Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| automorphism | Aut(G) = C2×D4×AGL(1,𝔽5)×AGL(1,𝔽7) (order 13440) · Inn(G) = C22⋊D35 · Out(G) = C22×C3×C4 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C7 ⋊ SD16 |
| Sylow | C7 ⋊ #687 |
| Sylow | C5 ⋊ #1142 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^4,5,7|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^6,c^b=cd92 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#687, #11764932, D5×#1142, … |
| maximal normal subgroup of | D7×#687, #11764932, D5×#1142, … |
| maximal quotient of | #11764561, #11764563, #11764586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 76);