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C₂×C₃×C₄⁴×C₉ #72192058

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 36528696852480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁴×C₃×C₄⁶

Aliases

abelian	C₂×C₃×C₄⁴×C₉
multiplicative	(ℤ/38480)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂⁴×C₃	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₂⁴×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

135060 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×C₄³×C₈×C₉, C₃×C₄⁵×C₉, C₂²×C₃×C₄⁴×C₉
maximal normal subgroup of	C₂×C₃×C₄³×C₈×C₉, C₃×C₄⁵×C₉, C₂²×C₃×C₄⁴×C₉
maximal quotient of	C₂×C₃×C₄³×C₈×C₉, C₃×C₄⁵×C₉, C₂²×C₃×C₄⁴×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.