Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×H(3,𝔽3) ⋊ C8 |
| Sylow | H(3,𝔽3) ⋊ #168 |
| Sylow | C5 ⋊ #6188 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #4379 |
| commutator, hypocenter | C5×H(3,𝔽3) | C8 |
| Fitting, prime radical | C2×C5×H(3,𝔽3) | C4 |
| socle | C2×C3×C5 | #157 |
| cosocle | C5×#1084 | C2 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^3,3^2,5,3|a^2=b,b^2=c,d^a=de,e^a=de^2g^2,f^a=f^4,d^b=d^2,e^b=e^2g,e^d=eg68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 74);