Finite Group Databasebeta

← Group #10697225

Character table — Group #10697225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212888888881212242424242424242424242424242424248824242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ411111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ9222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2000000002-2000000000000000000000000002i2i−2i−2i0000
χ10222222222-2-2-2-2222-2-2-2-22-2-22222-2-2-2-2000000002-200000000000000000000000000−2i−2i2i2i0000
χ112222222-2-222222222222-2-2-222-2-22-2-2200000000-2-2000000000000000000000022-2-200000000
χ122222222-2-222222222222-2-2-222-2-22-2-2200000000-2-20000000000000000000000-2-22200000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-222-2000022-2-2-222222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-222-20000-2-222-22-2-2-2-2222200000000000000000000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111-1-11000022-2-21-1-1-1-1-111113333−3−3−3−30033−3−3000000000000
χ20222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111-1-11000022-2-21-1-1-1-1-11111−3−3−3−3333300−3−333000000000000
χ21222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111-1-110000-2-2221-11111-1-1-1-13333−3−3−3−300−3−333000000000000
χ22222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111-1-110000-2-2221-11111-1-1-1-1−3−3−3−333330033−3−3000000000000
χ232222-2-22222-22-22222222-22-2-2-222-222-200000000-2-20000000000000000000000000000002-200
χ242222-2-22222-22-22222222-22-2-2-222-222-200000000-2-2000000000000000000000000000000-2200
χ252222-2-2222-22-22222-2-2-2-2-2-22-2-2222-2-2222-2-20000-220000000022-2-222-2-2000000000000000000
χ262222-2-2222-22-22222-2-2-2-2-2-22-2-2222-2-22-2-2220000-2200000000-2-222-2-222000000000000000000
χ272222-2-22-2-22-22-222222222-22-2-2-2-2-2-2-2-2000000002200000000000000002-22-22-2000000000000
χ282222-2-22-2-22-22-222222222-22-2-2-2-2-2-2-2-200000000220000000000000000-22-22-22000000000000
χ292222-2-22-2-2-22-22222-2-2-2-222-2-2-2-2-22222000000002-2000000000000000000000000000000002-2
χ302222-2-22-2-2-22-22222-2-2-2-222-2-2-2-2-22222000000002-200000000000000000000000000000000-22
χ312222-2-2-122-22-22-1-1-11111-2-2211-1-1-111-122-2-200001-133−3−333−3−3-1-111-1-111003−3−33000000000000
χ322222-2-2-122-22-22-1-1-11111-2-2211-1-1-111-122-2-200001-1−3−333−3−333-1-111-1-11100−333−3000000000000
χ332222-2-2-122-22-22-1-1-11111-2-2211-1-1-111-1-2-22200001-133−3−333−3−311-1-111-1-100−333−3000000000000
χ342222-2-2-122-22-22-1-1-11111-2-2211-1-1-111-1-2-22200001-1−3−333−3−33311-1-111-1-1003−3−33000000000000
χ352222-2-2-1-2-22-22-2-1-1-1-1-1-1-12-221111111100000000-1-133−3−3−3−33333−3−3−3−333-221-11-1000000000000
χ362222-2-2-1-2-22-22-2-1-1-1-1-1-1-12-221111111100000000-1-133−3−3−3−333−3−33333−3−32-2-11-11000000000000
χ372222-2-2-1-2-22-22-2-1-1-1-1-1-1-12-221111111100000000-1-1−3−33333−3−333−3−3−3−3332-2-11-11000000000000
χ382222-2-2-1-2-22-22-2-1-1-1-1-1-1-12-221111111100000000-1-1−3−33333−3−3−3−33333−3−3-221-11-1000000000000
χ392-2-222-22002-2-222-2-222-2-20002-200-20020000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200000000000000002-2−i2i2−i2i20000
χ402-2-222-22002-2-222-2-222-2-20002-200-20020000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000000000-22i2−i2i2−i20000
χ412-2-222-22002-2-222-2-222-2-20002-200-20020000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200000000000000002-2i2−i2i2−i20000
χ422-2-222-22002-2-222-2-222-2-20002-200-20020000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000000000-22−i2i2−i2i20000
χ432-2-222-2200-222-22-2-2-2-2220002-200200-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002i−2i002−2−220000
χ442-2-222-2200-222-22-2-2-2-2220002-200200-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000−2i2i00−222−20000
χ452-2-222-2200-222-22-2-2-2-2220002-200200-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002i−2i00−222−20000
χ462-2-222-2200-222-22-2-2-2-2220002-200200-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000−2i2i002−2−220000
χ47444444-244-4-4-4-4-2-2-222224-4-4-2-2-2-2222200000000-220000000000000000000000000000000000
χ48444444-2-4-44444-2-2-2-2-2-2-2-4-4-4-2-222-222-200000000220000000000000000000000000000000000
χ494444-4-4-2444-44-4-2-2-2-2-2-2-2-44-422-2-22-2-2200000000220000000000000000000000000000000000
χ504444-4-4-2-4-4-44-44-2-2-2222244-42222-2-2-2-200000000-220000000000000000000000000000000000
χ5144-4-40044-40000-44-40000000004-400000022−22000000000000000022−220022−22000000000000000000
χ5244-4-40044-40000-44-40000000004-4000000−22220000000000000000−222200−2222000000000000000000
χ5344-4-4004-440000-44-4000000000-44000022−22000000000000000022−220022−2200000000000000000000
χ5444-4-4004-440000-44-4000000000-440000−22220000000000000000−222200−222200000000000000000000
χ5544-4-400-24-400002-2223−2323−2300000-22023−2300022−22000000000000006−6−22−66−22000000000000000000
χ5644-4-400-24-400002-2223−2323−2300000-22023−23000−222200000000000000−662−26−62−2000000000000000000
χ5744-4-400-24-400002-22−2323−232300000-220−232300022−2200000000000000−66−226−6−22000000000000000000
χ5844-4-400-24-400002-22−2323−232300000-220−2323000−2222000000000000006−62−2−662−2000000000000000000
χ5944-4-400-2-4400002-2223−2323−23000002-20−2323022−220000000000000000−226−6−22−66000000000000000000
χ6044-4-400-2-4400002-2223−2323−23000002-20−23230−222200000000000000002−2−662−26−6000000000000000000
χ6144-4-400-2-4400002-22−2323−2323000002-2023−23022−220000000000000000−22−66−226−6000000000000000000
χ6244-4-400-2-4400002-22−2323−2323000002-2023−230−222200000000000000002−26−62−2−66000000000000000000
χ634-4-444-4-2004-4-44-222-2-222000-2200200-20000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ644-4-444-4-2004-4-44-222-2-222000-2200200-200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ654-4-444-4-200-444-4-22222-2-2000-2200-20020000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ664-4-444-4-200-444-4-22222-2-2000-2200-200200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ674-4-44-4440044-4-44-4-444-4-4000-4400400-400000000000000000000000000000000000000000000
χ684-4-44-44400-4-4444-4-4-4-444000-4400-400400000000000000000000000000000000000000000000
χ694-4-44-44-20044-4-4-222-2-2220002-200-20020000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ704-4-44-44-20044-4-4-222-2-2220002-200-20020000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ714-4-44-44-200-4-444-22222-2-20002-200200-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ724-4-44-44-200-4-444-22222-2-20002-200200-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ738-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ758-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).