Finite Group Databasebeta

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C₃×C₈×C₁₇×C₂₃ #72188146

order	9384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₁₁×C₁₆ (order 2816) · Inn(G) = C₁ · Out(G) = C₂⁴×C₁₁×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₉₃₈₄
abelian	C₃×C₈×C₁₇×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₇×C₂₃
socle, prime radical	C₂×C₃×C₁₇×C₂₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

derived subgroup of	Dic₉₃₈₄, D₁₈₇₆₈
maximal subgroup of	C₃×C₁₆×C₁₇×C₂₃, C₂×C₃×C₈×C₁₇×C₂₃, C₈×C₉×C₁₇×C₂₃, …
maximal normal subgroup of	C₃×C₁₆×C₁₇×C₂₃, C₂×C₃×C₈×C₁₇×C₂₃, C₈×C₉×C₁₇×C₂₃, …
maximal quotient of	C₃×C₁₆×C₁₇×C₂₃, C₂×C₃×C₈×C₁₇×C₂₃, C₈×C₉×C₁₇×C₂₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.