C₁₃×(C₅⋊AGL(1,𝔽₇))⋊D₇ #50304052

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×(C₅⋊AGL(1,𝔽₇))⋊D₇
unambiguous semidirect product	(C₅⋊AGL(1,𝔽₇))⋊(C₁₃×D₇)
unambiguous semidirect product	(ΓL(1,𝔽₈)⋊D₇)⋊(D₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	(C₅⋊AGL(1,𝔽₇))⋊D₇
commutator, cosocle, hypocenter	C₅×C₇²	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₁₃

168 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

μ_t(G) = 2730

1027 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 738);