Finite Group Databasebeta

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C₂×#20266221 #27187899

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 119 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 21277);