Finite Group DatabasebetaFinite Group Databasebeta| order | 30972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D87⋊D89 |
| unambiguous semidirect product | D267⋊D29 |
| unambiguous semidirect product | D2581⋊D3 |
| Fitting, socle, derived, Hall | C3×C29×C89 ⋊ C22 |
| Hall | C29×C89 ⋊ C2×D3 |
| Hall | C3×C89 ⋊ C2×D29 |
| Sylow | C89 ⋊ D3×D29 |
| Hall | C3×C29 ⋊ C2×D89 |
| Sylow | C29 ⋊ D3×D89 |
| Sylow | C3 ⋊ D29×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29×C89 | C22 |
| LCS | G ▷ C3×C29×C89 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7743 |
Polycyclic presentation:
2^2,3,29,89|d^a=d^28,e^a=e^88,c^b=c^2,d^b=d^282028 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30972, 28);