Finite Group Databasebeta

← Prev (#72192803) Next (#72192805) →

C₂³×C₃³×C₄×C₁₇ #72192804

order	14688
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3864526848
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃³

Aliases

abelian	C₂³×C₃³×C₄×C₁₇
multiplicative	(ℤ/28119)ˣ, (ℤ/32445)ˣ, (ℤ/37492)ˣ, (ℤ/48204)ˣ, (ℤ/56238)ˣ, (ℤ/64890)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₃³×C₁₇
socle, prime radical	C₂⁴×C₃³×C₁₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

6608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14688 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃³×C₈×C₁₇, C₂²×C₃³×C₄²×C₁₇, C₂⁴×C₃³×C₄×C₁₇
maximal normal subgroup of	C₂³×C₃³×C₈×C₁₇, C₂²×C₃³×C₄²×C₁₇, C₂⁴×C₃³×C₄×C₁₇
maximal quotient of	C₂³×C₃³×C₈×C₁₇, C₂²×C₃³×C₄²×C₁₇, C₂⁴×C₃³×C₄×C₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.