C₃×D₅×ΓL(1,𝔽₈)⋊D₁₉ #37561284

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

Aliases

direct product	C₃×D₅×ΓL(1,𝔽₈)⋊D₁₉
unambiguous semidirect product	(D₅×ΓL(1,𝔽₈))⋊(C₃×D₁₉)

	subgroup	G/H
center, hypercenter	C₃	D₅×ΓL(1,𝔽₈)⋊D₁₉
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₃

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

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

μ_t(G) = 1995

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 416);