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C₂³×C₃×C₈²×C₉ #72192043

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 114152177664
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₃×C₈

Aliases

abelian	C₂³×C₃×C₈²×C₉
multiplicative	(ℤ/49056)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄²	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₃×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

41620 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	C₂³×C₃×C₈×C₉×C₁₆, C₂²×C₃×C₄×C₈²×C₉, C₂⁴×C₃×C₈²×C₉
maximal normal subgroup of	C₂³×C₃×C₈×C₉×C₁₆, C₂²×C₃×C₄×C₈²×C₉, C₂⁴×C₃×C₈²×C₉
maximal quotient of	C₂³×C₃×C₈×C₉×C₁₆, C₂²×C₃×C₄×C₈²×C₉, C₂⁴×C₃×C₈²×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.