D₃×#19149507 #45684341

order	33174
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#19149507
unambiguous semidirect product	C₃⋊(C₂×#19149507)

Splittings

Fitting, socle, derived	C₃×C₁₉×C₉₇ ⋊ C₂×C₃
Hall	C₃×#19149507 ⋊ C₂
Hall	C₁₉×C₉₇ ⋊ C₃×D₃
Sylow	C₉₇ ⋊ D₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ D₃×C₉₇⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₉₇	C₂×C₃
LCS	G ▷ C₃×C₁₉×C₉₇
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 5529

A minimal faithful permutation representation — 2 generators on 119 points:

(2,3)(5,6,8)(7,10,11)(9,13,12)(14,18,16)(15,19,17)(20,22,21)(24,25,27)(26,29,34)(28,32,31)(30,36,44)(33,39,41)(35,42,38)(37,46,57)(40,49,54)(43,52,51)(45,55,48)(47,59,73)(50,62,70)(53,65,67)(56,68,64)(58,71,61)(60,75,81)(63,77,88)(66,80,85)(69,83,82)(72,86,79)(74,89,76)(78,93,95)(84,97,99)(87,100,96)(90,102,94)(91,98,92)(101,108,107)(103,110,106)(104,109,105)(111,115,114)(112,116,113)(117,119,118);(1,2,3)(4,5,7,11,16,21,18,6,9,14,19,8,12,17,10,15,20,22,13)(23,24,26,30,37,47,60,62,36,45,56,69,84,98,73,88,75,91,104,112,117,119,110,86,55,34,41,51,64,79,94,105,97,65,39,25,28,33,40,50,63,78,77,46,58,72,87,101,109,89,57,70,85,99,107,114,118,115,100,68,42,27,31,38,48,61,76,92,80,49,29,35,43,53,66,81,95,93,59,74,90,103,111,116,102,71,44,54,67,82,96,106,113,108,83,52,32)

Conjugacy classes & character table

1851 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33174, 65);

D3×#19149507 #45684341