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#520×C₁₃₇ #22577055

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

Aliases

#520×C₁₃₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂⁴
commutator	C₂	C₂³×C₄×C₁₃₇
Frattini, cosocle	C₂²	C₂⁴×C₁₃₇
prime radical	C₂×#41×C₁₃₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ G

294 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	#31781015, #31781022, #31781158, …
maximal subgroup of	#1859×C₁₃₇, #1860×C₁₃₇, #1882×C₁₃₇, …
maximal normal subgroup of	#1859×C₁₃₇, #1860×C₁₃₇, #1882×C₁₃₇, …
maximal quotient of	#2274×C₁₃₇, #2275×C₁₃₇, #2276×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 201);