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C₂×#117×C₁₃₉ #22580599

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×#117×C₁₃₉

Subgroups

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

330 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	#31804718, #31804738, #31806101, …
maximal subgroup of	#1458×C₁₃₉, #1464×C₁₃₉, #1729×C₁₃₉, …
maximal normal subgroup of	#1458×C₁₃₉, #1464×C₁₃₉, #1729×C₁₃₉, …
maximal quotient of	C₂×#376×C₁₃₉, C₂×C₄×C₂²⋊C₄×C₁₃₉, C₂×C₄×C₄⋊C₄×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 195);