Finite Group Databasebeta

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C₂×#20276691 #27538037

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 323513);