Finite Group DatabasebetaFinite Group Databasebeta| order | 8164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C157 ⋊ C2×C13 |
| derived, Sylow | C157 ⋊ C22×C13 |
| Hall | C157⋊C13 ⋊ C22 |
| Hall | C2×D157 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D157⋊C13 |
| commutator, hypocenter | C157 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C157 | C2×C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D157⋊C3)⋊C13, D3×D157⋊C13, C2×C3×D157⋊C13, … |
| maximal normal subgroup of | C2×(D157⋊C3)⋊C13, C2×C3×D157⋊C13 |
| maximal quotient of | D3×D157⋊C13, C2×C3×D157⋊C13, C2×C3⋊(D157⋊C13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8164, 9);