17) |
| unambiguous semidirect product | (C17×C3⋊#5997)⋊C3 |
| Fitting, socle | C3×C72×C17 ⋊ C3×C4 |
| derived | C3×C72 ⋊ C3×C4×C17 |
| Hall | C3×C17×#3861 ⋊ C4 |
| Hall | C72×C17 ⋊ C3×Dic3 |
| Hall | C3×#3861 ⋊ C4×C17 |
| Sylow | C72 ⋊ C3×Dic3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊(#5997⋊C3) |
| commutator, hypocenter | C3×C72 | C3×C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C3×C4 |
| prime radical | C3×C17×#64424 | C2 |
| cosocle | C3×C7⋊D7 | C2×C3×C17 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C17 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 416);