Finite Group Databasebeta

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C₃²×C₄×C₁₃×C₂₇ #72190976

order	12636
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1679616
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃²×C₄×C₁₃×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉	C₂×C₃³×C₁₃
socle, prime radical	C₂×C₃³×C₁₃	C₂×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12636 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₈×C₁₃×C₂₇, C₂×C₃²×C₄×C₁₃×C₂₇
maximal normal subgroup of	C₃²×C₈×C₁₃×C₂₇, C₂×C₃²×C₄×C₁₃×C₂₇
maximal quotient of	C₃²×C₈×C₁₃×C₂₇, C₂×C₃²×C₄×C₁₃×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.