Dic₅×ΓL(1,𝔽₈)×C₁₉⋊C₃ #37561083

order	23940
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

direct product	Dic₅×ΓL(1,𝔽₈)×C₁₉⋊C₃
unambiguous semidirect product	(C₇×Dic₅×C₁₉⋊C₃)⋊C₃
unambiguous semidirect product	(C₁₉×Dic₅×ΓL(1,𝔽₈))⋊C₃
unambiguous semidirect product	(Dic₅×#87704)⋊C₃
unambiguous semidirect product	(Dic₅×#87705)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×ΓL(1,𝔽₈)×C₁₉⋊C₃
commutator, hypocenter	C₅×C₇×C₁₉	C₃²×C₄
Fitting, socle, cosocle	C₂×C₅×C₇×C₁₉	C₂×C₃²
prime radical	C₂×C₅×ΓL(1,𝔽₈)×C₁₉⋊C₃	C₂
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂

144 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

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

μ_t(G) = 2660

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 215);