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#518×C₁₃₉ #22580603

order	8896
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₉ · Schur multiplier (H₂) = C₂⁵

Aliases

#518×C₁₃₉

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂⁴
commutator	C₂	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²	C₂⁴×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ G

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4726 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31806512, #31806515, #31806614, …
maximal subgroup of	#1828×C₁₃₉, #1829×C₁₃₉, #1856×C₁₃₉, …
maximal normal subgroup of	#1828×C₁₃₉, #1829×C₁₃₉, #1856×C₁₃₉, …
maximal quotient of	#2273×C₁₃₉, #2274×C₁₃₉, #2275×C₁₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8896, 199);