C₅×C₃⋊(C₃⋊(D₇₁⋊C₅)) #44544062

order	31950
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₅×C₃⋊(C₃⋊(D₇₁⋊C₅))
unambiguous semidirect product	C₃⋊(C₅×C₃⋊(D₇₁⋊C₅))
unambiguous semidirect product	(C₇₁⋊C₅)⋊(C₅×C₃⋊D₃)
unambiguous semidirect product	(C₃⋊D₂₁₃)⋊C₅²
unambiguous semidirect product	(C₅×C₃⋊D₂₁₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(C₃⋊(D₇₁⋊C₅))
commutator, cosocle, hypocenter	C₃²×C₇₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇₁	C₂×C₅
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₅

192 conjugacy classes of subgroups.

μ_t(G) = 3195

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 65);