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C₂×C₃²×C₂₅×C₃₂ #72192544

order	14400
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 61440
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂×C₃²×C₂₅×C₃₂
multiplicative	(ℤ/14647)ˣ, (ℤ/29294)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅×C₁₆	C₂²×C₃²×C₅
socle, prime radical	C₂²×C₃²×C₅	C₅×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

306 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	C₂×C₃²×C₂₅×C₆₄, C₃²×C₄×C₂₅×C₃₂, C₂²×C₃²×C₂₅×C₃₂
maximal normal subgroup of	C₂×C₃²×C₂₅×C₆₄, C₃²×C₄×C₂₅×C₃₂, C₂²×C₃²×C₂₅×C₃₂
maximal quotient of	C₂×C₃²×C₂₅×C₆₄, C₃²×C₄×C₂₅×C₃₂, C₂²×C₃²×C₂₅×C₃₂
automorphism group of	C₉₇×C₁₅₁
outer automorphism group of	C₉₇×C₁₅₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.