C₁₃×C₅⋊D₅×C₅₃ #46828019

order	34450
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₅₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₁₃×C₅⋊D₅×C₅₃
unambiguous semidirect product	C₅⋊(D₅×C₁₃×C₅₃)

	subgroup	G/H
center, hypercenter	C₁₃×C₅₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₁₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₅₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₃×C₅₃

64 conjugacy classes of subgroups.

μ_t(G) = 17225

9646 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34450, 27);