Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #11761920 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C5×H(3,𝔽3) ⋊ C8 |
| Sylow | H(3,𝔽3) ⋊ #168 |
| Sylow | C5 ⋊ #6249 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×H(3,𝔽3) | C8 |
| Frattini | C3 | #67194 |
| socle | C3×C5 | AGL(1,𝔽9) |
| prime radical | C5×#272 | C4 |
| cosocle | C5×#1088 | C2 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2^3,3^2,5,3|a^2=b,b^2=c,d^a=eg,e^a=de^2g,f^a=f^4,g^a=g^2,d^b=de^2,e^b=d^2e^2,d^c=d^2,e^c=e^2g,e^d=eg41 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 266);