Finite Group Databasebeta

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C₄₉×C₂₅₆ #72190880

order	12544
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×C₇×C₆₄ (order 5376) · Inn(G) = C₁ · Out(G) = C₂²×C₃×C₇×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₂₅₄₄
abelian	C₄₉×C₂₅₆

Subgroups

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

27 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12544 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₂₅₄₄, D₂₅₀₈₈
Fitting subgroup of	Dic₆₂₇₂
maximal subgroup of	C₄₉×C₅₁₂, C₂×C₄₉×C₂₅₆, D₁₂₅₄₄, …
maximal normal subgroup of	C₄₉×C₅₁₂, C₂×C₄₉×C₂₅₆, D₁₂₅₄₄, …
maximal quotient of	C₄₉×C₅₁₂, C₂×C₄₉×C₂₅₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.