Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of #6290 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×#6291 |
| Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ C5×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×C3⋊D3 |
| commutator, cosocle | C2×C33 | C22×C5 |
| Frattini | C2 | C5×D3×C3⋊D3 |
| Fitting, socle | C2×C33×C5 | C22 |
| hypocenter | C33 | C5×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C5 | |
272 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#6291, C5×#88952, #72269781 |
| maximal normal subgroup of | D5×#6291, C5×#88952, #72269781 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 417);