Finite Group Databasebeta

← Group #10698975

Character table — Group #10698975

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121288888888121224242424242424242424242424242424888888882266662244888844
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
χ9222222222222-2-2-2-222222222-2-2222-2-2-22-200000000-2-200000000000000000000000000000022-2-2000000
χ10222222222222-2-2-2-222222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000-2-222000000
χ11222222222-2-2-22222-22222222-2-2-2-2-2222-2200000000-2-200000000000000002222-2-2-2-20000000000000000
χ12222222222-2-2-22222-22222222-2-2-2-2-2222-2200000000-2-20000000000000000-2-2-2-222220000000000000000
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
χ23222-2-2-22-220002-22-2022-2-22-2-20000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i200002i2i−2i−2i000000000022−2−200
χ24222-2-2-22-220002-22-2022-2-22-2-20000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i20000−2i−2i2i2i0000000000−2−22200
χ25222-2-2-22-220002-22-2022-2-22-2-20000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i200002i2i−2i−2i0000000000−2−22200
χ26222-2-2-22-220002-22-2022-2-22-2-20000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i20000−2i−2i2i2i000000000022−2−200
χ2722-2-22-2-22222-20000-22-22-2-22-20022-2000-20−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i20000000022−2−22−22−2000000002i−2i000000
χ2822-2-22-2-22222-20000-22-22-2-22-20022-2000-20−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i200000000−2−222−22−2200000000−2i2i000000
χ2922-2-22-2-22222-20000-22-22-2-22-20022-2000-20i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i20000000022−2−22−22−200000000−2i2i000000
χ3022-2-22-2-22222-20000-22-22-2-22-20022-2000-20i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i200000000−2−222−22−22000000002i−2i000000
χ3122-2-22-2-222-2-22000022-22-2-22-200-2-22000202−2−2200000022−2−2−2−2220000000022−2−2−22−220000002-200000000
χ3222-2-22-2-222-2-22000022-22-2-22-200-2-22000202−2−2200000022−2−2−2−22200000000−2−2222−22−2000000-2200000000
χ3322-2-22-2-222-2-22000022-22-2-22-200-2-2200020−222−2000000−2−22222−2−20000000022−2−2−22−22000000-2200000000
χ3422-2-22-2-222-2-22000022-22-2-22-200-2-2200020−222−2000000−2−22222−2−200000000−2−2222−22−20000002-200000000
χ352-2-22-2-2222000-222-20-2-2222-2-2000002-2-20200002−22−200000000002−22−22−22−22-22-2000000000000002−22−200
χ362-2-22-2-2222000-222-20-2-2222-2-2000002-2-20200002−22−200000000002−22−22−22−2-22-2200000000000000−22−2200
χ372-2-22-2-2222000-222-20-2-2222-2-2000002-2-2020000−22−220000000000−22−22−22−222-22-200000000000000−22−2200
χ382-2-22-2-2222000-222-20-2-2222-2-2000002-2-2020000−22−220000000000−22−22−22−22-22-22000000000000002−22−200
χ392-2-2-2222-222-2222-2-2-2-2-2-2-22222-22-22-22-2-22000000002-2000000000000000000000000000000000000002i−2i
χ402-2-2-2222-222-2222-2-2-2-2-2-2-22222-22-22-22-2-22000000002-200000000000000000000000000000000000000−2i2i
χ412-2-2-2222-222-22-2-222-2-2-2-2-2222-222-222-22-2-200002i−2i−2i2i-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ422-2-2-2222-222-22-2-222-2-2-2-2-2222-222-222-22-2-20000−2i2i2i−2i-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ432-2-2-2222-22-22-222-2-22-2-2-2-2222-22-22-2-22-22200000000-220000000000000000000000002-22-22-20000000000
χ442-2-2-2222-22-22-222-2-22-2-2-2-2222-22-22-2-22-22200000000-22000000000000000000000000-22-22-220000000000
χ452-2-2-2222-22-22-2-2-2222-2-2-2-22222-2-22-22-222-2000000002-200000000000000000000000000000000002-2-2200
χ462-2-2-2222-22-22-2-2-2222-2-2-2-22222-2-22-22-222-2000000002-20000000000000000000000000000000000-222-200
χ472-2-2-2222-2-12-22-2-222-21111-1-1-1-22-11-1-11-11100002i−2i−2i2i1-13−33−33−33−3−iii−i−iii−i0000000000−i3i3i3−i30000000000
χ482-2-2-2222-2-12-22-2-222-21111-1-1-1-22-11-1-11-11100002i−2i−2i2i1-1−33−33−33−33−iii−i−iii−i0000000000i3−i3−i3i30000000000
