Finite Group DatabasebetaFinite Group Databasebeta| order | 21054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C11 |
| direct product | C29×(C11⋊D11)⋊C3 |
| unambiguous semidirect product | (C11⋊D11)⋊(C3×C29) |
| unambiguous semidirect product | (C29×C11⋊D11)⋊C3 |
| Fitting, socle, Hall | C112×C29 ⋊ C2×C3 |
| derived, Sylow | C112 ⋊ C2×C3×C29 |
| Hall | C29×C112⋊C3 ⋊ C2 |
| Hall | C29×C11⋊D11 ⋊ C3 |
| Hall | C112⋊C3 ⋊ C2×C29 |
| Hall | C11⋊D11 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | (C11⋊D11)⋊C3 |
| commutator, cosocle, hypocenter | C112 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C112×C29 | C2×C3 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C29 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 957 |
754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21054, 13);