C₇×D₅×D₉×C₁₉ #37561017

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₅×D₉×C₁₉
unambiguous semidirect product	(C₅×D₉)⋊(C₂×C₇×C₁₉)
unambiguous semidirect product	(C₉×D₅)⋊(C₂×C₇×C₁₉)
unambiguous semidirect product	D₄₅⋊(C₂×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉	D₅×D₉
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₇×C₁₉
Frattini	C₃	D₃×C₇×D₅×C₁₉
Fitting	C₅×C₇×C₉×C₁₉	C₂²
socle	C₃×C₅×C₇×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₇×C₁₉

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

normal subgroups only

This group has 120 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) = 5985

3192 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 149);