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C₂×C₄×Q₈×C₁₃₉ #22580601

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×Q₈×C₁₃₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂²
commutator	C₂	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²	C₂⁴×C₁₃₉
socle, prime radical	C₂³×C₁₃₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ G

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5560 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31804728, #31804748, C₂×Q₈⋊(C₁₃₉⋊C₈), …
maximal subgroup of	#1461×C₁₃₉, #1467×C₁₃₉, C₂×Q₈⋊C₈×C₁₃₉, …
maximal normal subgroup of	#1461×C₁₃₉, #1467×C₁₃₉, C₂×Q₈⋊C₈×C₁₃₉, …
maximal quotient of	C₂×C₄×C₄⋊C₄×C₁₃₉, C₄²×Q₈×C₁₃₉, C₂×#387×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 197);