C₂×C₅⋊D₅×C₁₀₉ #24926286

order	10900
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₁₀₉
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₁₀₉)

	subgroup	G/H
center, hypercenter	C₂×C₁₀₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₀₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₀₉

80 conjugacy classes of subgroups.

3052 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10900, 47);