C₂×C₃×C₇×C₁₃×D₁₇ #32915641

order	18564
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×C₇×C₁₃×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂²×C₃×C₇×C₁₃)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₂×C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂²×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₃×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

80 conjugacy classes of subgroups.

μ_t(G) = 9282

5460 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 236);