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C₄²×C₇×C₄₃ #72184249

order	4816
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24192
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₇×C₄₃
multiplicative	(ℤ/5017)ˣ, (ℤ/10034)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₇×C₄₃
socle, prime radical	C₂²×C₇×C₄₃	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4816 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₈×C₄₃, C₂×C₄²×C₇×C₄₃, C₃×C₄²×C₇×C₄₃, …
maximal normal subgroup of	C₄×C₇×C₈×C₄₃, C₂×C₄²×C₇×C₄₃, C₃×C₄²×C₇×C₄₃, …
maximal quotient of	C₄×C₇×C₈×C₄₃, C₂×C₄²×C₇×C₄₃, C₃×C₄²×C₇×C₄₃, …
automorphism group of	C₂₉×C₁₇₃, C₂×C₂₉×C₁₇₃
outer automorphism group of	C₂₉×C₁₇₃, C₂×C₂₉×C₁₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.