Finite Group Databasebeta

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C₂³×C₃²×C₅²×C₈ #72192565

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 990904320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₃×C₅

Aliases

abelian	C₂³×C₃²×C₅²×C₈
multiplicative	(ℤ/26691)ˣ, (ℤ/28413)ˣ, (ℤ/35588)ˣ, (ℤ/45756)ˣ, (ℤ/53382)ˣ, (ℤ/56826)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₃²×C₅²
socle, prime radical	C₂⁴×C₃²×C₅²	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

8112 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×C₃²×C₅²×C₁₆, C₂²×C₃²×C₄×C₅²×C₈, C₂⁴×C₃²×C₅²×C₈
maximal normal subgroup of	C₂³×C₃²×C₅²×C₁₆, C₂²×C₃²×C₄×C₅²×C₈, C₂⁴×C₃²×C₅²×C₈
maximal quotient of	C₂³×C₃²×C₅²×C₁₆, C₂²×C₃²×C₄×C₅²×C₈, C₂⁴×C₃²×C₅²×C₈

GAP

Past the SmallGroups library coverage — no SmallGroups id.