C₂×C₃×C₁₉⋊C₃×D₅₃ #49136289

order	36252
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃×C₁₉⋊C₃×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂²×C₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₅₃)⋊(C₂×C₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₁₉×D₅₃)⋊C₃²
unambiguous semidirect product	(C₂×C₃×C₁₉×D₅₃)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₉⋊C₃×D₅₃
commutator, cosocle, hypocenter	C₁₉×C₅₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₅₃	C₂×C₃
LCS	G ▷ C₁₉×C₅₃
UCS	C₁ ◁ C₂×C₃

120 conjugacy classes of subgroups.

μ_t(G) = 6042

1512 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 88);