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C₈×Q₈×C₁₄₉ #23749202

order	9536
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₄₉ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₄₉

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₄₉	C₂²
commutator	C₂	C₂²×C₈×C₁₄₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₄₉
socle, prime radical	C₂²×C₁₄₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₄₉ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Q₈⋊#14558711, C₈×#14558723, C₈×#14558726, …
maximal subgroup of	Q₈⋊C₁₆×C₁₄₉, C₈×SD₁₆×C₁₄₉, C₈×Q₁₆×C₁₄₉, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₄₉, C₈×SD₁₆×C₁₄₉, C₈×Q₁₆×C₁₄₉, …
maximal quotient of	C₈×C₄⋊C₄×C₁₄₉, #1916×C₁₄₉, #1939×C₁₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 126);