D₇×C₁₉×C₃⋊D₁₅ #37561600

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₇×C₁₉×C₃⋊D₁₅
unambiguous semidirect product	(C₃×D₇)⋊(C₁₉×D₁₅)
unambiguous semidirect product	(C₅×D₇)⋊(C₃⋊D₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₇×C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₁₉

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

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

μ_t(G) = 5985

2280 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 732);