C₂×C₅⋊(D₁₃⋊#3862) #50304327

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

Aliases

direct product	C₂×C₅⋊(D₁₃⋊#3862)
unambiguous semidirect product	(C₂×C₅)⋊(D₁₃⋊#3862)
unambiguous semidirect product	(C₂×D₆₅)⋊#3862

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(D₁₃⋊#3862)
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

200 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

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

μ_t(G) = 2730

1132 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1013);