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C₂⁶×C₃×C₈×C₉ #72192055

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 35670272476446720
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²¹×C₃

Aliases

C₂⁶×C₃×C₈×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂⁷×C₃²
socle, prime radical	C₂⁷×C₃²	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

819860 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	C₂⁶×C₃×C₉×C₁₆, C₂⁵×C₃×C₄×C₈×C₉, C₂⁷×C₃×C₈×C₉
maximal normal subgroup of	C₂⁶×C₃×C₉×C₁₆, C₂⁵×C₃×C₄×C₈×C₉, C₂⁷×C₃×C₈×C₉
maximal quotient of	C₂⁶×C₃×C₉×C₁₆, C₂⁵×C₃×C₄×C₈×C₉, C₂⁷×C₃×C₈×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.