Finite Group Databasebeta

← Group #10868449

Character table — Group #10868449

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-111-111-1-1-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-111111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-11111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-111-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1111-1-1-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-222220000-200-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-20000-200-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220000200220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000200220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-2-2-2222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-10000-2-222-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-100002222-222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-222-2-2-222-2-222-2-2-22-22002i2i−2i−2i0000000022-2-22i2i−2i−2i0000000002i2i−2i−2i000000000000002i−2i0000000002-200000000
χ3022-222-2-2-222-2-222-2-2-22-22002i2i−2i−2i0000000022-2-2−2i−2i2i2i0000000002i2i−2i−2i00000000000000−2i2i000000000-2200000000
χ3122-222-2-2-222-2-222-2-2-22-2200−2i−2i2i2i0000000022-2-22i2i−2i−2i000000000−2i−2i2i2i000000000000002i−2i000000000-2200000000
χ3222-222-2-2-222-2-222-2-2-22-2200−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000−2i−2i2i2i00000000000000−2i2i0000000002-200000000
χ3322-222-2-2-22-222-22-2-2-22-2200000000000000-2-2222i2i−2i−2i2-20000000000022-2-20000000000−2i2i000000000000002i−2i000
χ3422-222-2-2-22-222-22-2-2-22-2200000000000000-2-2222i2i−2i−2i-2200000000000-2-2220000000000−2i2i00000000000000−2i2i000
χ3522-222-2-2-22-222-22-2-2-22-2200000000000000-2-222−2i−2i2i2i2-20000000000022-2-200000000002i−2i00000000000000−2i2i000
χ3622-222-2-2-22-222-22-2-2-22-2200000000000000-2-222−2i−2i2i2i-2200000000000-2-22200000000002i−2i000000000000002i−2i000
χ372-222-22-2-2222-2-2-2-2-22-222002-22-2000000002-22-200000000000002-22-200000000000000002i2i−2i−2i000000002i−2i00000
χ382-222-22-2-2222-2-2-2-2-22-222002-22-2000000002-22-200000000000002-22-20000000000000000−2i−2i2i2i00000000−2i2i00000
χ392-222-22-2-2222-2-2-2-2-22-22200-22-22000000002-22-20000000000000-22-2200000000000000002i2i−2i−2i00000000−2i2i00000
χ402-222-22-2-2222-2-2-2-2-22-22200-22-22000000002-22-20000000000000-22-220000000000000000−2i−2i2i2i000000002i−2i00000
χ412-2-22-2-22222-22-2-222-2-2-22002i−2i−2i2i22-2-200002-2-220000002i−2i000002i−2i−2i2i000022-2-200000000000002i−2i000000000000
χ422-2-22-2-22222-22-2-222-2-2-22002i−2i−2i2i-2-22200002-2-22000000−2i2i000002i−2i−2i2i0000-2-2220000000000000−2i2i000000000000
χ432-2-22-2-22222-22-2-222-2-2-2200−2i2i2i−2i22-2-200002-2-22000000−2i2i00000−2i2i2i−2i000022-2-20000000000000−2i2i000000000000
χ442-2-22-2-22222-22-2-222-2-2-2200−2i2i2i−2i-2-22200002-2-220000002i−2i00000−2i2i2i−2i0000-2-22200000000000002i−2i000000000000
χ452-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i22-2-233−3−3-111-10000002i−2i0003−3−iii−i−i3i3−i3i3-1-11133−3−3000000000−ii−i3i30000000000
χ462-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i22-2-2−3−333-111-10000002i−2i000−33−iii−ii3−i3i3−i3-1-111−3−333000000000−iii3−i30000000000
χ472-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-2-22233−3−3-111-1000000−2i2i0003−3−iii−i−i3i3−i3i311-1-1−3−333000000000i−ii3−i30000000000
χ482-2-22-2-222-12-22-21-1-1111-1002i−2i−2i2i-2-222−3−333-111-1000000−2i2i000−33−iii−ii3−i3i3−i311-1-133−3−3000000000i−i−i3i30000000000
χ492-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i22-2-233−3−3-111-1000000−2i2i0003−3i−i−iii3−i3i3−i3-1-11133−3−3000000000i−ii3−i30000000000
χ502-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i22-2-2−3−333-111-1000000−2i2i000−33i−i−ii−i3i3−i3i3-1-111−3−333000000000i−i−i3i30000000000
χ512-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-2-22233−3−3-111-10000002i−2i0003−3i−i−iii3−i3i3−i311-1-1−3−333000000000−ii−i3i30000000000
χ522-2-22-2-222-12-22-21-1-1111-100−2i2i2i−2i-2-222−3−333-111-10000002i−2i000−33i−i−ii−i3i3−i3i311-1-133−3−3000000000−iii3−i30000000000
