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#446×C₁₉₁ #27132241

order	12224
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉₁ · Schur multiplier (H₂) = C₂

Aliases

#446×C₁₉₁

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉₁	C₂³
commutator	C₂²	C₂²×C₄×C₁₉₁
Frattini, cosocle	C₂×C₄	C₂³×C₁₉₁
socle, prime radical	C₂²×C₁₉₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉₁ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5348 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37570502, #37571354, #37571368, …
maximal subgroup of	#1338×C₁₉₁, #1582×C₁₉₁, #1584×C₁₉₁, …
maximal normal subgroup of	#1338×C₁₉₁, #1582×C₁₉₁, #1584×C₁₉₁, …
maximal quotient of	#1770×C₁₉₁, #1771×C₁₉₁, #1916×C₁₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 127);