C₃²×C₇×D₅×D₁₉ #37561514

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃²×C₇×D₅×D₁₉

	subgroup	G/H
center, hypercenter	C₃²×C₇	D₅×D₁₉
commutator, cosocle, hypocenter	C₅×C₁₉	C₂²×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃²×C₇

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

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

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

μ_t(G) = 5985

2772 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 646);