Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×#11925892 |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C22×C5 |
| Hall | C32×#10597243 ⋊ C22 |
| Hall | C3⋊D3×C11⋊D11 ⋊ C5 |
| Hall | #10597243 ⋊ C2×C3⋊D3 |
| Sylow | C112 ⋊ C2×C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×#11925892 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C112 | C22×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
840 conjugacy classes of subgroups.
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72225758 |
| maximal normal subgroup of | #72225758 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 507);