Finite Group DatabasebetaFinite Group Databasebeta| order | 21054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C11 |
| direct product | C29×C3⋊(C11⋊D11) |
| unambiguous semidirect product | C3⋊(C29×C11⋊D11) |
| unambiguous semidirect product | C11⋊(C29×D33) |
| Fitting, socle, Hall | C3×C112×C29 ⋊ C2 |
| derived, Hall | C3×C112 ⋊ C2×C29 |
| Hall | C112×C29 ⋊ D3 |
| Sylow | C112 ⋊ D3×C29 |
| Hall | C3×C29 ⋊ C11⋊D11 |
| Sylow | C3 ⋊ C29×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C3⋊(C11⋊D11) |
| commutator, cosocle, hypocenter | C3×C112 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C29 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C29 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10527 |
5307 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21054, 25);