Finite Group Databasebeta

← Prev (#72181979) Next (#72181981) →

C₂²×C₃×C₈×C₁₆ #72181980

order	1536
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 6291456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₈

Aliases

abelian	C₂²×C₃×C₈×C₁₆
multiplicative	(ℤ/3808)ˣ, (ℤ/4896)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1924 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1536 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₈×C₃₂, C₂²×C₃×C₁₆², C₂³×C₃×C₈×C₁₆, …
maximal normal subgroup of	C₂²×C₃×C₈×C₃₂, C₂²×C₃×C₁₆², C₂³×C₃×C₈×C₁₆, …
maximal quotient of	C₂²×C₃×C₈×C₃₂, C₂²×C₃×C₁₆², C₂³×C₃×C₈×C₁₆, …
automorphism group of	C₇×C₁₇×C₃₂, C₉×C₁₇×C₃₂
outer automorphism group of	C₇×C₁₇×C₃₂, C₉×C₁₇×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.