C₁₃×C₅₂₁⋊C₅ #46799685

order	33865
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₅₂₁⋊C₅
unambiguous semidirect product	(C₁₃×C₅₂₁)⋊C₅

Fitting, socle, Hall	C₁₃×C₅₂₁ ⋊ C₅
derived, Sylow	C₅₂₁ ⋊ C₅×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	C₅₂₁⋊C₅
commutator, cosocle, hypocenter	C₅₂₁	C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₅₂₁	C₅
LCS	G ▷ C₅₂₁
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

μ_t(G) = 6773

1417 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33865, 3);