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C₂×C₈×D₄×C₆₁ #21442967

order	7808
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₆₁ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₈×D₄×C₆₁

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₆₁	C₂²
commutator	C₂	C₂³×C₈×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂²×C₄
prime radical	C₂²×D₄×C₆₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₆₁ ◁ G

616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₈×#14519692, #29570559, C₈×#14519694, …
maximal subgroup of	C₈×#99×C₆₁, C₆₁×#8160, C₈×#100×C₆₁, …
maximal normal subgroup of	C₈×#99×C₆₁, C₆₁×#8160, C₈×#100×C₆₁, …
maximal quotient of	C₂×C₈×D₈×C₆₁, C₂×C₈×SD₁₆×C₆₁, C₂×C₈×Q₁₆×C₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7808, 1658);