C₂×C₅×D₃×C₇×C₁₉⋊C₃ #37561466

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₇×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×D₃×C₁₉)⋊(C₃×C₅×C₇)
unambiguous semidirect product	(C₂×C₅×D₃×C₁₉)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇	D₃×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₃×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₅×C₇

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

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

μ_t(G) = 3990

1890 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 598);