Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×#5997 |
| unambiguous semidirect product | (C11×#5997)⋊C5 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C4×C5 |
| Hall | C72×C11⋊C5 ⋊ C4 |
| Hall | C11×#5997 ⋊ C5 |
| Sylow | C72 ⋊ C4×C11⋊C5 |
| Sylow | C11 ⋊ C5×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C11 | C4×C5 |
| prime radical | C11⋊C5×C7⋊D7 | C2 |
| cosocle | C11×C7⋊D7 | C2×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
112 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#10596885, C11⋊C5×#5997⋊C3, C3×C11⋊C5×#5997, … |
| maximal normal subgroup of | C11⋊C5×#5997⋊C3, C3×C11⋊C5×#5997 |
| maximal quotient of | C3×C11⋊C5×#5997, C11⋊C5×C3⋊#5997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 62);