Finite Group Databasebeta

← Prev (#72189460) Next (#72189462) →

C₃×C₅×C₇×C₈×C₁₃ #72189461

order	10920
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂⁴×C₃²×C₄² (order 2304) · Inn(G) = C₁ · Out(G) = C₂⁴×C₃²×C₄²
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₉₂₀
abelian	C₃×C₅×C₇×C₈×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅×C₇×C₁₃
socle, prime radical	C₂×C₃×C₅×C₇×C₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10920 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₉₂₀, D₂₁₈₄₀
maximal subgroup of	C₃×C₅×C₇×C₁₃×C₁₆, C₂×C₃×C₅×C₇×C₈×C₁₃, C₅×C₇×C₈×C₉×C₁₃, …
maximal normal subgroup of	C₃×C₅×C₇×C₁₃×C₁₆, C₂×C₃×C₅×C₇×C₈×C₁₃, C₅×C₇×C₈×C₉×C₁₃, …
maximal quotient of	C₃×C₅×C₇×C₁₃×C₁₆, C₂×C₃×C₅×C₇×C₈×C₁₃, C₅×C₇×C₈×C₉×C₁₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.