Finite Group Databasebeta

← Group #10697811

Character table — Group #10697811

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ92222222222-2-22-222-22222222-2-2222-2-2-22-200000000-2-200000000000000002222-2-2-2-20000000000000000
χ102222222222-2-22-222-22222222-2-2222-2-2-22-200000000-2-20000000000000000-2-2-2-222220000000000000000
χ11222222222-222-22-2-222222222-2-2-2-2-2222-2200000000-2-200000000000000000000000000000022-2-2000000
χ12222222222-222-22-2-222222222-2-2-2-2-2222-2200000000-2-2000000000000000000000000000000-2-222000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22i2i−2i−2i0000222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2−2i−2i2i2i000022−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i0000-1-1−i−i−i−iiiii3333−3−3−3−30000000000−i3−i3i3i30000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i0000-1-1−i−i−i−iiiii−3−3−3−333330000000000i3i3−i3−i30000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i0000-1-1iiii−i−i−i−i3333−3−3−3−30000000000i3i3−i3−i30000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i0000-1-1iiii−i−i−i−i−3−3−3−333330000000000−i3−i3i3i30000000000
χ23222-2-22-2-22200-202-2022-2-22-2-20022-2000-20000022−2−2000000000022−2−222−2−2000022-2-2000000000022−2−200
χ24222-2-22-2-22200-202-2022-2-22-2-20022-2000-20000022−2−2000000000022−2−222−2−20000-2-2220000000000−2−22200
χ25222-2-22-2-22200-202-2022-2-22-2-20022-2000-200000−2−2220000000000−2−222−2−222000022-2-20000000000−2−22200
χ26222-2-22-2-22200-202-2022-2-22-2-20022-2000-200000−2−2220000000000−2−222−2−2220000-2-222000000000022−2−200
χ2722-22-2-22-220220-200-22-22-2-22-20000022-20-22−22−200000022−2−222−2−20000000022−2−22−22−20000002-200000000
χ2822-22-2-22-220220-200-22-22-2-22-20000022-20-22−22−200000022−2−222−2−200000000−2−222−22−22000000-2200000000
χ2922-22-2-22-220220-200-22-22-2-22-20000022-20-2−22−22000000−2−222−2−2220000000022−2−22−22−2000000-2200000000
χ3022-22-2-22-220220-200-22-22-2-22-20000022-20-2−22−22000000−2−222−2−22200000000−2−222−22−220000002-200000000
χ3122-22-2-22-220-2-2020022-22-2-22-200000-2-2202−i2i2i2−i2000000−i2−i2i2i2i2i2−i2−i20000000022−2−2−22−22000000002i−2i000000
χ3222-22-2-22-220-2-2020022-22-2-22-200000-2-2202−i2i2i2−i2000000−i2−i2i2i2i2i2−i2−i200000000−2−2222−22−200000000−2i2i000000
χ3322-22-2-22-220-2-2020022-22-2-22-200000-2-2202i2−i2−i2i2000000i2i2−i2−i2−i2−i2i2i20000000022−2−2−22−2200000000−2i2i000000
χ3422-22-2-22-220-2-2020022-22-2-22-200000-2-2202i2−i2−i2i2000000i2i2−i2−i2−i2−i2i2i200000000−2−2222−22−2000000002i−2i000000
χ352-2-2222-2-22200-20-220-2-2222-2-2002-22000-2000002−22−200000000002−22−22−22−22-22-2000000000000002−22−200
χ362-2-2222-2-22200-20-220-2-2222-2-2002-22000-2000002−22−200000000002−22−22−22−2-22-2200000000000000−22−2200
χ372-2-2222-2-22200-20-220-2-2222-2-2002-22000-200000−22−220000000000−22−22−22−222-22-200000000000000−22−2200
χ382-2-2222-2-22200-20-220-2-2222-2-2002-22000-200000−22−220000000000−22−22−22−22-22-22000000000000002−22−200
χ392-2-2-2-2222222-222-2-2-2-2-2-2-22222-22-2-22-2-22200002-2-222-2000000002-2-222-2-22000000000000000000000000
χ402-2-2-2-2222222-222-2-2-2-2-2-2-22222-22-2-22-2-2220000-222-22-200000000-222-2-222-2000000000000000000000000
χ412-2-2-2-222222-222-2-2-22-2-2-2-2222-222-2-2-2222-200000000-2200000000000000000000000000000000002-2-2200
χ422-2-2-2-222222-222-2-2-22-2-2-2-2222-222-2-2-2222-200000000-220000000000000000000000000000000000-222-200
χ432-2-2-2-22222-22-2-2222-2-2-2-2-2222-22-2222-2-2-2200000000-22000000000000000000000000000000000000002-2
χ442-2-2-2-22222-22-2-2222-2-2-2-2-2222-22-2222-2-2-2200000000-2200000000000000000000000000000000000000-22
χ452-2-2-2-22222-2-22-2-2222-2-2-2-22222-2-222-222-2-2000000002-20000000000000000000000002-22-22-20000000000
χ462-2-2-2-22222-2-22-2-2222-2-2-2-22222-2-222-222-2-2000000002-2000000000000000000000000-22-22-220000000000
χ472-2-2-2-2222-122-222-2-2-21111-1-1-12-2-111-111-1-100002-2-22-11−i3i3−i3i3−i3i3−i3i3-111-1-111-10000000000−i3i3i3−i30000000000
