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#518×C₁₃₇ #22577053

order	8768
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

#518×C₁₃₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂⁴
commutator	C₂	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²	C₂⁴×C₁₃₇
prime radical	C₂²×D₄×C₁₃₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ G

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4658 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31780897, #31780900, #31780999, …
maximal subgroup of	#1828×C₁₃₇, #1829×C₁₃₇, #1856×C₁₃₇, …
maximal normal subgroup of	#1828×C₁₃₇, #1829×C₁₃₇, #1856×C₁₃₇, …
maximal quotient of	#2273×C₁₃₇, #2274×C₁₃₇, #2275×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 199);