Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C8 · Schur multiplier (H2) = C33 |
| direct product | C33×#170 |
| derived, Sylow | C5 ⋊ C33×C8 |
| Hall | C33×C5 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C33 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C33×C8 |
| Frattini | C2 | C33×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C2×C33×C5 | C4 |
| cosocle | Dic5 | C2×C33 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C33 | |
224 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1080 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 364);