C₂×C₁₉×C₃⋊#64422 #45692651

order	33516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×C₃⋊#64422
unambiguous semidirect product	(C₂×C₃)⋊(C₁₉×#64422)

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₃⋊#64422
commutator, cosocle, hypocenter	C₃×C₇²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₁₉

184 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 4788

1368 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1449);