Finite Group Databasebeta

← Prev (#72186246) Next (#72186248) →

C₂³×C₃×C₁₃×C₂₃ #72186247

order	7176
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 88704
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂³×C₃×C₁₃×C₂₃
multiplicative	(ℤ/11139)ˣ, (ℤ/12579)ˣ, (ℤ/14852)ˣ, (ℤ/16772)ˣ, (ℤ/21564)ˣ, (ℤ/22278)ˣ, (ℤ/25158)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7176 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₄×C₁₃×C₂₃, C₂⁴×C₃×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, …
maximal normal subgroup of	C₂²×C₃×C₄×C₁₃×C₂₃, C₂⁴×C₃×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, …
maximal quotient of	C₂²×C₃×C₄×C₁₃×C₂₃, C₂⁴×C₃×C₁₃×C₂₃, C₂³×C₉×C₁₃×C₂₃, …
automorphism group of	C₃×C₄₇×C₇₉
outer automorphism group of	C₃×C₄₇×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.