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C₂²×C₂₅×C₁₀₉ #24926244

order	10900
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 12960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₂₅×C₁₀₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₀₉
socle, prime radical	C₂²×C₅×C₁₀₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₂²×C₂₅×C₁₀₉⋊C₃, A₄×C₂₅×C₁₀₉, C₂₅×C₂²⋊(C₁₀₉⋊C₃)
maximal subgroup of	C₂²×C₃×C₂₅×C₁₀₉, C₂²×C₂₅×C₁₀₉⋊C₃, A₄×C₂₅×C₁₀₉, …
maximal normal subgroup of	C₂²×C₃×C₂₅×C₁₀₉, C₂²×C₂₅×C₁₀₉⋊C₃, A₄×C₂₅×C₁₀₉, …
maximal quotient of	C₂²×C₃×C₂₅×C₁₀₉, C₂×D₃×C₂₅×C₁₀₉, C₂×C₄×C₂₅×C₁₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10900, 5);