C₅×D₇×C₃⋊(D₁₉⋊C₃) #37561314

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

Aliases

direct product	C₅×D₇×C₃⋊(D₁₉⋊C₃)
unambiguous semidirect product	(D₇×C₁₉⋊C₃)⋊(C₅×D₃)

	subgroup	G/H
center, hypercenter	C₅	D₇×C₃⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₅

176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

μ_t(G) = 1995

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 446);