Finite Group Databasebeta

← Group #10868044

Character table — Group #10868044

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-111111111111-1-1-1-111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-1-11111-1-1-1-1-1
χ1011111111111111111111-1-111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-11-1-1-1-111111
χ1111111111111111111111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-111111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-111-1-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-11111111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-11-1-111-1-1-1-11
χ17222222222-2-2-2-222222222200000000-2-2-22222-222220000-200-2-20000000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222222200000000-2-2-22222-2-2-2-2-20000-200-2-2000000000000000022-2-20000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220000200220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-200002002200000000000000002222000000000-2000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-1-11111-10000-2-222-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-11111-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-100002222-222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-2-22-22-2222-2-22-22-2-2-2200000000002-2-2000022i2i−2i−2i2-20000000000022-2-2000000002i−2i00000000000000002i−2i000
χ3022-2-22-22-2222-2-22-22-2-2-2200000000002-2-2000022i2i−2i−2i-2200000000000-2-222000000002i−2i0000000000000000−2i2i000
χ3122-2-22-22-2222-2-22-22-2-2-2200000000002-2-200002−2i−2i2i2i2-20000000000022-2-200000000−2i2i0000000000000000−2i2i000
χ3222-2-22-22-2222-2-22-22-2-2-2200000000002-2-200002−2i−2i2i2i-2200000000000-2-22200000000−2i2i00000000000000002i−2i000
χ3322-2-22-22-22-2-2222-22-2-2-22002i2i−2i−2i0000-2220000-22i2i−2i−2i0000000002i2i−2i−2i000000000000−2i2i000000000000002-200000
χ3422-2-22-22-22-2-2222-22-2-2-22002i2i−2i−2i0000-2220000-2−2i−2i2i2i0000000002i2i−2i−2i0000000000002i−2i00000000000000-2200000
χ3522-2-22-22-22-2-2222-22-2-2-2200−2i−2i2i2i0000-2220000-22i2i−2i−2i000000000−2i−2i2i2i000000000000−2i2i00000000000000-2200000
χ3622-2-22-22-22-2-2222-22-2-2-2200−2i−2i2i2i0000-2220000-2−2i−2i2i2i000000000−2i−2i2i2i0000000000002i−2i000000000000002-200000
χ372-2222-2-2-220000-2-2-22-2222-2000022−2−200022-2-202i−2i2i−2i000002−2000000000022−2−222−2−2002i−2i−i2−i2i2i2000000000000−i2i20
χ382-2222-2-2-220000-2-2-22-2222-2000022−2−200022-2-20−2i2i−2i2i000002−2000000000022−2−222−2−200−2i2ii2i2−i2−i2000000000000i2−i20
χ392-2222-2-2-220000-2-2-22-2222-20000−2−22200022-2-202i−2i2i−2i00000−220000000000−2−222−2−222002i−2ii2i2−i2−i2000000000000i2−i20
χ402-2222-2-2-220000-2-2-22-2222-20000−2−22200022-2-20−2i2i−2i2i00000−220000000000−2−222−2−22200−2i2i−i2−i2i2i2000000000000−i2i20
χ412-2222-2-2-220000-2-2-22-222-22000022−2−2000-2-22202i−2i2i−2i00000−22000000000022−2−2−2−22200−2i2i−i2−i2i2i2000000000000i2−i20
χ422-2222-2-2-220000-2-2-22-222-22000022−2−2000-2-2220−2i2i−2i2i00000−22000000000022−2−2−2−222002i−2ii2i2−i2−i2000000000000−i2i20
χ432-2222-2-2-220000-2-2-22-222-220000−2−222000-2-22202i−2i2i−2i000002−20000000000−2−22222−2−200−2i2ii2i2−i2−i2000000000000−i2i20
χ442-2222-2-2-220000-2-2-22-222-220000−2−222000-2-2220−2i2i−2i2i000002−20000000000−2−22222−2−2002i−2i−i2−i2i2i2000000000000i2−i20
χ452-22-2-222-22-222-2-2-2222-2-2002i−2i2i−2i2-22-2-22-2000020000002i−2i000002i−2i2i−2i00002-22-200000000000002i−2i000000000000
χ462-22-2-222-22-222-2-2-2222-2-2002i−2i2i−2i-22-22-22-200002000000−2i2i000002i−2i2i−2i0000-22-220000000000000−2i2i000000000000
χ472-22-2-222-22-222-2-2-2222-2-200−2i2i−2i2i2-22-2-22-200002000000−2i2i00000−2i2i−2i2i00002-22-20000000000000−2i2i000000000000
χ482-22-2-222-22-222-2-2-2222-2-200−2i2i−2i2i-22-22-22-2000020000002i−2i00000−2i2i−2i2i0000-22-2200000000000002i−2i000000000000
χ492-22-2-222-2-1-222-211-1-1-111002i−2i2i−2i2-22-21-11−i3i3−i3i3-10000002i−2i000−i3i3−ii−ii3−33−3-11-11−i3i3−i3i3000000000−ii3−30000000000
χ502-22-2-222-2-1-222-211-1-1-111002i−2i2i−2i2-22-21-11i3−i3i3−i3-10000002i−2i000i3−i3−ii−ii−33−33-11-11i3−i3i3−i3000000000−ii−330000000000
χ512-22-2-222-2-1-222-211-1-1-111002i−2i2i−2i-22-221-11−i3i3−i3i3-1000000−2i2i000−i3i3−ii−ii3−33−31-11-1i3−i3i3−i3000000000i−i−330000000000
