C₂×C₃²×C₄₁×C₅⋊D₅ #49147207

order	36900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₄₁ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₃²×C₄₁×C₅⋊D₅
unambiguous semidirect product	(C₂×C₅)⋊(C₃²×D₅×C₄₁)

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₄₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃²×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₄₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃²×C₄₁

480 conjugacy classes of subgroups.

μ_t(G) = 18450

10332 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 608);