Finite Group Databasebeta

← Prev (#72183118) Next (#72183120) →

C₂³×C₁₆×C₂₇ #72183119

order	3456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1548288
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₁₆×C₂₇
multiplicative	(ℤ/10392)ˣ, (ℤ/11016)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₉	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₈×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

880 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	C₂³×C₂₇×C₃₂, C₂²×C₄×C₁₆×C₂₇, C₂⁴×C₁₆×C₂₇, …
maximal normal subgroup of	C₂³×C₂₇×C₃₂, C₂²×C₄×C₁₆×C₂₇, C₂⁴×C₁₆×C₂₇, …
maximal quotient of	C₂³×C₂₇×C₃₂, C₂²×C₄×C₁₆×C₂₇, C₂⁴×C₁₆×C₂₇, …
automorphism group of	C₃×C₈×C₄₃₃, C₈×C₁₇×C₈₁
outer automorphism group of	C₃×C₈×C₄₃₃, C₈×C₁₇×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.