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C₂×C₃×C₄×C₁₇×C₃₇ #72193142

order	15096
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 9216
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₁₇×C₃₇
multiplicative	(ℤ/15347)ˣ, (ℤ/16367)ˣ, (ℤ/22647)ˣ, (ℤ/30196)ˣ, (ℤ/30694)ˣ, (ℤ/32734)ˣ, (ℤ/45294)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₇×C₃₇
socle, prime radical	C₂²×C₃×C₁₇×C₃₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇, C₂²×C₃×C₄×C₁₇×C₃₇
maximal normal subgroup of	C₃×C₄²×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇, C₂²×C₃×C₄×C₁₇×C₃₇
maximal quotient of	C₃×C₄²×C₁₇×C₃₇, C₂×C₃×C₈×C₁₇×C₃₇, C₂²×C₃×C₄×C₁₇×C₃₇
automorphism group of	C₁₀₃×C₁₄₉, C₁₃×C₁₂₅₉
outer automorphism group of	C₁₀₃×C₁₄₉, C₁₃×C₁₂₅₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.