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C₂×#17985755 #22588040

order	9088
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×#17985755

Splittings

C₇₁ ⋊ C₂×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄×Dic₇₁
commutator	C₄×C₇₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₇₁
Fitting	C₂×#117×C₇₁	C₂
socle	C₂²×C₇₁	#95
hypercenter	C₂×#117	D₇₁
hypocenter	C₇₁	C₂×H(3,ℤ/4)
LCS	G ▷ C₄×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	H(3,ℤ/4)×Dic₇₁, C₄×#17985755, #31902620, …
maximal normal subgroup of	H(3,ℤ/4)×Dic₇₁, C₄×#17985755, #31902620, …
maximal quotient of	C₂×#22586168, C₂×#22586169, #31886850, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 4210);