Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C7 · Schur multiplier (H2) = C4 |
| direct product | C4×C7×Dic5 |
| derived, Sylow | C5 ⋊ C42×C7 |
| Hall | C5×C7 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C7 | D5 |
| commutator, hypocenter | C5 | C42×C7 |
| Frattini | C22 | C2×C7×D5 |
| Fitting | C2×C4×C5×C7 | C2 |
| socle, prime radical | C22×C5×C7 | C22 |
| cosocle | C22×C5 | C22×C7 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C4×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 560 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×C7⋊C8, #11764423, #11764447, … |
| maximal normal subgroup of | Dic5×C7⋊C8, #11764423, #11764447, … |
| maximal quotient of | C4×C7×#168, C7×#3935, C7×C8×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 55);