Finite Group Databasebeta

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D₇×#4095 #72218500

order	2240
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₅×C₇×#41 ⋊ C₂²
Hall	C₅×C₇ ⋊ C₂×AGL(1,ℤ/8)
Sylow	C₇ ⋊ C₂×#4095
Sylow	C₅ ⋊ D₇×AGL(1,ℤ/8)

Subgroups

	subgroup	G/H
center	C₂	C₂×D₇×C₂²⋊D₅
commutator, cosocle	C₄×C₅×C₇	C₂⁴
Frattini	C₄	C₂²×D₅×D₇
Fitting	C₅×C₇×#41	C₂²
socle	C₂×C₅×C₇	C₂²×D₄
hypercenter	#41	D₅×D₇
hypocenter	C₅×C₇	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

596 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

155 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₇)×#4095, D₅×D₇×AGL(1,ℤ/8)
maximal normal subgroup of	AGL(1,𝔽₇)×#4095, D₅×D₇×AGL(1,ℤ/8)

GAP

Past the SmallGroups library coverage — no SmallGroups id.