Finite Group Databasebeta

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M₁₆×D₅⋊AGL(1,𝔽₅) #72220833

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

M₁₆×D₅⋊AGL(1,𝔽₅)

Splittings

Fitting	C₅²×M₁₆ ⋊ C₂×C₄
Sylow	C₅² ⋊ C₂×C₄×M₁₆

Subgroups

	subgroup	G/H
center, Frattini	C₄	C₂²×D₅⋊AGL(1,𝔽₅)
commutator, socle	C₂×C₅²	C₂²×C₄²
Fitting	C₅²×M₁₆	C₂×C₄
prime radical	C₂²×D₅²	C₂×C₄
cosocle	C₄×C₅⋊D₅	C₂⁴
hypercenter	M₁₆	D₅⋊AGL(1,𝔽₅)
hypocenter	C₅²	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄ ◁ M₁₆

1454 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72221166, AGL(1,ℤ/8)×D₅⋊AGL(1,𝔽₅), #72223009
maximal normal subgroup of	#72221166, AGL(1,ℤ/8)×D₅⋊AGL(1,𝔽₅), #72223009

GAP

Past the SmallGroups library coverage — no SmallGroups id.