Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C11 |
| direct product | C2×C32×C5⋊(C11⋊D11) |
| unambiguous semidirect product | (C2×C5)⋊(C32×C11⋊D11) |
| unambiguous semidirect product | (C2×C11)⋊(C32×D55) |
| Fitting, socle | C2×C32×C5×C112 ⋊ C2 |
| derived, Hall | C5×C112 ⋊ C22×C32 |
| Hall | C32×C5×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C2×D5 |
| Sylow | C112 ⋊ C2×C32×D5 |
| Hall | C32×C5 ⋊ C2×C11⋊D11 |
| Sylow | C5 ⋊ C2×C32×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C5⋊(C11⋊D11) |
| commutator, cosocle, hypocenter | C5×C112 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C112 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2×C32 | |
840 conjugacy classes of subgroups.
5472 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 727);