Finite Group DatabasebetaFinite Group Databasebeta| order | 8107 |
| automorphism | ? |
| homology | Abelianization (H1) = C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊C121 |
| derived, Sylow | C67 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | C67⋊C11 |
| commutator, hypocenter | C67 | C121 |
| Fitting, socle | C11×C67 | C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C11 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
11^2,67|a^11=b,c^a=c^64187 conjugacy classes — view the full character table.
| maximal subgroup of | D67⋊C121, C2×C67⋊C121, (C67⋊C3)⋊C121, … |
| maximal normal subgroup of | D67⋊C121, C2×C67⋊C121, (C67⋊C3)⋊C121, … |
| maximal quotient of | C2×C67⋊C121, C3×C67⋊C121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8107, 1);