Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×#272 |
| Fitting | C2×C5×H(3,𝔽3) ⋊ C22 |
| derived, Hall | C5×H(3,𝔽3) ⋊ C23 |
| Sylow | H(3,𝔽3) ⋊ C22×D5 |
| Sylow | C5 ⋊ C22×#272 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×C3⋊D3 |
| commutator, cosocle, hypocenter | C5×H(3,𝔽3) | C23 |
| Frattini | C3 | C2×D5×C3⋊D3 |
| Fitting | C2×C5×H(3,𝔽3) | C22 |
| socle | C2×C3×C5 | C2×C3⋊D3 |
| LCS | G ▷ C5×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
352 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 332);