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C₄×C₂₅×C₁₀₉ #24926240

order	10900
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₄²×C₅×C₂₇ (order 4320) · Inn(G) = C₁ · Out(G) = C₂×C₄²×C₅×C₂₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₀₉₀₀
abelian	C₄×C₂₅×C₁₀₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₅×C₁₀₉
socle, prime radical	C₂×C₅×C₁₀₉	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10900 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	Dic₁₀₉₀₀, D₂₁₈₀₀
Fitting subgroup of	C₄×C₂₅×C₁₀₉⋊C₃
maximal subgroup of	C₃×C₄×C₂₅×C₁₀₉, C₄×C₂₅×C₁₀₉⋊C₃, Dic₃×C₂₅×C₁₀₉, …
maximal normal subgroup of	C₃×C₄×C₂₅×C₁₀₉, C₄×C₂₅×C₁₀₉⋊C₃, C₈×C₂₅×C₁₀₉, …
maximal quotient of	C₃×C₄×C₂₅×C₁₀₉, Dic₃×C₂₅×C₁₀₉, C₈×C₂₅×C₁₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10900, 1);