Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of SL(2,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C32×SL(2,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, socle, hypercenter | C2×C32 | A5 |
| commutator, hypocenter | SL(2,𝔽5) | C32 |
| Frattini, cosocle | C2 | C32×A5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C32 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
81 conjugacy classes — view the full character table.
| derived subgroup of | C3⋊D3×SL(2,𝔽5), #157×SL(2,𝔽5), #72228179, … |
| maximal subgroup of | C3⋊D3×SL(2,𝔽5), #72228179 |
| maximal normal subgroup of | C3⋊D3×SL(2,𝔽5), #72228179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 363);