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C₈×Q₈×C₁₇₉ #26038016

order	11456
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇₉ · Schur multiplier (H₂) = C₂²

Aliases

C₈×Q₈×C₁₇₉

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇₉	C₂²
commutator	C₂	C₂²×C₈×C₁₇₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₇₉
socle, prime radical	C₂²×C₁₇₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇₉ ◁ G

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7160 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37506979, C₈×#15668246, C₈×#15668249, …
maximal subgroup of	Q₈⋊C₁₆×C₁₇₉, C₈×SD₁₆×C₁₇₉, C₈×Q₁₆×C₁₇₉, …
maximal normal subgroup of	Q₈⋊C₁₆×C₁₇₉, C₈×SD₁₆×C₁₇₉, C₈×Q₁₆×C₁₇₉, …
maximal quotient of	C₈×C₄⋊C₄×C₁₇₉, #1916×C₁₇₉, #1939×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 126);