C₂×C₅⋊#16838460 #50304319

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

Aliases

direct product	C₂×C₅⋊#16838460
unambiguous semidirect product	(C₂×C₅)⋊#16838460

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#16838460
commutator, cosocle, hypocenter	C₅×C₇²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₅×C₇²×C₁₃
UCS	C₁ ◁ C₂

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

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

μ_t(G) = 1820

1250 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1005);