AGL(1,𝔽₇)×D₂₈₅ #37561347

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

Aliases

direct product	AGL(1,𝔽₇)×D₂₈₅
unambiguous semidirect product	D₇⋊(C₃×D₂₈₅)
unambiguous semidirect product	(C₃×AGL(1,𝔽₇))⋊D₉₅
unambiguous semidirect product	(C₅×AGL(1,𝔽₇))⋊D₅₇
unambiguous semidirect product	(C₁₉×AGL(1,𝔽₇))⋊D₁₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₅×C₇×C₁₉
UCS	C₁

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

normal subgroups only

This group has 176 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) = 1995

1008 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 479);