C₁₃×D₁₅×AGL(1,𝔽₇) #30655458

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×D₁₅×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₁₃×D₁₅)
unambiguous semidirect product	(C₃×AGL(1,𝔽₇))⋊(D₅×C₁₃)
unambiguous semidirect product	(C₅×AGL(1,𝔽₇))⋊(D₃×C₁₃)
unambiguous semidirect product	(D₇×D₁₅)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₁₅×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₁₃

176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

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

μ_t(G) = 1365

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 508);