Dic₃×#15667865 #46802776

order	34164
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×#15667865
unambiguous semidirect product	C₃⋊(C₄×#15667865)

Splittings

derived	C₃×C₁₃×C₇₃ ⋊ C₃×C₄
Hall	C₃×#15667865 ⋊ C₄
Hall	C₁₃×C₇₃ ⋊ C₃×Dic₃
Sylow	C₇₃ ⋊ Dic₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ Dic₃×C₇₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#15667865
commutator, hypocenter	C₃×C₁₃×C₇₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₇₃	C₂×C₃
prime radical	C₂×C₃×#15667865	C₂
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁ ◁ C₂

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 11388

A minimal faithful permutation representation — 2 generators on 93 points:

(2,3)(4,5,6,7)(9,10,12)(11,14,18)(13,16,15)(17,19,20)(22,23,25)(24,27,32)(26,30,29)(28,34,42)(31,37,39)(33,40,36)(35,44,55)(38,47,52)(41,50,49)(43,53,46)(45,57,70)(48,60,67)(51,58,64)(54,65,62)(56,68,59)(61,73,82)(63,74,79)(66,78,77)(69,80,75)(71,83,72)(76,86,89)(81,88,87)(84,90,85)(91,93,92);(1,2,3)(8,9,11,12,15,14,18,20,19,10,13,17,16)(21,22,24,28,35,45,58,37,23,26,31,38,48,61,74,47,27,33,41,51,63,76,86,60,34,43,54,66,70,82,89,73,44,56,69,81,83,55,67,79,57,71,84,91,90,68,42,52,64,77,87,92,93,80,53,32,39,49,62,75,85,88,65,40,25,29,36,46,59,72,78,50,30)

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34164, 142);

Dic3×#15667865 #46802776