Finite Group Databasebeta

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C₂×#131×#1043 #72253246

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

C₂×#131×#1043

Splittings

Fitting	C₂×C₅²×#131 ⋊ C₄
Sylow	C₅² ⋊ C₂×C₄×#131

Subgroups

	subgroup	G/H
center	C₂×C₈	C₂²×#1043
commutator	C₂×C₅²	C₂³×C₄²
Frattini	C₄	C₂⁴×#1043
Fitting	C₂×C₅²×#131	C₄
socle	C₂²×C₅²	C₂²×C₄²
prime radical	C₂×#41×C₅⋊D₅	C₂²
cosocle	C₄×C₅⋊D₅	C₂⁵
hypercenter	C₂×#131	#1043
hypocenter	C₅²	C₂×C₄×#131
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#131

13464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 800

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×#444×#1043
maximal normal subgroup of	C₂×#444×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.