C₃×D₃×D₆₈₉ #37613732

order	24804
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₃×D₆₈₉
unambiguous semidirect product	(D₃×C₅₃)⋊(C₃×D₁₃)

	subgroup	G/H
center, hypercenter	C₃	D₃×D₆₈₉
commutator, cosocle, hypocenter	C₃×C₁₃×C₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₅₃	C₂²
LCS	G ▷ C₃×C₁₃×C₅₃
UCS	C₁ ◁ C₃

88 conjugacy classes of subgroups.

μ_t(G) = 4134

3114 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 164);