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C₂×C₃²×C₄²×C₂₇ #72186719

order	7776
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 107495424
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₃³×C₄

Aliases

abelian	C₂×C₃²×C₄²×C₂₇
multiplicative	(ℤ/9919)ˣ, (ℤ/12753)ˣ, (ℤ/19838)ˣ, (ℤ/25506)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₉	C₂³×C₃³
socle, prime radical	C₂³×C₃³	C₂²×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

3888 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃²×C₄×C₈×C₂₇, C₃²×C₄³×C₂₇, C₂²×C₃²×C₄²×C₂₇, …
maximal normal subgroup of	C₂×C₃²×C₄×C₈×C₂₇, C₃²×C₄³×C₂₇, C₂²×C₃²×C₄²×C₂₇, …
maximal quotient of	C₂×C₃²×C₄×C₈×C₂₇, C₃²×C₄³×C₂₇, C₂²×C₃²×C₄²×C₂₇, …
automorphism group of	C₇×C₁₃×C₁₀₉
outer automorphism group of	C₇×C₁₃×C₁₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.