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C₃²×C₄²×C₂₇ #72183459

order	3888
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6718464
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³×C₄

Aliases

C₃²×C₄²×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₉	C₂²×C₃³
socle, prime radical	C₂²×C₃³	C₂²×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

1080 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃²×C₄×C₈×C₂₇, C₂×C₃²×C₄²×C₂₇, C₃²×C₄²×C₈₁, …
maximal normal subgroup of	C₃²×C₄×C₈×C₂₇, C₂×C₃²×C₄²×C₂₇, C₃²×C₄²×C₈₁, …
maximal quotient of	C₃²×C₄×C₈×C₂₇, C₂×C₃²×C₄²×C₂₇, C₃²×C₄²×C₈₁, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.