C₃×C₁₃⋊D₄₀₃ #44537697

order	31434
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₃

Aliases

direct product

C₃×C₁₃⋊D₄₀₃

Splittings

Fitting, socle, Hall	C₃×C₁₃²×C₃₁ ⋊ C₂
derived, Hall	C₁₃²×C₃₁ ⋊ C₂×C₃
Hall	C₃×C₁₃² ⋊ D₃₁
Sylow	C₁₃² ⋊ C₃×D₃₁
Hall	C₃×C₃₁ ⋊ C₁₃⋊D₁₃
Sylow	C₃₁ ⋊ C₃×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊D₄₀₃
commutator, cosocle, hypocenter	C₁₃²×C₃₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₃₁	C₂
LCS	G ▷ C₁₃²×C₃₁
UCS	C₁ ◁ C₃

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 15717

A minimal faithful permutation representation — 3 generators on 60 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60);(17,18,20,22,24,26,28,29,27,25,23,21,19)(30,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32);(4,5,7,9,11,13,15,16,14,12,10,8,6)

Conjugacy classes & character table

7863 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31434, 94);

C3×C13⋊D403 #44537697