D₃×#19153446 #46829397

order	34596
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₃×#19153446

Splittings

Fitting, socle, derived	C₃×C₃₁² ⋊ C₂²×C₃
Hall	C₃×#15668333 ⋊ C₂²
Sylow	C₃₁² ⋊ C₂×C₃×D₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁²	C₂²×C₃
LCS	G ▷ C₃×C₃₁²
UCS	C₁

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 558

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2,3)(5,9,10,6,7,11)(8,17,18,12,13,25)(14,28,29,20,21,33)(15,27,23,22,19,16)(24,26,34,30,31,32)(36,37,39)(38,41,46)(40,44,43)(42,48,55)(45,51,53)(47,49,50)(52,58,62)(54,59,60)(56,63,57)(61,64,65);(2,3)(4,5,8,14,22,7,11,16,24,31,13,19,25,29,34,21,28,32,33,18,27,17,26,30,23,10,9,15,20,12,6)(35,36,38,42,49,39,43,50,57,63,46,53,60,48,56,55,62,65,58,41,47,54,61,64,51,37,40,45,52,59,44)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 157);

D3×#19153446 #46829397