Finite Group Databasebeta

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C₂×C₃×C₄³×C₃₂ #72190664

order	12288
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2886218022912
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁴×C₄⁶

Aliases

C₂×C₃×C₄³×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₁₆	C₂⁵×C₃
socle, prime radical	C₂⁵×C₃	C₂³×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

83766 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄³×C₆₄, C₂×C₃×C₄²×C₈×C₃₂, C₃×C₄⁴×C₃₂, …
maximal normal subgroup of	C₂×C₃×C₄³×C₆₄, C₂×C₃×C₄²×C₈×C₃₂, C₃×C₄⁴×C₃₂, …
maximal quotient of	C₂×C₃×C₄³×C₆₄, C₂×C₃×C₄²×C₈×C₃₂, C₃×C₄⁴×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.