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C₂×C₄²×C₈×C₄₃ #24940342

order	11008
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 264241152
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄²×C₈×C₄₃
multiplicative	(ℤ/27680)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

2046 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	C₂×C₄²×C₁₆×C₄₃, C₂×C₄×C₈²×C₄₃, C₄³×C₈×C₄₃, …
maximal normal subgroup of	C₂×C₄²×C₁₆×C₄₃, C₂×C₄×C₈²×C₄₃, C₄³×C₈×C₄₃, …
maximal quotient of	C₂×C₄²×C₁₆×C₄₃, C₂×C₄×C₈²×C₄₃, C₄³×C₈×C₄₃, …
automorphism group of	C₅×C₃₂×C₁₇₃
outer automorphism group of	C₅×C₃₂×C₁₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 13313);