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C₂×C₄³×C₂₇ #72183134

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 99090432
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₄³×C₂₇
multiplicative	(ℤ/8720)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₉	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

2544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₈×C₂₇, C₄⁴×C₂₇, C₂²×C₄³×C₂₇, …
maximal normal subgroup of	C₂×C₄²×C₈×C₂₇, C₄⁴×C₂₇, C₂²×C₄³×C₂₇, …
maximal quotient of	C₂×C₄²×C₈×C₂₇, C₄⁴×C₂₇, C₂²×C₄³×C₂₇, …
automorphism group of	C₅×C₁₆×C₁₀₉
outer automorphism group of	C₅×C₁₆×C₁₀₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.