D₃×D₂₅×C₁₉⋊C₃ #30685473

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₂₅×C₁₉⋊C₃
unambiguous semidirect product	(D₃×C₂₅)⋊(C₂×C₁₉⋊C₃)
unambiguous semidirect product	(C₃×D₂₅)⋊(C₂×C₁₉⋊C₃)
unambiguous semidirect product	D₇₅⋊(C₂×C₁₉⋊C₃)
unambiguous semidirect product	(D₃×C₁₉×D₂₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₁₉×C₂₅	C₂²×C₃
Frattini	C₅	D₃×D₅×C₁₉⋊C₃
socle	C₃×C₅×C₁₉	C₂×C₃×D₅
LCS	G ▷ C₃×C₁₉×C₂₅
UCS	C₁

132 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 1425

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 110);