Finite Group Databasebeta

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C₂×#20256538 #27122801

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 113 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)(53,67)(58,81)(63,91)(68,95)(69,96)(78,104)(82,106)(83,100)(89,111)(92,103)(93,101)(97,110)(98,113)(99,107)(105,109)(108,112);(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)(50,53)(51,58)(52,63)(54,68)(55,69)(56,67)(57,78)(59,82)(60,83)(61,81)(62,89)(64,92)(65,93)(66,91)(70,97)(71,98)(72,96)(73,99)(74,95)(75,100)(76,101)(77,103)(79,105)(80,104)(84,107)(85,108)(86,106)(87,109)(88,110)(90,111)(94,112)(102,113);(50,52,56,66)(51,57,61,80)(53,63,67,91)(54,71,74,102)(55,76,72,65)(58,78,81,104)(59,85,86,94)(60,87,75,79)(62,88,90,70)(64,84,77,73)(68,98,95,113)(69,101,96,93)(82,108,106,112)(83,109,100,105)(89,110,111,97)(92,107,103,99);(50,51,56,61)(52,62,66,90)(53,58,67,81)(54,70,74,88)(55,75,72,60)(57,77,80,64)(59,84,86,73)(63,89,91,111)(65,94,76,85)(68,97,95,110)(69,100,96,83)(71,87,102,79)(78,103,104,92)(82,107,106,99)(93,112,101,108)(98,109,113,105);(48,49)

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076091);