Finite Group Databasebeta

← Prev (#72194076) Next (#72194078) →

C₇×C₉×C₂₅₆ #72194077

order	16128
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₆₄ (order 4608) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₆₁₂₈
abelian	C₇×C₉×C₂₅₆

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₁₂₈	C₂×C₃×C₇
socle, prime radical	C₂×C₃×C₇	C₃×C₁₂₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16128 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₆₁₂₈, D₃₂₂₅₆
Fitting subgroup of	Dic₈₀₆₄, D₁₆₁₂₈
maximal subgroup of	C₇×C₉×C₅₁₂, C₂×C₇×C₉×C₂₅₆, Dic₈₀₆₄, …
maximal normal subgroup of	C₇×C₉×C₅₁₂, C₂×C₇×C₉×C₂₅₆, Dic₈₀₆₄, …
maximal quotient of	C₇×C₉×C₅₁₂, C₂×C₇×C₉×C₂₅₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.