Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C11⋊#11758266 |
| Fitting, socle, derived, Hall | C5×C72×C11 ⋊ C4 |
| Hall | C72×C11 ⋊ AGL(1,𝔽5) |
| Hall | C5×C72 ⋊ Dic11 |
| Hall | C5×C11 ⋊ #5997 |
| Sylow | C72 ⋊ C11⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ #11758266 |
| Sylow | C5 ⋊ C11⋊#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C11 | C4 |
| prime radical, cosocle | C11×C5⋊(C7⋊D7) | C2 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7^2,11|a^2=b,c^a=c^2,d^a=d^4e^6,e^a=d^3e^3,f^a=f^10,c^b=c^4,d^b=d^6,e^b=e^6685 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, C3⋊(C11⋊#11758266) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 83);