D₃×C₄₁×(C₅⋊D₅)⋊C₃ #49147016

order	36900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄₁ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₃×C₄₁×(C₅⋊D₅)⋊C₃
unambiguous semidirect product	(D₃×C₅⋊D₅)⋊(C₃×C₄₁)
unambiguous semidirect product	(D₃×C₄₁×C₅⋊D₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₄₁	D₃×(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₄₁	C₂²×C₃
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₄₁

128 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.

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

μ_t(G) = 1845

1230 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 417);