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C₄²×C₁₉×C₃₁ #72188191

order	9424
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 51840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₁₉×C₃₁
multiplicative	(ℤ/11785)ˣ, (ℤ/23570)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₁₉×C₃₁
socle, prime radical	C₂²×C₁₉×C₃₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9424 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₈×C₁₉×C₃₁, C₂×C₄²×C₁₉×C₃₁, C₃×C₄²×C₁₉×C₃₁
maximal normal subgroup of	C₄×C₈×C₁₉×C₃₁, C₂×C₄²×C₁₉×C₃₁, C₃×C₄²×C₁₉×C₃₁
maximal quotient of	C₄×C₈×C₁₉×C₃₁, C₂×C₄²×C₁₉×C₃₁, C₃×C₄²×C₁₉×C₃₁
automorphism group of	C₅×C₂₃₅₇
outer automorphism group of	C₅×C₂₃₅₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.