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C₂×M₃₂×C₁₆₃ #23781300

order	10432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₆₃ · Schur multiplier (H₂) = C₂²

Aliases

C₂×M₃₂×C₁₆₃

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₆₃	C₂²
commutator	C₂	C₂²×C₈×C₁₆₃
Frattini, cosocle	C₈	C₂³×C₁₆₃
socle	C₂²×C₁₆₃	C₂×C₈
prime radical	C₂³×C₁₆₃	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₆₃ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6520 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35212615, #35212617, #35212619, …
maximal subgroup of	#1375×C₁₆₃, #1376×C₁₆₃, #1377×C₁₆₃, …
maximal normal subgroup of	#1375×C₁₆₃, #1376×C₁₆₃, #1377×C₁₆₃, …
maximal quotient of	C₂×#346×C₁₆₃, C₄×M₃₂×C₁₆₃, C₂×C₂²⋊C₁₆×C₁₆₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 184);