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C₂²×C₄×C₁₆×C₄₃ #24953337

order	11008
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 16515072
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄×C₁₆×C₄₃
multiplicative	(ℤ/23528)ˣ, (ℤ/33216)ˣ, (ℤ/35292)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂⁴×C₄₃
socle, prime radical	C₂⁴×C₄₃	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₃₂×C₄₃, C₂²×C₈×C₁₆×C₄₃, C₂×C₄²×C₁₆×C₄₃, …
maximal normal subgroup of	C₂²×C₄×C₃₂×C₄₃, C₂²×C₈×C₁₆×C₄₃, C₂×C₄²×C₁₆×C₄₃, …
maximal quotient of	C₂²×C₄×C₃₂×C₄₃, C₂²×C₈×C₁₆×C₄₃, C₂×C₄²×C₁₆×C₄₃, …
automorphism group of	C₈×C₁₇×C₁₇₃
outer automorphism group of	C₈×C₁₇×C₁₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 26308);