Finite Group Databasebeta

← Prev (#72193220) Next (#72193222) →

C₂²×C₅²×C₈×C₁₉ #72193221

order	15200
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3317760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₅

Aliases

abelian	C₂²×C₅²×C₈×C₁₉
multiplicative	(ℤ/23493)ˣ, (ℤ/25113)ˣ, (ℤ/31324)ˣ, (ℤ/33484)ˣ, (ℤ/46986)ˣ, (ℤ/50226)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂³×C₅²×C₁₉
socle, prime radical	C₂³×C₅²×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₅²×C₁₆×C₁₉, C₂×C₄×C₅²×C₈×C₁₉, C₂³×C₅²×C₈×C₁₉
maximal normal subgroup of	C₂²×C₅²×C₁₆×C₁₉, C₂×C₄×C₅²×C₈×C₁₉, C₂³×C₅²×C₈×C₁₉
maximal quotient of	C₂²×C₅²×C₁₆×C₁₉, C₂×C₄×C₅²×C₈×C₁₉, C₂³×C₅²×C₈×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.