D₃×C₇²×D₅×C₁₃ #50304451

order	38220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇²×C₁₃ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	D₃×C₇²×D₅×C₁₃
unambiguous semidirect product	(C₅×D₃)⋊(C₂×C₇²×C₁₃)
unambiguous semidirect product	(C₃×D₅)⋊(C₂×C₇²×C₁₃)
unambiguous semidirect product	D₁₅⋊(C₂×C₇²×C₁₃)

	subgroup	G/H
center, hypercenter	C₇²×C₁₃	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₇²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇²×C₁₃

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

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.

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

μ_t(G) = 9555

7644 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1137);