Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic35 |
| derived, Hall | C5×C7 ⋊ C22×C4 |
| Sylow | C7 ⋊ C22×Dic5 |
| Sylow | C5 ⋊ C22×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D35 |
| commutator, hypocenter | C5×C7 | C22×C4 |
| Frattini | C2 | C22×D35 |
| Fitting, socle, prime radical | C23×C5×C7 | C2 |
| cosocle | C2×C5×C7 | C23 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C23 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #11764464, #11764584, C2×Dic5×Dic7, … |
| maximal normal subgroup of | #11764464, #11764584, C2×Dic5×Dic7, … |
| maximal quotient of | C22×C7⋊#168, C2×#10587898, C2×C4×Dic35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 164);