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C₂×M₃₂×C₁₃₇ #22577038

order	8768
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃₇ · Schur multiplier (H₂) = C₂²

Aliases

C₂×M₃₂×C₁₃₇

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₃₇	C₂²
commutator	C₂	C₂²×C₈×C₁₃₇
Frattini, cosocle	C₈	C₂³×C₁₃₇
socle	C₂²×C₁₃₇	C₂×C₈
prime radical	C₂³×C₁₃₇	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₇ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5480 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#31778868, #31778870, #31778872, …
maximal subgroup of	#1375×C₁₃₇, #1376×C₁₃₇, #1377×C₁₃₇, …
maximal normal subgroup of	#1375×C₁₃₇, #1376×C₁₃₇, #1377×C₁₃₇, …
maximal quotient of	C₂×#346×C₁₃₇, C₄×M₃₂×C₁₃₇, C₂×C₂²⋊C₁₆×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 184);