Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D53 |
| unambiguous semidirect product | D159⋊D13 |
| unambiguous semidirect product | D689⋊D3 |
| Fitting, socle, derived, Hall | C3×C13×C53 ⋊ C22 |
| Hall | C13×C53 ⋊ C2×D3 |
| Hall | C3×C53 ⋊ C2×D13 |
| Sylow | C53 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D53 |
| Sylow | C13 ⋊ D3×D53 |
| Sylow | C3 ⋊ D13×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C53 | C22 |
| LCS | G ▷ C3×C13×C53 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,53|d^a=d^12,e^a=e^52,c^b=c^2,d^b=d^12570 conjugacy classes — view the full character table.
| maximal subgroup of | D117⋊D53, (C3⋊(D13⋊C3))⋊D53, C3×D39⋊D53, … |
| maximal normal subgroup of | (C3⋊(D13⋊C3))⋊D53, C3×D39⋊D53 |
| maximal quotient of | D117⋊D53, C3×D39⋊D53, D159⋊D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 54);