C₂×C₃×C₇×D₅×C₁₉⋊C₃ #37561450

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃×C₇×D₅×C₁₉⋊C₃
unambiguous semidirect product	C₅⋊(C₂²×C₃×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃×C₇×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×D₅×C₁₉)⋊(C₃²×C₇)
unambiguous semidirect product	(C₂×C₃×D₅×C₁₉)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇	D₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₃×C₇

240 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

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

μ_t(G) = 3990

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 582);