Finite Group Databasebeta

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C₃×C₈×C₁₉×C₂₃ #72189105

order	10488
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁵×C₉×C₁₁ (order 3168) · Inn(G) = C₁ · Out(G) = C₂⁵×C₉×C₁₁
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₄₈₈
abelian	C₃×C₈×C₁₉×C₂₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₁₉×C₂₃
socle, prime radical	C₂×C₃×C₁₉×C₂₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10488 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₄₈₈, D₂₀₉₇₆
maximal subgroup of	C₃×C₁₆×C₁₉×C₂₃, C₂×C₃×C₈×C₁₉×C₂₃, C₈×C₉×C₁₉×C₂₃, …
maximal normal subgroup of	C₃×C₁₆×C₁₉×C₂₃, C₂×C₃×C₈×C₁₉×C₂₃, C₈×C₉×C₁₉×C₂₃, …
maximal quotient of	C₃×C₁₆×C₁₉×C₂₃, C₂×C₃×C₈×C₁₉×C₂₃, C₈×C₉×C₁₉×C₂₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.