C₅₃×C₁₉₃⋊C₃ #44501631

order	30687
automorphism	?
homology	Abelianization (H₁) = C₃×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×C₁₉₃⋊C₃
unambiguous semidirect product	C₁₉₃⋊(C₃×C₅₃)
unambiguous semidirect product	(C₅₃×C₁₉₃)⋊C₃

Fitting, socle, Hall	C₅₃×C₁₉₃ ⋊ C₃
derived, Sylow	C₁₉₃ ⋊ C₃×C₅₃

	subgroup	G/H
center, hypercenter	C₅₃	C₁₉₃⋊C₃
commutator, cosocle, hypocenter	C₁₉₃	C₃×C₅₃
Frattini	C₁	G
Fitting, socle	C₅₃×C₁₉₃	C₃
LCS	G ▷ C₁₉₃
UCS	C₁ ◁ C₅₃

8 conjugacy classes of subgroups.

μ_t(G) = 10229

3551 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30687, 1);