AGL(1,𝔽₇)×D₄₅₅ #50304049

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

Aliases

direct product	AGL(1,𝔽₇)×D₄₅₅
unambiguous semidirect product	D₇⋊(C₃×D₄₅₅)
unambiguous semidirect product	(C₅×AGL(1,𝔽₇))⋊D₉₁
unambiguous semidirect product	(C₇×AGL(1,𝔽₇))⋊D₆₅
unambiguous semidirect product	(C₁₃×AGL(1,𝔽₇))⋊D₃₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁

168 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.

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

μ_t(G) = 2730

1603 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 735);