Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C7 |
| direct product | C11×#11758266 |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C4 |
| derived, Hall | C5×C72 ⋊ C4×C11 |
| Hall | C72×C11 ⋊ AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ #5997 |
| Sylow | C72 ⋊ C11×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #11758266 |
| commutator, hypocenter | C5×C72 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C4 |
| prime radical | C11×C5⋊(C7⋊D7) | C2 |
| cosocle | C5⋊(C7⋊D7) | C2×C11 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#15668774, C11×#11758266⋊C3, C3×C11×#11758266, … |
| maximal normal subgroup of | C11×#11758266⋊C3, C3×C11×#11758266 |
| maximal quotient of | C3×C11×#11758266, C11×C3⋊#11758266 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 82);