Finite Group Databasebeta

← Prev (#72192562) Next (#72192564) →

C₂³×C₅²×C₈×C₉ #72192563

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 123863040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

abelian	C₂³×C₅²×C₈×C₉
multiplicative	(ℤ/25707)ˣ, (ℤ/34276)ˣ, (ℤ/48708)ˣ, (ℤ/51414)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂⁴×C₃×C₅²
socle, prime radical	C₂⁴×C₃×C₅²	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

4056 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	C₂³×C₅²×C₉×C₁₆, C₂²×C₄×C₅²×C₈×C₉, C₂⁴×C₅²×C₈×C₉
maximal normal subgroup of	C₂³×C₅²×C₉×C₁₆, C₂²×C₄×C₅²×C₈×C₉, C₂⁴×C₅²×C₈×C₉
maximal quotient of	C₂³×C₅²×C₉×C₁₆, C₂²×C₄×C₅²×C₈×C₉, C₂⁴×C₅²×C₈×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.