Finite Group Databasebeta

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C₄×#11717435 #72220922

order	3200
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₄×#11717435

Splittings

C₅² ⋊ C₂×C₄×M₁₆

Subgroups

	subgroup	G/H
center	C₄²	C₂×#1043
commutator	C₂×C₅²	C₂²×C₄²
Frattini	C₂²	C₂³×#1043
Fitting	C₂×C₄²×C₅²	C₄
socle	C₂²×C₅²	C₂³×C₄
prime radical	C₂³×C₅⋊D₅	C₂×C₄
cosocle	C₂×#1039	C₂⁴
hypercenter	C₂×C₄²	#1043
hypocenter	C₅²	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

2624 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×M₁₆×#1043, #72221141, #72221144, …
maximal normal subgroup of	C₄×M₁₆×#1043, #72221141, #72221144, …
maximal quotient of	#72221173

GAP

Past the SmallGroups library coverage — no SmallGroups id.