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C₂²×C₃×C₄²×C₃₁ #72185162

order	5952
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8847360
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₃×C₄²×C₃₁
multiplicative	(ℤ/14920)ˣ, (ℤ/17904)ˣ, (ℤ/22380)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁴×C₃×C₃₁
socle, prime radical	C₂⁴×C₃×C₃₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

996 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5952 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₈×C₃₁, C₂×C₃×C₄³×C₃₁, C₂³×C₃×C₄²×C₃₁, …
maximal normal subgroup of	C₂²×C₃×C₄×C₈×C₃₁, C₂×C₃×C₄³×C₃₁, C₂³×C₃×C₄²×C₃₁, …
maximal quotient of	C₂²×C₃×C₄×C₈×C₃₁, C₂×C₃×C₄³×C₃₁, C₂³×C₃×C₄²×C₃₁, …
automorphism group of	C₅×C₈×C₃₇₃, C₃×C₁₆×C₃₇₃
outer automorphism group of	C₅×C₈×C₃₇₃, C₃×C₁₆×C₃₇₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.