C₃×C₄₁×D₁₅⋊D₅ #49147125

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

Aliases

direct product	C₃×C₄₁×D₁₅⋊D₅
unambiguous semidirect product	D₁₅⋊(C₃×D₅×C₄₁)

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₁₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₄₁	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃×C₄₁

224 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

μ_t(G) = 1230

3690 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 526);