Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#272 |
| Fitting | C22×C5×H(3,𝔽3) ⋊ C2 |
| derived, Sylow | H(3,𝔽3) ⋊ C23×C5 |
| Hall | C5×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C3×C5 | C3⋊D3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C23×C5 |
| Frattini | C3 | C22×C5×C3⋊D3 |
| Fitting | C22×C5×H(3,𝔽3) | C2 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3×C5 | |
352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 357);