Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic385 |
| unambiguous semidirect product | C7⋊(C7×Dic55) |
| unambiguous semidirect product | C11⋊(C7×Dic35) |
| derived | C5×C7×C11 ⋊ C4×C7 |
| Hall | C5×C72×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ Dic5 |
| Hall | C5×C72 ⋊ Dic11 |
| Hall | C5×C11 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ Dic55 |
| Sylow | C11 ⋊ C7×Dic35 |
| Sylow | C5 ⋊ C7×Dic77 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D385 |
| commutator, hypocenter | C5×C7×C11 | C4×C7 |
| Frattini | C2 | C7×D385 |
| Fitting, socle, prime radical | C2×C5×C72×C11 | C2 |
| cosocle | C2×C5×C7×C11 | C2×C7 |
| LCS | G ▷ C5×C7×C11 | |
| UCS | C1 ◁ C2×C7 | |
72 conjugacy classes of subgroups.
2716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C11⋊(ΓL(1,𝔽8)⋊Dic5), C11⋊#15668736, C11⋊#15668737, … |
| maximal normal subgroup of | C7×C11⋊(ΓL(1,𝔽8)⋊Dic5), C11⋊#15668736, C11⋊#15668737, … |
| maximal quotient of | C7×Dic1155, C3×C7×Dic385 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 52);