C₅×C₃⋊D₃×D₄₁⋊C₅ #49146979

order	36900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅² · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₅×C₃⋊D₃×D₄₁⋊C₅
unambiguous semidirect product	D₄₁⋊(C₅²×C₃⋊D₃)
unambiguous semidirect product	(C₃×D₄₁⋊C₅)⋊(C₅×D₃)
unambiguous semidirect product	(C₃⋊D₃×D₄₁)⋊C₅²
unambiguous semidirect product	(C₅×C₃⋊D₃×D₄₁)⋊C₅

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₃×D₄₁⋊C₅
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₄₁	C₂²×C₅
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₅

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

normal subgroups only

This group has 480 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) = 1845

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 380);