Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×C11⋊#5997 |
| Fitting, socle, Hall | C5×C72×C11 ⋊ C4 |
| derived, Hall | C72×C11 ⋊ C4×C5 |
| Hall | C5×C72 ⋊ Dic11 |
| Hall | C5×C11 ⋊ #5997 |
| Sylow | C72 ⋊ C5×Dic11 |
| Sylow | C11 ⋊ C5×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊#5997 |
| commutator, hypocenter | C72×C11 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C4 |
| prime radical | C5×C11×C7⋊D7 | C2 |
| cosocle | C11×C7⋊D7 | C2×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C5 | |
56 conjugacy classes of subgroups.
730 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C11⋊#10596885, C5×C11⋊(#5997⋊C3), C3×C5×C11⋊#5997, … |
| maximal normal subgroup of | C5×C11⋊(#5997⋊C3), C3×C5×C11⋊#5997 |
| maximal quotient of | C3×C5×C11⋊#5997, C5×C3⋊(C11⋊#5997) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 75);