Finite Group Databasebeta

← Prev (#22576341) Next (#22576343) →

Q₈×C₁₀₈₇ #22576342

order	8696
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₈₇ · Schur multiplier (H₂) = C₁

Aliases

Q₈×C₁₀₈₇

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₈₇	C₂²
commutator, Frattini	C₂	C₂²×C₁₀₈₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₈₇ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5435 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31775020, #31775023, Q₈×D₁₀₈₇, …
maximal subgroup of	SD₁₆×C₁₀₈₇, Q₁₆×C₁₀₈₇, C₂×Q₈×C₁₀₈₇, …
maximal normal subgroup of	SD₁₆×C₁₀₈₇, Q₁₆×C₁₀₈₇, C₂×Q₈×C₁₀₈₇, …
maximal quotient of	C₄⋊C₄×C₁₀₈₇, C₂×Q₈×C₁₀₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8696, 4);