C₂×D₃×C₇×C₁₇×C₂₃ #45659332

order	32844
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₇×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₇×C₁₇×C₂₃
unambiguous semidirect product	C₃⋊(C₂²×C₇×C₁₇×C₂₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₇×C₁₇×C₂₃)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₇×C₂₃	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₇×C₁₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₇×C₂₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇×C₁₇×C₂₃

80 conjugacy classes of subgroups.

μ_t(G) = 16422

16422 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 97);