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#338×C₁₃₇ #22576873

order	8768
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃₇ · Schur multiplier (H₂) = C₂²

Aliases

#338×C₁₃₇

Subgroups

	subgroup	G/H
center	C₄×C₁₃₇	C₄²
commutator	C₄	C₄²×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂²×C₁₃₇
socle	C₂×C₁₃₇	#95
prime radical	C₂³×C₁₃₇	Q₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃₇ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3014 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31778779, #31778782, #338×D₁₃₇, …
maximal subgroup of	#1341×C₁₃₇, #1342×C₁₃₇, C₂×#338×C₁₃₇, …
maximal normal subgroup of	#1341×C₁₃₇, #1342×C₁₃₇, C₂×#338×C₁₃₇, …
maximal quotient of	#1275×C₁₃₇, #1291×C₁₃₇, #1292×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 19);