D₃×D₅×#87705 #37561406

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

Aliases

direct product	D₃×D₅×#87705
unambiguous semidirect product	(C₅×D₃)⋊(C₂×#87705)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×#87705)
unambiguous semidirect product	D₁₅⋊(C₂×#87705)

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

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 1995

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 538);