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C₄×C₅×C₃₄₉ #20296114

order	6980
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₄²×C₂₉ (order 2784) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₄²×C₂₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₉₈₀
abelian	C₄×C₅×C₃₄₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂	C₂×C₅×C₃₄₉
socle	C₂×C₅×C₃₄₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6980 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₃₉₆₀, Dic₆₉₈₀
Fitting subgroup of	C₄×C₅×C₃₄₉⋊C₃
maximal subgroup of	C₃×C₄×C₅×C₃₄₉, C₄×C₅×C₃₄₉⋊C₃, C₅×Dic₃×C₃₄₉, …
maximal normal subgroup of	C₃×C₄×C₅×C₃₄₉, C₄×C₅×C₃₄₉⋊C₃, C₄×C₂₅×C₃₄₉, …
maximal quotient of	C₃×C₄×C₅×C₃₄₉, C₅×Dic₃×C₃₄₉, C₄×C₂₅×C₃₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6980, 1);