C₇₁⋊((C₅⋊D₅)⋊C₉) #44544039

order	31950
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₅

Aliases

unambiguous semidirect product	C₇₁⋊((C₅⋊D₅)⋊C₉)
unambiguous semidirect product	(C₅⋊D₃₅₅)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₇₁⋊((C₅⋊D₅)⋊C₃)
commutator, hypocenter	C₅²×C₇₁	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²×C₇₁	C₂×C₃
prime radical	C₃×C₅⋊D₃₅₅	C₃
LCS	G ▷ C₅²×C₇₁
UCS	C₁ ◁ C₃

40 conjugacy classes of subgroups.

μ_t(G) = 3195

Polycyclic presentation:

2,3,5^2,71,3|b^3=f,c^a=c^4,d^a=d^4,e^a=e^70,c^b=cd,d^b=c^2d^3

1185 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 42);