χ482-2-2-2-2222-122-222-2-2-21111-1-1-12-2-111-111-1-100002-2-22-11i3−i3i3−i3i3−i3i3−i3-111-1-111-10000000000i3−i3−i3i30000000000
χ492-2-2-2-2222-122-222-2-2-21111-1-1-12-2-111-111-1-10000-222-2-11−i3i3−i3i3−i3i3−i3i31-1-111-1-110000000000i3−i3−i3i30000000000
χ502-2-2-2-2222-122-222-2-2-21111-1-1-12-2-111-111-1-10000-222-2-11i3−i3i3−i3i3−i3i3−i31-1-111-1-110000000000−i3i3i3−i30000000000
χ512-2-2-2-2222-1-2-22-2-22221111-1-1-12-21-1-11-1-11100000000-113−33−3−33−333−3−33−333−3000000002-2-11-110000000000
χ522-2-2-2-2222-1-2-22-2-22221111-1-1-12-21-1-11-1-11100000000-113−33−3−33−33−333−33−3−3300000000-221-11-10000000000
χ532-2-2-2-2222-1-2-22-2-22221111-1-1-12-21-1-11-1-11100000000-11−33−333−33−33−3−33−333−300000000-221-11-10000000000
χ542-2-2-2-2222-1-2-22-2-22221111-1-1-12-21-1-11-1-11100000000-11−33−333−33−3−333−33−3−33000000002-2-11-110000000000
χ5544444444-24-4-44-444-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5644444444-2-444-44-4-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ57444-4-44-4-44-40040-44044-4-44-4-400-4-440004000000000000000000000000000000000000000000000000000
χ58444-4-44-4-4-2400-404-40-2-222-22200-2-220002000002222−22−220000000000−2−222−2−222000000000000000000000000
χ59444-4-44-4-4-2400-404-40-2-222-22200-2-22000200000−22−222222000000000022−2−222−2−2000000000000000000000000
χ60444-4-44-4-4-2-40040-440-2-222-2220022-2000-2000000000000000000066−6−6−6−666000000000000000000000000
χ61444-4-44-4-4-2-40040-440-2-222-2220022-2000-20000000000000000000−6−66666−6−6000000000000000000000000
χ6244-44-4-44-4-20440-400-4-22-222-2200000-2-220222−2222−22000000−2−222−2−22200000000000000000000000000000000
χ6344-44-4-44-4-20440-400-4-22-222-2200000-2-2202−2222−222200000022−2−222−2−200000000000000000000000000000000
χ6444-44-4-44-4-20-4-404004-22-222-220000022-20-2−2i22i22i2−2i2000000i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ6544-44-4-44-4-20-4-404004-22-222-220000022-20-22i2−2i2−2i22i2000000−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ6644-4-44-4-444000000004-4-44-4-44000000000000000000000000000000000000000022−22−22220000000000000000
χ6744-4-44-4-444000000004-4-44-4-440000000000000000000000000000000000000000−222222−220000000000000000
χ684-444-4-4-44400000000-444-4-4-4400000000000000000000000000000000000022−22−222200000000000000000000
χ694-444-4-4-44400000000-444-4-4-44000000000000000000000000000000000000−222222−2200000000000000000000
χ704-44-44-44-4404-40-4004-44-44-44-4000004-440-400000000000000000000000000000000000000000000000000
χ714-44-44-44-440-440400-4-44-44-44-400000-44-40400000000000000000000000000000000000000000000000000
χ724-44-44-44-4-204-40-40042-22-22-2200000-22-2020000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ734-44-44-44-4-204-40-40042-22-22-2200000-22-2020000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ744-44-44-44-4-20-440400-42-22-22-22000002-220-200000000006−6−66−666−600000000000000000000000000000000
χ754-44-44-44-4-20-440400-42-22-22-22000002-220-20000000000−666−66−6−6600000000000000000000000000000000
χ764-4-4444-4-44-400404-40-4-4444-4-400-44-40004000000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-2400-40-44022-2-2-22200-22-200020000022−2222−220000000000−22−22−22−22000000000000000000000000
χ784-4-4444-4-4-2400-40-44022-2-2-22200-22-2000200000−2222−222200000000002−22−22−22−2000000000000000000000000
χ794-4-4444-4-4-2-400404-4022-2-2-222002-22000-200000000000000000006−66−6−66−66000000000000000000000000
χ804-4-4444-4-4-2-400404-4022-2-2-222002-22000-20000000000000000000−66−666−66−6000000000000000000000000
χ814-4-4-4-4444-24-444-4-4-442222-2-2-2-44-2222-2-2-22000000002-20000000000000000000000000000000000000000
χ824-4-4-4-4444-2-44-4-4444-42222-2-2-2-442-2-2-2222-2000000002-20000000000000000000000000000000000000000
χ8388-8-88-8-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-888-8-8-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000

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