Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C7⋊AGL(1,𝔽11))⋊D7 |
| unambiguous semidirect product | ((C7⋊D7)⋊D11)⋊C5 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C22×C5 |
| Hall | C72×C11⋊C5 ⋊ C22 |
| Hall | (C7⋊D7)⋊D11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ D72 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽11) |
| Sylow | C11 ⋊ C5×D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C11 | C22×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,7^2,11|d^a=d^6,f^a=f^10,d^b=d^6,e^b=e^6,f^c=f^4151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 59);