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C₈×D₄×C₁₇₉ #26038005

order	11456
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇₉ · Schur multiplier (H₂) = C₂³

Aliases

C₈×D₄×C₁₇₉

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇₉	C₂²
commutator	C₂	C₂²×C₈×C₁₇₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₇₉
socle	C₂²×C₁₇₉	C₂²×C₄
prime radical	C₂×D₄×C₁₇₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇₉ ◁ G

134 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	#37506955, C₈×#15668244, C₈×#15668247, …
maximal subgroup of	D₄⋊C₁₆×C₁₇₉, C₈×D₈×C₁₇₉, C₈×SD₁₆×C₁₇₉, …
maximal normal subgroup of	D₄⋊C₁₆×C₁₇₉, C₈×D₈×C₁₇₉, C₈×SD₁₆×C₁₇₉, …
maximal quotient of	C₈×D₈×C₁₇₉, C₈×SD₁₆×C₁₇₉, C₈×Q₁₆×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 115);