Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×C7⋊Dic7 |
| unambiguous semidirect product | C7⋊(Dic7×C11⋊C5) |
| unambiguous semidirect product | (C11×C7⋊Dic7)⋊C5 |
| derived, Hall | C72×C11 ⋊ C4×C5 |
| Hall | C72×C11⋊C5 ⋊ C4 |
| Hall | C11×C7⋊Dic7 ⋊ C5 |
| Sylow | C72 ⋊ C4×C11⋊C5 |
| Sylow | C11 ⋊ C5×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊C5×C7⋊D7 |
| commutator, hypocenter | C72×C11 | C4×C5 |
| Fitting, socle, cosocle | C2×C72×C11 | C2×C5 |
| prime radical | C2×C72×C11⋊C5 | C2 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 42);