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C₂×C₈×D₄×C₇₁ #22585488

order	9088
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₇₁ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₈×D₄×C₇₁

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₇₁	C₂²
commutator	C₂	C₂³×C₈×C₇₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₇₁
socle	C₂³×C₇₁	C₂²×C₄
prime radical	C₂²×D₄×C₇₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₇₁ ◁ G

616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5680 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₈×#14556043, #31887998, C₈×#14556045, …
maximal subgroup of	C₈×#99×C₇₁, C₇₁×#8160, C₈×#100×C₇₁, …
maximal normal subgroup of	C₈×#99×C₇₁, C₇₁×#8160, C₈×#100×C₇₁, …
maximal quotient of	C₂×C₈×D₈×C₇₁, C₂×C₈×SD₁₆×C₇₁, C₂×C₈×Q₁₆×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9088, 1658);