C₃×D₄₈₉₇ #44440445

order	29382
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₈₉₇
unambiguous semidirect product	C₅₉⋊(C₃×D₈₃)
unambiguous semidirect product	C₈₃⋊(C₃×D₅₉)

Splittings

Fitting, socle, Hall	C₃×C₅₉×C₈₃ ⋊ C₂
derived, Hall	C₅₉×C₈₃ ⋊ C₂×C₃
Hall	C₃×C₈₃ ⋊ D₅₉
Hall	C₃×C₅₉ ⋊ D₈₃
Sylow	C₈₃ ⋊ C₃×D₅₉
Sylow	C₅₉ ⋊ C₃×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₈₉₇
commutator, cosocle, hypocenter	C₅₉×C₈₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅₉×C₈₃	C₂
LCS	G ▷ C₅₉×C₈₃
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 145
transitive degree	μ_t(G) = 14691

A minimal faithful permutation representation — 2 generators on 145 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)(63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145);(5,62)(6,61)(7,60)(8,59)(9,58)(10,57)(11,56)(12,55)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)(64,145)(65,144)(66,143)(67,142)(68,141)(69,140)(70,139)(71,138)(72,137)(73,136)(74,135)(75,134)(76,133)(77,132)(78,131)(79,130)(80,129)(81,128)(82,127)(83,126)(84,125)(85,124)(86,123)(87,122)(88,121)(89,120)(90,119)(91,118)(92,117)(93,116)(94,115)(95,114)(96,113)(97,112)(98,111)(99,110)(100,109)(101,108)(102,107)(103,106)(104,105)

Conjugacy classes & character table

7350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29382, 4);

C3×D4897 #44440445