Finite Group Databasebeta

← Prev (#22549044) Next (#22549046) →

Q₈×C₁₀₀₉ #22549045

order	8072
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₀₉ · Schur multiplier (H₂) = C₁

Aliases

Q₈×C₁₀₀₉

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₀₉	C₂²
commutator, Frattini	C₂	C₂²×C₁₀₀₉
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₀₉ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5045 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30633319, #30633322, Q₈×D₁₀₀₉, …
maximal subgroup of	SD₁₆×C₁₀₀₉, Q₁₆×C₁₀₀₉, C₂×Q₈×C₁₀₀₉, …
maximal normal subgroup of	SD₁₆×C₁₀₀₉, Q₁₆×C₁₀₀₉, C₂×Q₈×C₁₀₀₉, …
maximal quotient of	C₄⋊C₄×C₁₀₀₉, C₂×Q₈×C₁₀₀₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8072, 4);