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C₃×C₄³×C₄₃ #72187191

order	8256
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7225344
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³

Aliases

abelian	C₃×C₄³×C₄₃
multiplicative	(ℤ/11245)ˣ, (ℤ/22490)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³	C₂³×C₃×C₄₃
socle, prime radical	C₂³×C₃×C₄₃	C₂³
LCS	G ▷ C₁
UCS	C₁ ◁ G

516 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₈×C₄₃, C₂×C₃×C₄³×C₄₃, C₄³×C₉×C₄₃, …
maximal normal subgroup of	C₃×C₄²×C₈×C₄₃, C₂×C₃×C₄³×C₄₃, C₄³×C₉×C₄₃, …
maximal quotient of	C₃×C₄²×C₈×C₄₃, C₂×C₃×C₄³×C₄₃, C₄³×C₉×C₄₃, …
automorphism group of	C₅×C₁₃×C₁₇₃
outer automorphism group of	C₅×C₁₃×C₁₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.