C₂×C₁₃×ΓL(1,𝔽₈)×D₁₅ #30655607

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

Aliases

direct product	C₂×C₁₃×ΓL(1,𝔽₈)×D₁₅
unambiguous semidirect product	(C₂×C₃)⋊(D₅×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₅)⋊(D₃×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₇×D₁₅)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₁₃	ΓL(1,𝔽₈)×D₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₂×C₁₃

176 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

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

μ_t(G) = 2730

1170 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 657);