Finite Group Databasebeta

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C₂⁴×C₄×C₅²×C₉ #72192575

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 29727129600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₅

Aliases

abelian	C₂⁴×C₄×C₅²×C₉
multiplicative	(ℤ/41800)ˣ, (ℤ/47784)ˣ, (ℤ/59400)ˣ, (ℤ/62700)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂⁵×C₃×C₅²
socle, prime radical	C₂⁵×C₃×C₅²	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

16344 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	C₂⁴×C₅²×C₈×C₉, C₂³×C₄²×C₅²×C₉, C₂⁵×C₄×C₅²×C₉
maximal normal subgroup of	C₂⁴×C₅²×C₈×C₉, C₂³×C₄²×C₅²×C₉, C₂⁵×C₄×C₅²×C₉
maximal quotient of	C₂⁴×C₅²×C₈×C₉, C₂³×C₄²×C₅²×C₉, C₂⁵×C₄×C₅²×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.