χ532-2-2-2222-220000-22-2-222-22i−2i00002−22−22i−2i2i−2i00002-22-200000−i2i200000000002−22−2−i2i2−i2i22i−2i002−22−2000000000000−i2i20
χ542-2-2-2222-220000-22-2-222-22i−2i00002−22−22i−2i2i−2i0000-22-2200000−i2i200000000002−22−2−i2i2−i2i2−2i2i00−22−22000000000000i2−i20
χ552-2-2-2222-220000-22-2-222-22i−2i0000−22−222i−2i2i−2i00002-22-200000i2−i20000000000−22−22i2−i2i2−i22i−2i00−22−22000000000000i2−i20
χ562-2-2-2222-220000-22-2-222-22i−2i0000−22−222i−2i2i−2i0000-22-2200000i2−i20000000000−22−22i2−i2i2−i2−2i2i002−22−2000000000000−i2i20
χ572-2-2-2222-220000-22-2-222-2−2i2i00002−22−2−2i2i−2i2i00002-22-200000i2−i200000000002−22−2i2−i2i2−i2−2i2i002−22−2000000000000i2−i20
χ582-2-2-2222-220000-22-2-222-2−2i2i00002−22−2−2i2i−2i2i0000-22-2200000i2−i200000000002−22−2i2−i2i2−i22i−2i00−22−22000000000000−i2i20
χ592-2-2-2222-220000-22-2-222-2−2i2i0000−22−22−2i2i−2i2i00002-22-200000−i2i20000000000−22−22−i2i2−i2i2−2i2i00−22−22000000000000−i2i20
χ602-2-2-2222-220000-22-2-222-2−2i2i0000−22−22−2i2i−2i2i0000-22-2200000−i2i20000000000−22−22−i2i2−i2i22i−2i002−22−2000000000000i2−i20
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-2222200000000-40022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200000000400-2-2000000000000000000000000000000000000000
χ63444-4-4-44-44000044-44-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ64444-4-4-44-44000044-44-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ65444-4-4-44-4-20000-2-22-222200000022−22−2222−2i32i32i3−2i30000000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ66444-4-4-44-4-20000-2-22-222200000022−22−22222i3−2i3−2i32i30000000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ67444-4-4-44-4-20000-2-22-2222000000−222222−22−2i32i32i3−2i300000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ68444-4-4-44-4-20000-2-22-2222000000−222222−222i3−2i3−2i32i300000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ6944-444-4-4-4-24-4-44-2222-22-2004i4i−4i−4i00000000-2-2220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7044-444-4-4-4-24-4-44-2222-22-200−4i−4i4i4i00000000-2-22200000000000002i2i−2i−2i00000000000000000000000000000000000
χ7144-444-4-4-4-2-444-4-2222-22-20000000000000022-2-200004-400000000000-2-2220000000000000000000000000000000
χ7244-444-4-4-4-2-444-4-2222-22-20000000000000022-2-20000-440000000000022-2-20000000000000000000000000000000
χ7344-4-4-44-44400004-44-4-44-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ7444-4-4-44-44400004-44-4-44-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ754-444-44-4-44-4-444-4-4-44-44400000000000000-44-440000000000000000000000000000000000000000000000000000
χ764-444-44-4-4-244-4-4222-22-2-2004-44-400000000-22-220000000000000-22-2200000000000000000000000000000000000
χ774-444-44-4-4-244-4-4222-22-2-200-44-4400000000-22-2200000000000002-22-200000000000000000000000000000000000
χ784-444-44-4-4-2-4-444222-22-2-2000000000000002-22-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ794-444-44-4-4-2-4-444222-22-2-2000000000000002-22-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ804-44-44-4-4440000-4-4444-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ814-44-44-4-4440000-4-4444-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ824-4-44-4-4444-44-44-444-4-4-4400000000000000-444-40000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-2-44-442-2-2222-200000000002323−23−232-2-2200000000000−2323000000000000000000000000000000000000000
χ844-4-44-4-444-2-44-442-2-2222-20000000000−23−2323232-2-220000000000023−23000000000000000000000000000000000000000
χ854-4-4-4444-4-200002-222-2-224i−4i000022−2222−22−2i2i−2i2i0000000000000−2i22i20000000000−22−22i2−i2i2−i200000000000000000000000
χ864-4-4-4444-4-200002-222-2-224i−4i0000−2222−2222−2i2i−2i2i00000000000002i2−2i200000000002−22−2−i2i2−i2i200000000000000000000000
χ874-4-4-4444-4-200002-222-2-22−4i4i000022−2222−222i−2i2i−2i00000000000002i2−2i20000000000−22−22−i2i2−i2i200000000000000000000000
χ884-4-4-4444-4-200002-222-2-22−4i4i0000−2222−22222i−2i2i−2i0000000000000−2i22i200000000002−22−2i2−i2i2−i200000000000000000000000
χ8988-8-8-88-88-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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