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C₂×#97×C₁₃₉ #22580488

order	8896
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₃₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂×#97×C₁₃₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂²
commutator	C₂	C₂×C₄²×C₁₃₉
Frattini, cosocle	C₂×C₄	C₂³×C₁₃₉
socle, prime radical	C₂³×C₁₃₉	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ G

146 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	#31804235, #31804249, #31804286, …
maximal subgroup of	#1275×C₁₃₉, #1281×C₁₃₉, #1295×C₁₃₉, …
maximal normal subgroup of	#1275×C₁₃₉, #1281×C₁₃₉, #1295×C₁₃₉, …
maximal quotient of	C₂×#322×C₁₃₉, #1451×C₁₃₉, #1452×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 84);