Finite Group Databasebeta

← Prev (#72192570) Next (#72192572) →

C₂²×C₄²×C₅²×C₉ #72192571

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 424673280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄×C₅

Aliases

abelian	C₂²×C₄²×C₅²×C₉
multiplicative	(ℤ/29865)ˣ, (ℤ/30525)ˣ, (ℤ/31856)ˣ, (ℤ/36200)ˣ, (ℤ/39820)ˣ, (ℤ/40700)ˣ, (ℤ/54300)ˣ, (ℤ/59730)ˣ, (ℤ/61050)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁴×C₃×C₅²
socle, prime radical	C₂⁴×C₃×C₅²	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

5976 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₅²×C₈×C₉, C₂×C₄³×C₅²×C₉, C₂³×C₄²×C₅²×C₉
maximal normal subgroup of	C₂²×C₄×C₅²×C₈×C₉, C₂×C₄³×C₅²×C₉, C₂³×C₄²×C₅²×C₉
maximal quotient of	C₂²×C₄×C₅²×C₈×C₉, C₂×C₄³×C₅²×C₉, C₂³×C₄²×C₅²×C₉
automorphism group of	C₁₁×C₁₆×C₁₈₁
outer automorphism group of	C₁₁×C₁₆×C₁₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.