Finite Group Databasebeta

← Prev (#72193332) Next (#72193334) →

C₇×C₁₆×C₁₃₇ #72193333

order	15344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₄×C₈×C₁₇ (order 6528) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₄×C₈×C₁₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₅₃₄₄
abelian	C₇×C₁₆×C₁₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₇×C₁₃₇
socle, prime radical	C₂×C₇×C₁₃₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15344 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₅₃₄₄, D₃₀₆₈₈
Fitting subgroup of	D₁₅₃₄₄, Dic₇₆₇₂
maximal subgroup of	C₇×C₃₂×C₁₃₇, C₂×C₇×C₁₆×C₁₃₇, D₁₅₃₄₄, …
maximal normal subgroup of	C₇×C₃₂×C₁₃₇, C₂×C₇×C₁₆×C₁₃₇, D₁₅₃₄₄, …
maximal quotient of	C₇×C₃₂×C₁₃₇, C₂×C₇×C₁₆×C₁₃₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.