Finite Group Databasebeta

← Group #10696861

Character table — Group #10696861

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888888888888888881616161616164848484848484848
order12222234466612121212444446612121212121288888888121224242424242424242424242424242424882424242444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111
χ92222222222222222-2-2-22-222-2-222-2-200000000-2-200000000000000000000002-2000000
χ102222222222222222-2-2-22-222-2-222-2-200000000-2-20000000000000000000000-22000000
χ112222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-200000000000000000000000000002i−2i
χ122222222-2-2222-2-2-2-222-2-2-22222-2-2-2-2000000002-20000000000000000000000000000−2i2i
χ132222222-2-2222-2-2-2-2-2-22-2222-2-2-2-222000022-2-2-22000000002222-2-2-2-200000000000000
χ142222222-2-2222-2-2-2-2-2-22-2222-2-2-2-2220000-2-222-2200000000-2-2-2-2222200000000000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000
χ19222222-1-2-2-1-1-11111-2-22-22-1-11111-1-1000022-2-21-13333−3−3−3−3-1-1-1-111110033−3−300000000
χ20222222-1-2-2-1-1-11111-2-22-22-1-11111-1-1000022-2-21-1−3−3−3−33333-1-1-1-1111100−3−33300000000
χ21222222-1-2-2-1-1-11111-2-22-22-1-11111-1-10000-2-2221-13333−3−3−3−31111-1-1-1-100−3−33300000000
χ22222222-1-2-2-1-1-11111-2-22-22-1-11111-1-10000-2-2221-1−3−3−3−333331111-1-1-1-10033−3−300000000
χ232222-2-222222222222-22-2-2-2-222-2-22200000000-2-2000000000000000000000000200-200
χ242222-2-222222222222-22-2-2-2-222-2-22200000000-2-2000000000000000000000000-200200
χ252222-2-22222222222-22-2-22-2-2-2-2-2-2-2-2000000002200000000000000002-22-22-200000000
χ262222-2-22222222222-22-2-22-2-2-2-2-2-2-2-200000000220000000000000000-22-22-2200000000
χ272222-2-22-2-2222-2-2-2-22-2-222-2-22222-2-222-2-20000-2222-2-222-2-20000000000000000000000
χ282222-2-22-2-2222-2-2-2-22-2-222-2-22222-2-2-2-2220000-22-2-222-2-2220000000000000000000000
χ292222-2-22-2-2222-2-2-2-2-2222-2-2-2-2-22222000000002-200000000000000000000000002-2000
χ302222-2-22-2-2222-2-2-2-2-2222-2-2-2-2-22222000000002-20000000000000000000000000-22000
χ312222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-133−3−3−3−33333−3−333−3−32-2-11-1100000000
χ322222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-133−3−3−3−333−3−333−3−333-221-11-100000000
χ332222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-1−3−33333−3−333−3−333−3−3-221-11-100000000
χ342222-2-2-122-1-1-1-1-1-1-1-22-2-221111111100000000-1-1−3−33333−3−3−3−333−3−3332-2-11-1100000000
χ352222-2-2-1-2-2-1-1-111112-2-22211-1-1-1-11122-2-200001-1-1-111-1-11133−3−3−3−33300−333−300000000
χ362222-2-2-1-2-2-1-1-111112-2-22211-1-1-1-11122-2-200001-1-1-111-1-111−3−33333−3−3003−3−3300000000
χ372222-2-2-1-2-2-1-1-111112-2-22211-1-1-1-111-2-22200001-111-1-111-1-133−3−3−3−333003−3−3300000000
χ382222-2-2-1-2-2-1-1-111112-2-22211-1-1-1-111-2-22200001-111-1-111-1-1−3−33333−3−300−333−300000000
χ39444444-244-2-2-2-2-2-2-2-4-4-44-4-2-222-2-2220000000022000000000000000000000000000000
χ40444444-2-4-4-2-2-2222244-4-4-4-2-2-2-2222200000000-22000000000000000000000000000000
χ414444-4-4-244-2-2-2-2-2-2-24-44-4-422-2-222-2-20000000022000000000000000000000000000000
χ424444-4-4-2-4-4-2-2-22222-4444-42222-2-2-2-200000000-22000000000000000000000000000000
χ4344-4-44-44004-4-40000000004-400000000000022−220000000000000022−2222−2200000000000000
χ4444-4-44-44004-4-40000000004-4000000000000−222200000000000000−2222−222200000000000000
χ4544-4-44-4-200-2222323−23−2300000-220023−230000000022−2200000000006−66−6−22−2200000000000000
χ4644-4-44-4-200-2222323−23−2300000-220023−2300000000−22220000000000−66−662−22−200000000000000
χ4744-4-44-4-200-222−23−23232300000-2200−23230000000022−220000000000−66−66−22−2200000000000000
χ4844-4-44-4-200-222−23−23232300000-2200−232300000000−222200000000006−66−62−22−200000000000000
χ4944-4-4-444004-4-4000000000-44000000000022−2200000000000022−22−2222000000000000000000
χ5044-4-4-444004-4-4000000000-440000000000−2222000000000000−222222−22000000000000000000
χ5144-4-4-44-200-2222323−23−23000002-200−232300000022−22000000000000−222−2−666−600000000000000
χ5244-4-4-44-200-2222323−23−23000002-200−2323000000−22220000000000002−2−226−6−6600000000000000
χ5344-4-4-44-200-222−23−232323000002-20023−2300000022−22000000000000−222−26−6−6600000000000000
χ5444-4-4-44-200-222−23−232323000002-20023−23000000−22220000000000002−2−22−666−600000000000000
χ554-4-440044-4-44-44-44-400000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ564-4-440044-4-44-44-44-40000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ574-4-44004-44-44-4-44-4400000000000002i−2i−2i2i0000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ584-4-44004-44-44-4-44-440000000000000−2i2i2i−2i000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ594-4-4400-24-42-22-22-22000000023−230023−232i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000
χ604-4-4400-24-42-22-22-22000000023−230023−23−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000
χ614-4-4400-24-42-22-22-220000000−232300−23232i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000
χ624-4-4400-24-42-22-22-220000000−232300−2323−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000
χ634-4-4400-2-442-222-22-2000000023−2300−23232i−2i−2i2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000
χ644-4-4400-2-442-222-22-2000000023−2300−2323−2i2i2i−2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000
χ654-4-4400-2-442-222-22-20000000−23230023−232i−2i−2i2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000
χ664-4-4400-2-442-222-22-20000000−23230023−23−2i2i2i−2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000
χ678-88-800800-8-88000000000000000000000000000000000000000000000000000000000
χ688-88-800-40044-443−43−434300000000000000000000000000000000000000000000000000000
χ698-88-800-40044-4−434343−4300000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.