Finite Group Databasebeta

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C₂×C₃×C₈×C₉×C₃₂ #72192007

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7077888
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃×C₈

Aliases

abelian	C₂×C₃×C₈×C₉×C₃₂
multiplicative	(ℤ/21243)ˣ, (ℤ/28324)ˣ, (ℤ/42486)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄×C₁₆	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₃×C₄×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

2580 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₉×C₆₄, C₂×C₃×C₉×C₁₆×C₃₂, C₃×C₄×C₈×C₉×C₃₂, …
maximal normal subgroup of	C₂×C₃×C₈×C₉×C₆₄, C₂×C₃×C₉×C₁₆×C₃₂, C₃×C₄×C₈×C₉×C₃₂, …
maximal quotient of	C₂×C₃×C₈×C₉×C₆₄, C₂×C₃×C₉×C₁₆×C₃₂, C₃×C₄×C₈×C₉×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.