Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| isoclinism | isoclinic class of Dic70 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D35 |
| unambiguous semidirect product | C23⋊D35 |
| Fitting | C23×C5×C7 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×D4 |
| Sylow | C7 ⋊ C2×C22⋊D5 |
| Sylow | C5 ⋊ C2×C22⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D35 |
| commutator, cosocle | C2×C5×C7 | C23 |
| Frattini | C2 | C22×D35 |
| Fitting | C23×C5×C7 | C2 |
| socle | C22×C5×C7 | C22 |
| hypercenter | C23 | D35 |
| hypocenter | C5×C7 | C2×D4 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C23 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
146 conjugacy classes — view the full character table.
| maximal subgroup of | #11764467, #11764559, #11764986, … |
| maximal normal subgroup of | #11764467, #11764559, #11764986, … |
| maximal quotient of | C2×#10587900, #11765254, C2×#10587902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 165);