Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×C7×D4 ⋊ C2 |
| Hall | C5×C7 ⋊ #41 |
| Sylow | C7 ⋊ #711 |
| Sylow | C5 ⋊ #1159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D35 |
| commutator, socle, cosocle | C2×C5×C7 | C23 |
| Fitting | C5×C7×D4 | C2 |
| hypercenter | D4 | D35 |
| hypocenter | C5×C7 | #41 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ D4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^4,5,7|b^2=d,c^a=cd,e^a=e^4,f^a=f^6,c^b=cd95 conjugacy classes — view the full character table.
| maximal subgroup of | #11764930, #11764936, #11764945, … |
| maximal normal subgroup of | #11764930, #11764936, #11764945, … |
| maximal quotient of | #11765207, #11765208, #11765209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 161);