C₂×C₅×D₃×C₁₃×ΓL(1,𝔽₈) #30655591

order	16380
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₁₃×ΓL(1,𝔽₈)
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×D₃×C₇)⋊(C₃×C₅×C₁₃)
unambiguous semidirect product	(C₂×C₅×D₃×C₇)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃	D₃×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₅×C₁₃

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

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

μ_t(G) = 2730

1950 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 641);