C₅²×C₁₃×D₅₁ #45684188

order	33150
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₁₃×D₅₁
unambiguous semidirect product	C₃⋊(C₅²×C₁₃×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅²×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅²×C₁₃	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂×C₅²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃×C₁₇	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅²×C₁₃

128 conjugacy classes of subgroups.

μ_t(G) = 16575

8775 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 70);