C₂×C₅⋊(C₁₃⋊#64418) #50304273

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

Aliases

direct product	C₂×C₅⋊(C₁₃⋊#64418)
unambiguous semidirect product	(C₂×C₅)⋊(C₁₃⋊#64418)
unambiguous semidirect product	(C₂×C₁₃)⋊(C₅⋊#64418)

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₁₃⋊#64418)
commutator, cosocle, hypocenter	C₅×C₁₃×#3862	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	D₃
LCS	G ▷ C₅×C₁₃×#3862
UCS	C₁ ◁ C₂

136 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 1820

1256 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 959);