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C₂²×C₁₆×C₁₈₁ #26040913

order	11584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 138240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₁₆×C₁₈₁
multiplicative	(ℤ/23176)ˣ, (ℤ/34764)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂³×C₁₈₁
socle, prime radical	C₂³×C₁₈₁	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11584 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37531798, #37531809, #37531813, …
maximal subgroup of	#1374×C₁₈₁, #1379×C₁₈₁, #1380×C₁₈₁, …
maximal normal subgroup of	#1374×C₁₈₁, #1379×C₁₈₁, #1380×C₁₈₁, …
maximal quotient of	C₂×C₄×C₁₆×C₁₈₁, C₂×C₂²⋊C₁₆×C₁₈₁, C₂×C₄⋊C₁₆×C₁₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 183);