C₂×C₃×C₄₁×C₅⋊D₅ #27134331

order	12300
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₃×C₄₁×C₅⋊D₅
unambiguous semidirect product	(C₂×C₅)⋊(C₃×D₅×C₄₁)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₄₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₄₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₄₁

160 conjugacy classes of subgroups.

3444 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 193);