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C₂²×C₁₆×C₁₉₁ #27132297

order	12224
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 145920
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₁₆×C₁₉₁
multiplicative	(ℤ/19533)ˣ, (ℤ/24512)ˣ, (ℤ/26044)ˣ, (ℤ/39066)ˣ

Subgroups

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

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12224 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37570597, #37570608, #37570612, …
maximal subgroup of	#1374×C₁₉₁, #1379×C₁₉₁, #1380×C₁₉₁, …
maximal normal subgroup of	#1374×C₁₉₁, #1379×C₁₉₁, #1380×C₁₉₁, …
maximal quotient of	C₂×C₄×C₁₆×C₁₉₁, C₂×C₂²⋊C₁₆×C₁₉₁, C₂×C₄⋊C₁₆×C₁₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12224, 183);