χ522-22-2-222-2-1-222-211-1-1-111002i−2i2i−2i-22-221-11i3−i3i3−i3-1000000−2i2i000i3−i3−ii−ii−33−331-11-1−i3i3−i3i3000000000i−i3−30000000000
χ532-22-2-222-2-1-222-211-1-1-11100−2i2i−2i2i2-22-21-11−i3i3−i3i3-1000000−2i2i000−i3i3i−ii−i−33−33-11-11−i3i3−i3i3000000000i−i−330000000000
χ542-22-2-222-2-1-222-211-1-1-11100−2i2i−2i2i2-22-21-11i3−i3i3−i3-1000000−2i2i000i3−i3i−ii−i3−33−3-11-11i3−i3i3−i3000000000i−i3−30000000000
χ552-22-2-222-2-1-222-211-1-1-11100−2i2i−2i2i-22-221-11−i3i3−i3i3-10000002i−2i000−i3i3i−ii−i−33−331-11-1i3−i3i3−i3000000000−ii3−30000000000
χ562-22-2-222-2-1-222-211-1-1-11100−2i2i−2i2i-22-221-11i3−i3i3−i3-10000002i−2i000i3−i3i−ii−i3−33−31-11-1−i3i3−i3i3000000000−ii−330000000000
χ572-2-22-2-22222-22-2-222-2-22-2002-2-22000022-20000-200000000000002-2-2200000000000000002i−2i2i−2i0000002i−2i0000000
χ582-2-22-2-22222-22-2-222-2-22-2002-2-22000022-20000-200000000000002-2-220000000000000000−2i2i−2i2i000000−2i2i0000000
χ592-2-22-2-22222-22-2-222-2-22-200-222-2000022-20000-20000000000000-222-200000000000000002i−2i2i−2i000000−2i2i0000000
χ602-2-22-2-22222-22-2-222-2-22-200-222-2000022-20000-20000000000000-222-20000000000000000−2i2i−2i2i0000002i−2i0000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000222-2-2-2-2200000000-40022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200000000400-2-2000000000000000000000000000000000000000
χ63444-4-4-4-444000044-44-4-4-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ64444-4-4-4-444000044-44-4-4-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ65444-4-4-4-44-20000-2-22-222200000022−22−2222000−2i32i32i3−2i30000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ66444-4-4-4-44-20000-2-22-222200000022−22−22220002i3−2i3−2i32i30000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ67444-4-4-4-44-20000-2-22-2222000000−222222−22000−2i32i32i3−2i300000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ68444-4-4-4-44-20000-2-22-2222000000−222222−220002i3−2i3−2i32i300000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ6944-44-44-4-4400004-4-4-444-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ7044-44-44-4-4400004-4-4-444-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ7144-4-44-44-4-244-4-4-22-2222-20000000000-2220000-200004-400000000000-2-2220000000000000000000000000000000
χ7244-4-44-44-4-244-4-4-22-2222-20000000000-2220000-20000-440000000000022-2-20000000000000000000000000000000
χ7344-4-44-44-4-2-4-444-22-2222-2004i4i−4i−4i00002-2-2000020000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7444-4-44-44-4-2-4-444-22-2222-200−4i−4i4i4i00002-2-20000200000000000002i2i−2i−2i00000000000000000000000000000000000
χ754-4444-4-4-4-20000222-22-2-24-400002222−22−22000-2-222000000000022−220000000000−2−222−2−22200000000000000000000000
χ764-4444-4-4-4-20000222-22-2-24-40000−22−222222000-2-2220000000000−2222000000000022−2−222−2−200000000000000000000000
χ774-4444-4-4-4-20000222-22-2-2-4400002222−22−2200022-2-20000000000−22220000000000−2−22222−2−200000000000000000000000
χ784-4444-4-4-4-20000222-22-2-2-440000−22−22222200022-2-2000000000022−22000000000022−2−2−2−22200000000000000000000000
χ794-44-4-444-444-4-44-4-4444-4-400000000004-440000-40000000000000000000000000000000000000000000000000000
χ804-44-4-444-4-24-4-4422-2-2-2220000000000-22-2−2i32i3−2i32i32000000000002i3−2i3000000000000000000000000000000000000000
χ814-44-4-444-4-24-4-4422-2-2-2220000000000-22-22i3−2i32i3−2i3200000000000−2i32i3000000000000000000000000000000000000000
χ824-4-44-4-4444-44-44-444-4-44-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-24-44-42-2-222-22004-4-440000-2-22000020000000000000-222-200000000000000000000000000000000000
χ844-4-44-4-444-24-44-42-2-222-2200-444-40000-2-220000200000000000002-2-2200000000000000000000000000000000000
χ854-4-44-4-444-2-44-442-2-222-22000000000022-20000-20000000000000000023−23−23230000000000000000000000000000000
χ864-4-44-4-444-2-44-442-2-222-22000000000022-20000-200000000000000000−232323−230000000000000000000000000000000
χ874-4-4-444-4440000-44-4-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-444-4440000-44-4-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ8988-88-88-8-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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