C₁₃×C₈₅₃⋊C₃ #45685357

order	33267
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₈₅₃⋊C₃
unambiguous semidirect product	C₈₅₃⋊(C₃×C₁₃)

Fitting, socle, Hall	C₁₃×C₈₅₃ ⋊ C₃
derived, Sylow	C₈₅₃ ⋊ C₃×C₁₃

	subgroup	G/H
center, hypercenter	C₁₃	C₈₅₃⋊C₃
commutator, cosocle, hypocenter	C₈₅₃	C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₈₅₃	C₃
LCS	G ▷ C₈₅₃
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

μ_t(G) = 11089

3731 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33267, 2);