Finite Group Databasebeta

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C₂×#72221208 #72221347

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

C₂×#72221208

Splittings

Fitting	C₂×C₅²×H(5,𝔽₂) ⋊ C₄
Sylow	C₅² ⋊ C₂×#1792

Subgroups

	subgroup	G/H
center	C₂²	#13104812
commutator	C₂×C₄×C₅²	C₂³×C₄
Frattini	C₂×C₄	C₂³×#1043
Fitting	C₂×C₅²×H(5,𝔽₂)	C₄
socle	C₂²×C₅²	#379
prime radical	C₂×H(5,𝔽₂)×C₅⋊D₅	C₂
cosocle	C₂×C₄×C₅⋊D₅	C₂⁴
hypercenter	C₂×H(5,𝔽₂)	#1043
hypocenter	C₅²	C₂×#1792
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×H(5,𝔽₂)

16456 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

268 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#453×#1043
maximal normal subgroup of	C₂×#453×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.