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C₂³×C₃³×C₄×C₈ #72186014

order	6912
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 989318873088
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₃³×C₄

Aliases

abelian	C₂³×C₃³×C₄×C₈
multiplicative	(ℤ/26208)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₃³
socle, prime radical	C₂⁵×C₃³	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

64932 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃³×C₄×C₁₆, C₂³×C₃³×C₈², C₂²×C₃³×C₄²×C₈, …
maximal normal subgroup of	C₂³×C₃³×C₄×C₁₆, C₂³×C₃³×C₈², C₂²×C₃³×C₄²×C₈, …
maximal quotient of	C₂³×C₃³×C₄×C₁₆, C₂³×C₃³×C₈², C₂²×C₃³×C₄²×C₈, …
automorphism group of	C₇×C₉×C₁₃×C₃₂
outer automorphism group of	C₇×C₉×C₁₃×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.