Finite Group Databasebeta

← Group #10854150

Character table — Group #10854150

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ911111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-11-11-1
χ1011111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-11-11
χ1111111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-11-11
χ1211111111111-1-1-1-1111111111-1-1111-1-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111111-11-1
χ1311111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-11-1-11
χ1411111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-111-1
χ1511111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11111-1-111-1-1-111-1
χ1611111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111-1-11
χ17222222222-2-22222-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000222200000000000000-2-200
χ18222222222-2-22222-2-22222222-2-2-2-2-22222-2000000000000-2-200000000000000000000-2-2-2-2000000000000002200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000022-2-200000000000000-2200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000-2-222000000000000002-200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-222-2-222-2-211-1-1-1-11111-1-1-1-111110000000000000000-1-111000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ29222-2-2-2-2222-200002-22-22-2-2-220022-20000-22i−2i0000000000002i2i−2i−2i0000000000002i2i−2i−2i000022-2-200000000000000
χ30222-2-2-2-2222-200002-22-22-2-2-220022-20000-22i−2i0000000000002i2i−2i−2i000000000000−2i−2i2i2i0000-2-22200000000000000
χ31222-2-2-2-2222-200002-22-22-2-2-220022-20000-2−2i2i000000000000−2i−2i2i2i0000000000002i2i−2i−2i0000-2-22200000000000000
χ32222-2-2-2-2222-200002-22-22-2-2-220022-20000-2−2i2i000000000000−2i−2i2i2i000000000000−2i−2i2i2i000022-2-200000000000000
χ332-222-22-2-222222-2-2-2-2-2-2222-2-22-22-2222-2-2-20000000000002-200000000000000002-22-200000000000000002-20000
χ342-222-22-2-222222-2-2-2-2-2-2222-2-22-22-2222-2-2-20000000000002-20000000000000000-22-220000000000000000-220000
χ352-222-22-2-2222-2-222-2-2-2-2222-2-2-222-22-2-222-2000000000000-2200000000000000002-22-20000000000000000-220000
χ362-222-22-2-2222-2-222-2-2-2-2222-2-2-222-22-2-222-2000000000000-220000000000000000-22-2200000000000000002-20000
χ372-222-22-2-22-2-222-2-222-2-2222-2-2-22-22-222-2-2200002i−2i2i−2i0000-22000000000000000000000000000000002i−2i2i−2i000000
χ382-222-22-2-22-2-222-2-222-2-2222-2-2-22-22-222-2-220000−2i2i−2i2i0000-2200000000000000000000000000000000−2i2i−2i2i000000
χ392-222-22-2-22-2-2-2-22222-2-2222-2-22-2-22-2-2-222200002i−2i−2i2i00002-2000000000000000000000000000000002i−2i−2i2i000000
χ402-222-22-2-22-2-2-2-22222-2-2222-2-22-2-22-2-2-22220000−2i2i2i−2i00002-200000000000000000000000000000000−2i2i2i−2i000000
χ412-222-22-2-2-1-2-222-2-22211-1-1-111-221-11-1-111-100002i−2i2i−2i00001-13−33−333−3−3−i3−i3i3i3−i3−i3i3i30000000000000000−ii−ii000000
χ422-222-22-2-2-1-2-222-2-22211-1-1-111-221-11-1-111-100002i−2i2i−2i00001-1−33−33−3−333i3i3−i3−i3i3i3−i3−i30000000000000000−ii−ii000000
χ432-222-22-2-2-1-2-222-2-22211-1-1-111-221-11-1-111-10000−2i2i−2i2i00001-13−33−333−3−3i3i3−i3−i3i3i3−i3−i30000000000000000i−ii−i000000
χ442-222-22-2-2-1-2-222-2-22211-1-1-111-221-11-1-111-10000−2i2i−2i2i00001-1−33−33−3−333−i3−i3i3i3−i3−i3i3i30000000000000000i−ii−i000000
χ452-222-22-2-2-1-2-2-2-2222211-1-1-1112-21-1111-1-1-100002i−2i−2i2i0000-113−33−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000−iii−i000000
χ462-222-22-2-2-1-2-2-2-2222211-1-1-1112-21-1111-1-1-100002i−2i−2i2i0000-11−33−3333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000−iii−i000000
χ472-222-22-2-2-1-2-2-2-2222211-1-1-1112-21-1111-1-1-10000−2i2i2i−2i0000-113−33−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000i−i−ii000000
χ482-222-22-2-2-1-2-2-2-2222211-1-1-1112-21-1111-1-1-10000−2i2i2i−2i0000-11−33−3333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000i−i−ii000000
