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C₄×C₇×C₁₃×C₂₉ #24902197

order	10556
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₄²×C₇ (order 4032) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₄²×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₅₅₆
abelian	C₄×C₇×C₁₃×C₂₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₁₃×C₂₉
socle, prime radical	C₂×C₇×C₁₃×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10556 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₅₅₆, D₂₁₁₁₂
Fitting subgroup of	C₄×C₇×C₂₉×C₁₃⋊C₃, C₄×C₁₃×ΓL(1,𝔽₈)×C₂₉, C₄×C₂₉×#63270, …
maximal subgroup of	C₃×C₄×C₇×C₁₃×C₂₉, C₄×C₇×C₂₉×C₁₃⋊C₃, C₄×C₁₃×ΓL(1,𝔽₈)×C₂₉, …
maximal normal subgroup of	C₃×C₄×C₇×C₁₃×C₂₉, C₄×C₇×C₂₉×C₁₃⋊C₃, C₄×C₁₃×ΓL(1,𝔽₈)×C₂₉, …
maximal quotient of	C₃×C₄×C₇×C₁₃×C₂₉, C₇×Dic₃×C₁₃×C₂₉, C₇×C₈×C₁₃×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10556, 1);