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C₂²×C₄×C₅×C₁₉₃ #72193448

order	15440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₅×C₁₉₃
multiplicative	(ℤ/25509)ˣ, (ℤ/28965)ˣ, (ℤ/30896)ˣ, (ℤ/34012)ˣ, (ℤ/38620)ˣ, (ℤ/51018)ˣ, (ℤ/57930)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₅×C₁₉₃
socle, prime radical	C₂³×C₅×C₁₉₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15440 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄²×C₅×C₁₉₃, C₂²×C₅×C₈×C₁₉₃, C₂³×C₄×C₅×C₁₉₃
maximal normal subgroup of	C₂×C₄²×C₅×C₁₉₃, C₂²×C₅×C₈×C₁₉₃, C₂³×C₄×C₅×C₁₉₃
maximal quotient of	C₂×C₄²×C₅×C₁₉₃, C₂²×C₅×C₈×C₁₉₃, C₂³×C₄×C₅×C₁₉₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.