Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D77 |
| Fitting, socle, derived, Hall | C5×C72×C11 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ D72 |
| Sylow | C72 ⋊ D5×D11 |
| Sylow | C11 ⋊ D7×D35 |
| Sylow | C5 ⋊ D7×D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C22 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
760 conjugacy classes — view the full character table.
| maximal subgroup of | #44568680, D77×C5⋊AGL(1,𝔽7), D35×C11⋊AGL(1,𝔽7), … |
| maximal normal subgroup of | D77×C5⋊AGL(1,𝔽7), D35×C11⋊AGL(1,𝔽7), #44568727, … |
| maximal quotient of | C3×D35×D77, D77×D105, D35×D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 97);