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C₂×M₃₂×C₁₉₁ #27132298

order	12224
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉₁ · Schur multiplier (H₂) = C₂²

Aliases

C₂×M₃₂×C₁₉₁

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉₁	C₂²
commutator	C₂	C₂²×C₈×C₁₉₁
Frattini, cosocle	C₈	C₂³×C₁₉₁
socle	C₂²×C₁₉₁	C₂×C₈
prime radical	C₂³×C₁₉₁	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉₁ ◁ G

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7640 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37570599, #37570601, #37570603, …
maximal subgroup of	#1375×C₁₉₁, #1376×C₁₉₁, #1377×C₁₉₁, …
maximal normal subgroup of	#1375×C₁₉₁, #1376×C₁₉₁, #1377×C₁₉₁, …
maximal quotient of	C₂×#346×C₁₉₁, C₄×M₃₂×C₁₉₁, C₂×C₂²⋊C₁₆×C₁₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 184);