Finite Group Databasebeta

← Prev (#72189624) Next (#72189626) →

C₈×C₁₃×C₁₀₇ #72189625

order	11128
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₄×C₅₃ (order 5088) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₄×C₅₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₁₂₈
abelian	C₈×C₁₃×C₁₀₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₃×C₁₀₇
socle, prime radical	C₂×C₁₃×C₁₀₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11128 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₁₁₂₈, D₂₂₂₅₆
maximal subgroup of	C₁₃×C₁₆×C₁₀₇, C₂×C₈×C₁₃×C₁₀₇, D₁₁₁₂₈, …
maximal normal subgroup of	C₁₃×C₁₆×C₁₀₇, C₂×C₈×C₁₃×C₁₀₇, D₁₁₁₂₈, …
maximal quotient of	C₁₃×C₁₆×C₁₀₇, C₂×C₈×C₁₃×C₁₀₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.