C₅×D₃²×C₇×C₁₉ #37561552

order	23940
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₃²×C₇×C₁₉
unambiguous semidirect product	(C₃×D₃)⋊(C₂×C₅×C₇×C₁₉)
unambiguous semidirect product	(C₃⋊D₃)⋊(C₂×C₅×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₉	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₇×C₁₉

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

normal subgroups only

This group has 176 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) = 3990

5985 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 684);