Finite Group Databasebeta

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C₃×C₄²×C₅²×C₈ #72188315

order	9600
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 94371840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄³×C₅

Aliases

abelian	C₃×C₄²×C₅²×C₈
multiplicative	(ℤ/12505)ˣ, (ℤ/13325)ˣ, (ℤ/25010)ˣ, (ℤ/26650)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅²
socle, prime radical	C₂³×C₃×C₅²	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

3264 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₅²×C₁₆, C₃×C₄×C₅²×C₈², C₂×C₃×C₄²×C₅²×C₈, …
maximal normal subgroup of	C₃×C₄²×C₅²×C₁₆, C₃×C₄×C₅²×C₈², C₂×C₃×C₄²×C₅²×C₈, …
maximal quotient of	C₃×C₄²×C₅²×C₁₆, C₃×C₄×C₅²×C₈², C₂×C₃×C₄²×C₅²×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.