C₂×C₇×D₅×C₁₃×ΓL(1,𝔽₈) #50304276

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₅×C₁₃×ΓL(1,𝔽₈)
unambiguous semidirect product	C₅⋊(C₂²×C₇×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₇×C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₂×C₇×D₅)⋊(C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃	D₅×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₇×C₁₃

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

normal subgroups only

This group has 200 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

3640 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 962);