χ492-2-2-2222-2-12-22-2-222-21111-1-1-1-22-11-1-11-1110000−2i2i2i−2i1-13−33−33−33−3i−i−iii−i−ii0000000000i3−i3−i3i30000000000
χ502-2-2-2222-2-12-22-2-222-21111-1-1-1-22-11-1-11-1110000−2i2i2i−2i1-1−33−33−33−33i−i−iii−i−ii0000000000−i3i3i3−i30000000000
χ512-2-2-2222-2-1-22-222-2-221111-1-1-1-221-111-11-1-1000000001-1−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3000000002-2-11-110000000000
χ522-2-2-2222-2-1-22-222-2-221111-1-1-1-221-111-11-1-1000000001-1−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3i3−i300000000-221-11-10000000000
χ532-2-2-2222-2-1-22-222-2-221111-1-1-1-221-111-11-1-1000000001-1i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3−i3i300000000-221-11-10000000000
χ542-2-2-2222-2-1-22-222-2-221111-1-1-1-221-111-11-1-1000000001-1i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3000000002-2-11-110000000000
χ5544444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ57444-4-4-44-44000-44-44044-4-44-4-400000-4-440400000000000000000000000000000000000000000000000000
χ58444-4-4-44-4-20004-44-40-2-222-22200000-2-22020000−2i2−2i22i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ59444-4-4-44-4-20004-44-40-2-222-22200000-2-220200002i22i2−2i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ60444-4-4-44-4-2000-44-440-2-222-2220000022-20-2000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ61444-4-4-44-4-2000-44-440-2-222-2220000022-20-2000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6244-44-44-4-44000000004-4-44-4-440000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6344-44-44-4-44000000004-4-44-4-4400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6444-4-44-4-44-244-40000-4-22-222-2200-2-2200020−2i22i2−2i22i2000000i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ6544-4-44-4-44-244-40000-4-22-222-2200-2-22000202i2−2i22i2−2i2000000−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ6644-4-44-4-44-2-4-4400004-22-222-220022-2000-2022−22−2222000000−2−22222−2−200000000000000000000000000000000
χ6744-4-44-4-44-2-4-4400004-22-222-220022-2000-20−222222−2200000022−2−2−2−22200000000000000000000000000000000
χ684-4444-4-4-444-4-400004-44-44-44-4004-4-40004000000000000000000000000000000000000000000000000000
χ694-4444-4-4-44-4440000-4-44-44-44-400-444000-4000000000000000000000000000000000000000000000000000
χ704-4444-4-4-4-24-4-4000042-22-22-2200-222000-200000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ714-4444-4-4-4-24-4-4000042-22-22-2200-222000-200000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ724-4444-4-4-4-2-4440000-42-22-22-22002-2-20002000000000006−6−66−666−600000000000000000000000000000000
χ734-4444-4-4-4-2-4440000-42-22-22-22002-2-2000200000000000−666−66−6−6600000000000000000000000000000000
χ744-44-4-44-44400000000-444-4-4-4400000000000000000000000000000000000022−22−222200000000000000000000
χ754-44-4-44-44400000000-444-4-4-44000000000000000000000000000000000000−222222−2200000000000000000000
χ764-4-44-4-44440004-4-440-4-4444-4-400000-4440-400000000000000000000000000000000000000000000000000
χ774-4-44-4-444-20004-4-44022-2-2-222000002-2-2020000000000000000006−66−6−66−66000000000000000000000000
χ784-4-44-4-444-20004-4-44022-2-2-222000002-2-202000000000000000000−66−666−66−6000000000000000000000000
χ794-4-44-4-444-2000-444-4022-2-2-22200000-2220-2000022−2222−220000000000−22−22−22−22000000000000000000000000
χ804-4-44-4-444-2000-444-4022-2-2-22200000-2220-20000−2222−222200000000002−22−22−22−2000000000000000000000000
χ814-4-4-4444-4-24-4444-4-4-42222-2-2-24-4-22-22-222-200000000-220000000000000000000000000000000000000000
χ824-4-4-4444-4-2-44-4-4-44442222-2-2-24-42-22-22-2-2200000000-220000000000000000000000000000000000000000
χ8388-88-88-8-8-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000

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