C₂×C₃×C₃⋊(C₅⋊D₁₁₅) #35208249

order	20700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₃×C₃⋊(C₅⋊D₁₁₅)
unambiguous semidirect product	(C₂×C₃)⋊(C₃×C₅⋊D₁₁₅)
unambiguous semidirect product	(C₂×C₅)⋊(C₃×D₃₄₅)
unambiguous semidirect product	(C₂×C₂₃)⋊(C₃×C₃⋊(C₅⋊D₅))

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(C₅⋊D₁₁₅)
commutator, cosocle, hypocenter	C₃×C₅²×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₂₃	C₂
LCS	G ▷ C₃×C₅²×C₂₃
UCS	C₁ ◁ C₂×C₃

352 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

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

μ_t(G) = 6900

5184 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 365);