Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C32 |
| direct product | H(3,𝔽3)×A5 |
| unambiguous semidirect product | C32⋊(C3×A5) |
| unambiguous semidirect product | (C32×A5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C3 | C32×A5 |
| commutator, socle | C3×A5 | C32 |
| Fitting, hypercenter | H(3,𝔽3) | A5 |
| hypocenter | A5 | H(3,𝔽3) |
| LCS | G ▷ C3×A5 ▷ A5 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
55 conjugacy classes — view the full character table.
| derived subgroup of | #272×A5, A5×#1088 |
| maximal subgroup of | #272×A5 |
| maximal normal subgroup of | #272×A5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 263);