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C₃×C₄²×C₉×C₃₂ #72192010

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 42467328
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄³

Aliases

abelian	C₃×C₄²×C₉×C₃₂
multiplicative	(ℤ/17945)ˣ, (ℤ/35890)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃×C₁₆	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₃×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

3540 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	C₃×C₄²×C₉×C₆₄, C₃×C₄×C₈×C₉×C₃₂, C₂×C₃×C₄²×C₉×C₃₂
maximal normal subgroup of	C₃×C₄²×C₉×C₆₄, C₃×C₄×C₈×C₉×C₃₂, C₂×C₃×C₄²×C₉×C₃₂
maximal quotient of	C₃×C₄²×C₉×C₆₄, C₃×C₄×C₈×C₉×C₃₂, C₂×C₃×C₄²×C₉×C₃₂
automorphism group of	C₅×C₃₇×C₉₇
outer automorphism group of	C₅×C₃₇×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.