Finite Group DatabasebetaFinite Group Databasebeta| order | 8268 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #14583754⋊C3 |
| Fitting, socle, derived, Hall | C13×C53 ⋊ C3×C4 |
| Hall | #14583754 ⋊ C3 |
| Hall | C13⋊C3×C53 ⋊ C4 |
| Sylow | C53 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ Dic53 |
| Sylow | C13 ⋊ C3×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C53 | C3×C4 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13,53|a^2=c,d^a=d^5,e^a=e^52,d^b=d^3,d^c=d^12221 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#14583754⋊C3, C3⋊(#14583754⋊C3) |
| maximal normal subgroup of | C3×#14583754⋊C3 |
| maximal quotient of | #14583754⋊C9, C3×#14583754⋊C3, C3⋊(#14583754⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8268, 29);