C₄₁×C₁₃₁⋊C₅ #41001675

order	26855
automorphism	?
homology	Abelianization (H₁) = C₅×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×C₁₃₁⋊C₅
unambiguous semidirect product	C₁₃₁⋊(C₅×C₄₁)

Fitting, socle, Hall	C₄₁×C₁₃₁ ⋊ C₅
derived, Sylow	C₁₃₁ ⋊ C₅×C₄₁

	subgroup	G/H
center, hypercenter	C₄₁	C₁₃₁⋊C₅
commutator, cosocle, hypocenter	C₁₃₁	C₅×C₄₁
Frattini	C₁	G
Fitting, socle	C₄₁×C₁₃₁	C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₄₁

8 conjugacy classes of subgroups.

μ_t(G) = 5371

1271 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26855, 2);