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C₂⁴×C₃²×C₄×C₂₅ #72192576

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9909043200
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁴×C₃²×C₄×C₂₅
multiplicative	(ℤ/42280)ˣ, (ℤ/47112)ˣ, (ℤ/50736)ˣ, (ℤ/50904)ˣ, (ℤ/54360)ˣ, (ℤ/63000)ˣ, (ℤ/63420)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂⁵×C₃²×C₅
socle, prime radical	C₂⁵×C₃²×C₅	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

12258 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×C₃²×C₈×C₂₅, C₂³×C₃²×C₄²×C₂₅, C₂⁵×C₃²×C₄×C₂₅
maximal normal subgroup of	C₂⁴×C₃²×C₈×C₂₅, C₂³×C₃²×C₄²×C₂₅, C₂⁵×C₃²×C₄×C₂₅
maximal quotient of	C₂⁴×C₃²×C₈×C₂₅, C₂³×C₃²×C₄²×C₂₅, C₂⁵×C₃²×C₄×C₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.