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C₂×C₄×Q₈×C₁₇₉ #26038087

order	11456
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₇₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₇₉	C₂²
commutator	C₂	C₂³×C₄×C₁₇₉
Frattini, cosocle	C₂²	C₂⁴×C₁₇₉
socle, prime radical	C₂³×C₁₇₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇₉ ◁ G

298 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	#37507324, #37507344, C₂×Q₈⋊(C₁₇₉⋊C₈), …
maximal subgroup of	#1461×C₁₇₉, #1467×C₁₇₉, C₂×Q₈⋊C₈×C₁₇₉, …
maximal normal subgroup of	#1461×C₁₇₉, #1467×C₁₇₉, C₂×Q₈⋊C₈×C₁₇₉, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₇₉, C₄²×Q₈×C₁₇₉, C₂×#387×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 197);