Finite Group Databasebeta

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C₂×#72221215 #72221355

order	6400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×#72221215

Splittings

Fitting	C₂×C₅²×#100 ⋊ C₄
Sylow	C₅² ⋊ C₂×#1856

Subgroups

	subgroup	G/H
center	C₂²	#13104711
commutator	C₂×C₄×C₅²	C₂³×C₄
Frattini	C₂×C₄	C₂³×#1043
Fitting	C₂×C₅²×#100	C₄
socle	C₂²×C₅²	#385
prime radical	C₂²×D₄×C₅⋊D₅	C₂²
cosocle	C₂×C₄×C₅⋊D₅	C₂⁴
hypercenter	C₂×#100	#1043
hypocenter	C₅²	C₂×#1856
LCS	G ▷ C₂×C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#100

6824 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.