Finite Group Databasebeta

← Prev (#72217823) Next (#72217825) →

C₂×D₄×D₅×D₇ #72217824

order	2240
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₄×D₅×D₇

Splittings

Fitting	C₂×C₅×C₇×D₄ ⋊ C₂²
Hall	C₅×C₇ ⋊ C₂³×D₄
Sylow	C₇ ⋊ C₂²×D₄×D₅
Sylow	C₅ ⋊ C₂²×D₄×D₇

Subgroups

2724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₄×D₅×AGL(1,𝔽₇), C₂×D₄×D₇×AGL(1,𝔽₅), D₅×D₇×AGL(1,ℤ/8), …
maximal normal subgroup of	C₂×D₄×D₅×AGL(1,𝔽₇), C₂×D₄×D₇×AGL(1,𝔽₅), D₅×D₇×AGL(1,ℤ/8), …
maximal quotient of	D₅×D₇×AGL(1,ℤ/8), D₅×D₇×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.