C₅×ΓL(1,𝔽₈)×C₂²⋊(C₁₉⋊C₃) #37561428

order	23940
automorphism	?
homology	Abelianization (H₁) = C₃²×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₅×ΓL(1,𝔽₈)×C₂²⋊(C₁₉⋊C₃)
unambiguous semidirect product	(C₂²×ΓL(1,𝔽₈))⋊(C₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₁₉×ΓL(1,𝔽₈))⋊(C₅×A₄)
unambiguous semidirect product	(C₂²×C₅×ΓL(1,𝔽₈))⋊(C₁₉⋊C₃)
unambiguous semidirect product	(C₅×C₁₉×ΓL(1,𝔽₈))⋊A₄

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

112 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 2660

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 560);