Finite Group Databasebeta

← Prev (#72186316) Next (#72186318) →

C₅×C₇×C₁₃×C₁₆ #72186317

order	7280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄³ (order 2304) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄³
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₇₂₈₀
abelian	C₅×C₇×C₁₃×C₁₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₇×C₁₃
socle, prime radical	C₂×C₅×C₇×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7280 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₄₅₆₀, Dic₇₂₈₀
maximal subgroup of	C₅×C₇×C₁₃×C₃₂, C₂×C₅×C₇×C₁₃×C₁₆, C₃×C₅×C₇×C₁₃×C₁₆, …
maximal normal subgroup of	C₅×C₇×C₁₃×C₃₂, C₂×C₅×C₇×C₁₃×C₁₆, C₃×C₅×C₇×C₁₃×C₁₆, …
maximal quotient of	C₅×C₇×C₁₃×C₃₂, C₂×C₅×C₇×C₁₃×C₁₆, C₃×C₅×C₇×C₁₃×C₁₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.