Finite Group Databasebeta

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C₂×#13100332 #72221043

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴×C₅

Aliases

C₂×#13100332

Splittings

Fitting	C₂×C₄²×C₅² ⋊ C₄
Sylow	C₅² ⋊ C₂×#339

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄⋊#1044
commutator	C₄×C₅²	C₂×C₄²
Frattini	C₂×C₄	C₂²×#1044
Fitting	C₂×C₄²×C₅²	C₄
socle	C₂²×C₅²	#95
prime radical	C₂³×C₅⋊D₅	D₄
cosocle	C₂×C₄×C₅⋊D₅	C₂³
hypercenter	C₂×C₄²	#1044
hypocenter	C₅²	C₂×#339
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

1474 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72213321, C₂×#72213383, #72223101, …
maximal normal subgroup of	C₂×#72213321, C₂×#72213383, #72223101, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.