Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #67077 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#67083 |
| Hall | C5×C9 ⋊ C2×D4 |
| Sylow | C9 ⋊ C2×D20 |
| Sylow | C5 ⋊ C2×#611 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×D9 |
| commutator, cosocle | C2×C5×C9 | C23 |
| Frattini | C2×C3 | C2×D3×D5 |
| Fitting | C22×C5×C9 | C22 |
| socle | C22×C3×C5 | C2×D3 |
| hypocenter | C5×C9 | C2×D4 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C22 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #13083927, #13084178, #13084192, … |
| maximal normal subgroup of | #13083927, #13084178, #13084192, … |
| maximal quotient of | #13084086, #13084087, #13084103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 148);