Finite Group Databasebeta

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C₂×#13104115 #72223543

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

C₂×#13104115

Splittings

C₅² ⋊ C₂×#390

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₅⋊AGL(1,𝔽₅)
commutator	C₂²×C₅²	C₂³×C₄
Frattini	C₂²	C₂²×D₅⋊AGL(1,𝔽₅)
Fitting	C₂⁴×C₅²	C₂×C₄
socle	C₂³×C₅²	C₂²×C₄
prime radical	C₂²×#87886	C₂
cosocle	C₂²×C₅⋊D₅	C₂⁴
hypercenter	C₂⁴	D₅⋊AGL(1,𝔽₅)
hypocenter	C₅²	C₂×#390
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂⁴

3394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72223544, #72226581, #72226590

GAP

Past the SmallGroups library coverage — no SmallGroups id.