Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D35 |
| Fitting | C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×Q8 |
| Sylow | C7 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D35 |
| commutator, socle, cosocle | C2×C5×C7 | C23 |
| Fitting | C5×C7×Q8 | C2 |
| prime radical | C2×D35 | C22 |
| hypercenter | Q8 | D35 |
| hypocenter | C5×C7 | C2×Q8 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
95 conjugacy classes — view the full character table.
| maximal subgroup of | #11764953, #11764959, #11764970, … |
| maximal normal subgroup of | #11764953, #11764959, #11764970, … |
| maximal quotient of | #11765217, #11765218, #11765219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 162);