C₁₃×C₅₂₃⋊C₃ #35205198

order	20397
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₅₂₃⋊C₃
unambiguous semidirect product	C₅₂₃⋊(C₃×C₁₃)

Fitting, socle, Hall	C₁₃×C₅₂₃ ⋊ C₃
derived, Sylow	C₅₂₃ ⋊ C₃×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	C₅₂₃⋊C₃
commutator, cosocle, hypocenter	C₅₂₃	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₅₂₃	C₃
LCS	G ▷ C₅₂₃
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

μ_t(G) = 6799

2301 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20397, 2);