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C₁₃×C₁₇×C₄₉ #24925294

order	10829
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃²×C₄×C₇×C₁₆ (order 8064) · Inn(G) = C₁ · Out(G) = C₂×C₃²×C₄×C₇×C₁₆
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₈₂₉
abelian	C₁₃×C₁₇×C₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇	C₇×C₁₃×C₁₇
socle, prime radical	C₇×C₁₃×C₁₇	C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10829 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₀₈₂₉
Fitting subgroup of	C₁₃×D₁₇×C₄₉, C₁₇×D₁₃×C₄₉, C₄₉×D₂₂₁, …
maximal subgroup of	C₂×C₁₃×C₁₇×C₄₉, C₁₃×D₁₇×C₄₉, C₁₇×D₁₃×C₄₉, …
maximal normal subgroup of	C₂×C₁₃×C₁₇×C₄₉, C₁₃×D₁₇×C₄₉, C₁₇×D₁₃×C₄₉, …
maximal quotient of	C₂×C₁₃×C₁₇×C₄₉, C₃×C₁₃×C₁₇×C₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10829, 1);