C₃×D₄₁₈₃ #38737191

order	25098
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₁₈₃
unambiguous semidirect product	C₄₇⋊(C₃×D₈₉)
unambiguous semidirect product	C₈₉⋊(C₃×D₄₇)

Splittings

Fitting, socle, Hall	C₃×C₄₇×C₈₉ ⋊ C₂
derived, Hall	C₄₇×C₈₉ ⋊ C₂×C₃
Hall	C₃×C₈₉ ⋊ D₄₇
Hall	C₃×C₄₇ ⋊ D₈₉
Sylow	C₈₉ ⋊ C₃×D₄₇
Sylow	C₄₇ ⋊ C₃×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₁₈₃
commutator, cosocle, hypocenter	C₄₇×C₈₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₄₇×C₈₉	C₂
LCS	G ▷ C₄₇×C₈₉
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 139
transitive degree	μ_t(G) = 12549

A minimal faithful permutation representation — 2 generators on 139 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50)(51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139);(5,50)(6,49)(7,48)(8,47)(9,46)(10,45)(11,44)(12,43)(13,42)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(52,139)(53,138)(54,137)(55,136)(56,135)(57,134)(58,133)(59,132)(60,131)(61,130)(62,129)(63,128)(64,127)(65,126)(66,125)(67,124)(68,123)(69,122)(70,121)(71,120)(72,119)(73,118)(74,117)(75,116)(76,115)(77,114)(78,113)(79,112)(80,111)(81,110)(82,109)(83,108)(84,107)(85,106)(86,105)(87,104)(88,103)(89,102)(90,101)(91,100)(92,99)(93,98)(94,97)(95,96)

Conjugacy classes & character table

6279 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25098, 4);

C3×D4183 #38737191