C₁₃×C₃⋊(C₃⋊(D₃₁⋊C₅)) #49136604

order	36270
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₃×C₃⋊(C₃⋊(D₃₁⋊C₅))
unambiguous semidirect product	C₃⋊(C₁₃×C₃⋊(D₃₁⋊C₅))
unambiguous semidirect product	ΓL(1,𝔽₃₂)⋊(C₁₃×C₃⋊D₃)
unambiguous semidirect product	(C₃⋊D₉₃)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₁₃×C₃⋊D₉₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊(C₃⋊(D₃₁⋊C₅))
commutator, cosocle, hypocenter	C₃²×C₃₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₃₁	C₂×C₅
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₁₃

96 conjugacy classes of subgroups.

μ_t(G) = 3627

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36270, 124);