Dic₃×#15668333 #46829359

order	34596
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₃₁

Aliases

direct product	Dic₃×#15668333
unambiguous semidirect product	C₃⋊(C₄×#15668333)

Splittings

derived	C₃×C₃₁² ⋊ C₃×C₄
Hall	C₃×#15668333 ⋊ C₄
Sylow	C₃₁² ⋊ C₃×Dic₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#15668333
commutator, hypocenter	C₃×C₃₁²	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₃₁²	C₂×C₃
prime radical	C₂×C₃×#15668333	C₂
LCS	G ▷ C₃×C₃₁²
UCS	C₁ ◁ C₂

116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1116

A minimal faithful permutation representation — 2 generators on 69 points:

(2,3)(4,5,6,7)(9,10,12)(11,14,19)(13,17,16)(15,21,28)(18,24,26)(20,22,23)(25,31,35)(27,32,33)(29,36,30)(34,37,38)(40,41,43)(42,45,50)(44,48,47)(46,52,59)(49,53,56)(51,57,54)(55,62,65)(58,64,63)(60,66,61)(67,69,68);(1,2,3)(8,9,11,15,22,12,16,23,30,36,19,26,33,21,29,28,35,38,31,14,20,27,34,37,24,10,13,18,25,32,17)(39,40,42,46,53,41,44,49,55,62,45,51,58,59,65,52,60,67,66,50,56,63,68,69,57,43,47,54,61,64,48)

Conjugacy classes & character table

1938 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34596, 119);

Dic3×#15668333 #46829359