D₃×#16860815 #37562967

order	24102
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×#16860815
unambiguous semidirect product	C₃⋊(C₂×#16860815)

Splittings

Fitting, socle, derived	C₃×C₁₃×C₁₀₃ ⋊ C₂×C₃
Hall	C₃×#16860815 ⋊ C₂
Hall	C₁₃×C₁₀₃ ⋊ C₃×D₃
Sylow	C₁₀₃ ⋊ D₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ D₃×C₁₀₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₁₀₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₁₀₃
UCS	C₁

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 4017

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

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

Conjugacy classes & character table

1347 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24102, 53);

D3×#16860815 #37562967