Finite Group Databasebeta

← Prev (#24922834) Next (#24922836) →

C₈×D₄×C₁₆₇ #24922835

order	10688
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₆₇ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₄×C₁₆₇

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₆₇	C₂²
commutator	C₂	C₂²×C₈×C₁₆₇
Frattini, cosocle	C₂×C₄	C₂³×C₁₆₇
socle	C₂²×C₁₆₇	C₂²×C₄
prime radical	C₂×D₄×C₁₆₇	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₆₇ ◁ G

134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6680 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	D₄⋊(C₁₆₇⋊C₁₆), C₈×#14581935, C₈×#14581938, …
maximal subgroup of	D₄⋊C₁₆×C₁₆₇, C₈×D₈×C₁₆₇, C₈×SD₁₆×C₁₆₇, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₆₇, C₈×D₈×C₁₆₇, C₈×SD₁₆×C₁₆₇, …
maximal quotient of	C₈×D₈×C₁₆₇, C₈×SD₁₆×C₁₆₇, C₈×Q₁₆×C₁₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 115);