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C₂⁷×C₃×C₄×C₉ #72192067

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order ≥ 2⁶³
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²⁸×C₃

Aliases

C₂⁷×C₃×C₄×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂⁸×C₃²
socle, prime radical	C₂⁸×C₃²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

8051860 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	C₂⁷×C₃×C₈×C₉, C₂⁶×C₃×C₄²×C₉, C₂⁸×C₃×C₄×C₉
maximal normal subgroup of	C₂⁷×C₃×C₈×C₉, C₂⁶×C₃×C₄²×C₉, C₂⁸×C₃×C₄×C₉
maximal quotient of	C₂⁷×C₃×C₈×C₉, C₂⁶×C₃×C₄²×C₉, C₂⁸×C₃×C₄×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.