Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×D5×D11 |
| unambiguous semidirect product | (D5×C11)⋊(C2×C72) |
| unambiguous semidirect product | (C5×D11)⋊(C2×C72) |
| unambiguous semidirect product | D55⋊(C2×C72) |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C22 |
| derived, Hall | C5×C11 ⋊ C22×C72 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×C72×D5 |
| Sylow | C5 ⋊ C2×C72×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D5×D11 |
| commutator, cosocle, hypocenter | C5×C11 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C72 | |
200 conjugacy classes of subgroups.
1372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 84);