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C₂×C₃²×C₄×C₈×C₁₃ #72186460

order	7488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1179648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

abelian	C₂×C₃²×C₄×C₈×C₁₃
multiplicative	(ℤ/10955)ˣ, (ℤ/12207)ˣ, (ℤ/14085)ˣ, (ℤ/16276)ˣ, (ℤ/21910)ˣ, (ℤ/24414)ˣ, (ℤ/28170)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃²×C₁₃
socle, prime radical	C₂³×C₃²×C₁₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

972 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7488 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₆, C₂×C₃²×C₈²×C₁₃, C₃²×C₄²×C₈×C₁₃, …
maximal normal subgroup of	C₂×C₃²×C₄×C₁₃×C₁₆, C₂×C₃²×C₈²×C₁₃, C₃²×C₄²×C₈×C₁₃, …
maximal quotient of	C₂×C₃²×C₄×C₁₃×C₁₆, C₂×C₃²×C₈²×C₁₃, C₃²×C₄²×C₈×C₁₃, …
automorphism group of	C₅×C₇×C₃₁₃
outer automorphism group of	C₅×C₇×C₃₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.