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C₂²×C₃³×C₄×C₃₂ #72192015

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8833204224
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₃³×C₄

Aliases

abelian	C₂²×C₃³×C₄×C₃₂
multiplicative	(ℤ/26481)ˣ, (ℤ/30555)ˣ, (ℤ/35308)ˣ, (ℤ/45396)ˣ, (ℤ/52962)ˣ, (ℤ/61110)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂⁴×C₃³
socle, prime radical	C₂⁴×C₃³	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

17976 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	C₂²×C₃³×C₄×C₆₄, C₂²×C₃³×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂, …
maximal normal subgroup of	C₂²×C₃³×C₄×C₆₄, C₂²×C₃³×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂, …
maximal quotient of	C₂²×C₃³×C₄×C₆₄, C₂²×C₃³×C₈×C₃₂, C₂×C₃³×C₄²×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.