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C₂³×C₉×C₃₂ #72182240

order	2304
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1032192
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₉×C₃₂
multiplicative	(ℤ/7296)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₆	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

813 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2304 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₉×C₆₄, C₂²×C₄×C₉×C₃₂, C₂⁴×C₉×C₃₂, …
maximal normal subgroup of	C₂³×C₉×C₆₄, C₂²×C₄×C₉×C₃₂, C₂⁴×C₉×C₃₂, …
maximal quotient of	C₂³×C₉×C₆₄, C₂²×C₄×C₉×C₃₂, C₂⁴×C₉×C₃₂, …
automorphism group of	C₃×C₁₉×C₁₂₈
outer automorphism group of	C₃×C₁₉×C₁₂₈

GAP

Past the SmallGroups library coverage — no SmallGroups id.