C₇×D₁₅×D₁₉⋊C₃ #37561334

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

Aliases

direct product	C₇×D₁₅×D₁₉⋊C₃
unambiguous semidirect product	D₁₉⋊(C₃×C₇×D₁₅)
unambiguous semidirect product	(C₃×D₁₉⋊C₃)⋊(C₇×D₅)
unambiguous semidirect product	(C₅×D₁₉⋊C₃)⋊(D₃×C₇)
unambiguous semidirect product	(D₁₅×D₁₉)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₇	D₁₅×D₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₁₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₅×C₁₉
UCS	C₁ ◁ C₇

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 1995

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 466);