Finite Group Databasebeta

← Prev (#72190778) Next (#72190780) →

C₂×C₅²×C₈×C₃₁ #72190779

order	12400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 230400
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂×C₅²×C₈×C₃₁
multiplicative	(ℤ/12751)ˣ, (ℤ/25502)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₅²×C₃₁
socle, prime radical	C₂²×C₅²×C₃₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅²×C₁₆×C₃₁, C₄×C₅²×C₈×C₃₁, C₂²×C₅²×C₈×C₃₁
maximal normal subgroup of	C₂×C₅²×C₁₆×C₃₁, C₄×C₅²×C₈×C₃₁, C₂²×C₅²×C₈×C₃₁
maximal quotient of	C₂×C₅²×C₁₆×C₃₁, C₄×C₅²×C₈×C₃₁, C₂²×C₅²×C₈×C₃₁
automorphism group of	C₄₁×C₃₁₁
outer automorphism group of	C₄₁×C₃₁₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.