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C₂²×C₄⋊C₄×C₁₃₉ #22580598

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×C₄⋊C₄×C₁₃₉

Subgroups

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

418 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	#31804633, #31804636, #31804646, …
maximal subgroup of	C₄⋊#95×C₁₃₉, #1436×C₁₃₉, #1439×C₁₃₉, …
maximal normal subgroup of	C₄⋊#95×C₁₃₉, #1436×C₁₃₉, #1439×C₁₃₉, …
maximal quotient of	C₂²×#95×C₁₃₉, C₂×C₄×C₄⋊C₄×C₁₃₉, C₂×#380×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 194);