Finite Group Databasebeta

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C₂³×C₃×C₄²×C₈ #72182829

order	3072
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8658654068736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹²×C₄³

Aliases

C₂³×C₃×C₄²×C₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

111402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₄²×C₁₆, C₂³×C₃×C₄×C₈², C₂²×C₃×C₄³×C₈, …
maximal normal subgroup of	C₂³×C₃×C₄²×C₁₆, C₂³×C₃×C₄×C₈², C₂²×C₃×C₄³×C₈, …
maximal quotient of	C₂³×C₃×C₄²×C₁₆, C₂³×C₃×C₄×C₈², C₂²×C₃×C₄³×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.