Dic₃×#15668332 #46829358

order	34596
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×#15668332
unambiguous semidirect product	C₃⋊(C₄×#15668332)

Splittings

derived	C₃×C₃₁² ⋊ C₃×C₄
Hall	C₃×#15668332 ⋊ C₄
Sylow	C₃₁² ⋊ C₃×Dic₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#15668332
commutator, hypocenter	C₃×C₃₁²	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₃₁²	C₂×C₃
prime radical	C₂×C₃×#15668332	C₂
LCS	G ▷ C₃×C₃₁²
UCS	C₁ ◁ C₂

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 11532

A minimal faithful permutation representation — 3 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)(49,55,57)(51,53,54)(56,62,66)(58,63,64)(60,67,61)(65,68,69);(1,2,3)(39,40,42,46,53,43,47,54,61,67,50,57,64,52,60,59,66,69,62,45,51,58,65,68,55,41,44,49,56,63,48);(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)

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, 118);

Dic3×#15668332 #46829358