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C₂×C₃×C₄×C₁₇×C₂₃ #72188147

order	9384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 5632
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₁₇×C₂₃
multiplicative	(ℤ/11735)ˣ, (ℤ/23470)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₁₇×C₂₃
socle, prime radical	C₂²×C₃×C₁₇×C₂₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₈×C₁₇×C₂₃, C₃×C₄²×C₁₇×C₂₃, C₂²×C₃×C₄×C₁₇×C₂₃, …
maximal normal subgroup of	C₂×C₃×C₈×C₁₇×C₂₃, C₃×C₄²×C₁₇×C₂₃, C₂²×C₃×C₄×C₁₇×C₂₃, …
maximal quotient of	C₂×C₃×C₈×C₁₇×C₂₃, C₃×C₄²×C₁₇×C₂₃, C₂²×C₃×C₄×C₁₇×C₂₃, …
automorphism group of	C₅×C₂₃₄₇
outer automorphism group of	C₅×C₂₃₄₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.