D₃×#19153444 #46829403

order	34596
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₃₁

Aliases

direct product

D₃×#19153444

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

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 279

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)(36,40,41,37,38,42)(39,48,49,43,44,56)(45,58,59,51,52,64)(46,57,53,54,50,47)(55,65,62,61,60,63);(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)(35,36,39,45,53,41,40,46,55,62,49,57,48,52,60,59,64,65,58,44,50,56,63,61,54,38,42,47,51,43,37)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 163);

D3×#19153444 #46829403