Finite Group Databasebeta

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C₂×#72213464 #72223511

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷×C₅

Aliases

C₂×#72213464

Splittings

Fitting	C₂×C₅²×#127 ⋊ C₄
Sylow	C₅² ⋊ C₂×#1887

Subgroups

	subgroup	G/H
center	C₂²	#13104917
commutator	C₂×C₄×C₅²	C₂³×C₄
Frattini	C₂×C₄	C₂³×#1044
Fitting	C₂×C₅²×#127	C₄
socle	C₂²×C₅²	#386
prime radical	C₂×#127×C₅⋊D₅	C₂
cosocle	C₂×C₄×C₅⋊D₅	C₂⁴
hypercenter	C₂×#127	#1044
hypocenter	C₅²	C₂×#1887
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#127

8052 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72213584
maximal normal subgroup of	C₂×#72213584

GAP

Past the SmallGroups library coverage — no SmallGroups id.