χ492-22-22-22-222-20000-22-222-2-22-2002-2-200002002i−2i000000000000002i−2i2i−2i000000002i−2i−2i2i0000000022-2-20000000000
χ502-22-22-22-222-20000-22-222-2-22-2002-2-200002002i−2i000000000000002i−2i2i−2i00000000−2i2i2i−2i00000000-2-2220000000000
χ512-22-22-22-222-20000-22-222-2-22-2002-2-20000200−2i2i00000000000000−2i2i−2i2i000000002i−2i−2i2i00000000-2-2220000000000
χ522-22-22-22-222-20000-22-222-2-22-2002-2-20000200−2i2i00000000000000−2i2i−2i2i00000000−2i2i2i−2i0000000022-2-20000000000
χ532-2-2-2-22222002-22-200-2-2-22-222000002-22-20000000002−22−200000000002−22−22−22−200002-22-22−22−22−22−20000000000
χ542-2-2-2-22222002-22-200-2-2-22-222000002-22-20000000002−22−200000000002−22−22−22−20000-22-22−22−22−22−220000000000
χ552-2-2-2-22222002-22-200-2-2-22-222000002-22-2000000000−22−220000000000−22−22−22−2200002-22-2−22−22−22−220000000000
χ562-2-2-2-22222002-22-200-2-2-22-222000002-22-2000000000−22−220000000000−22−22−22−220000-22-222−22−22−22−20000000000
χ572-2-2-2-2222200-22-2200-2-2-22-22200000-22-220000000002−2−2200000000002−22−2−22−2200002-2-222−22−2−22−220000000000
χ582-2-2-2-2222200-22-2200-2-2-22-22200000-22-220000000002−2−2200000000002−22−2−22−220000-222-2−22−222−22−20000000000
χ592-2-2-2-2222200-22-2200-2-2-22-22200000-22-22000000000−222−20000000000−22−222−22−200002-2-22−22−222−22−20000000000
χ602-2-2-2-2222200-22-2200-2-2-22-22200000-22-22000000000−222−20000000000−22−222−22−20000-222-22−22−2−22−220000000000
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ63444-4-4-4-444-440000-444-44-4-4-4400-4-440000400000000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-24-400004-4-22-2222-200-2-22000024i−4i000000000000−2i−2i2i2i00000000000000000000000000000000000000
χ65444-4-4-4-44-24-400004-4-22-2222-200-2-2200002−4i4i0000000000002i2i−2i−2i00000000000000000000000000000000000000
χ66444-4-4-4-44-2-440000-44-22-2222-20022-20000-2000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ67444-4-4-4-44-2-440000-44-22-2222-20022-20000-20000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ6844-44-4-44-44000000004-4-4-444-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ6944-44-4-44-44000000004-4-4-444-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ7044-4-444-4-44004-4-440044-44-4-4-4000004-4-44000000000000000000000000000000000000000000000000000000000
χ7144-4-444-4-4400-444-40044-44-4-4-400000-444-4000000000000000000000000000000000000000000000000000000000
χ7244-4-444-4-4-2004-4-4400-2-22-222200000-222-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ7344-4-444-4-4-2004-4-4400-2-22-222200000-222-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ7444-4-444-4-4-200-444-400-2-22-2222000002-2-2200000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000
χ7544-4-444-4-4-200-444-400-2-22-2222000002-2-2200000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000
χ764-444-44-4-4-24444-4-4-4-422-2-2-2224-4-22-2-2-2222000000000000-22000000000000000000000000000000000000000000
χ774-444-44-4-4-244-4-444-4-422-2-2-222-44-22-222-2-220000000000002-2000000000000000000000000000000000000000000
χ784-44-44-44-44-4400004-4-444-4-44-400-4440000-400000000000000000000000000000000000000000000000000000000
χ794-44-44-44-4-24-40000-442-2-222-2200-2220000-2004i−4i00000000000000−2i2i−2i2i0000000000000000000000000000000000
χ804-44-44-44-4-24-40000-442-2-222-2200-2220000-200−4i4i000000000000002i−2i2i−2i0000000000000000000000000000000000
χ814-44-44-44-4-2-4400004-42-2-222-22002-2-20000200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ824-44-44-44-4-2-4400004-42-2-222-22002-2-200002000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ834-4-444-4-44400000000-44-4-44-4400000000000000000000000000000000000000000000000022−22−222200000000000000
χ844-4-444-4-44400000000-44-4-44-44000000000000000000000000000000000000000000000000−222222−2200000000000000
χ854-4-4-4-4444-2004-44-400222-22-2-200000-22-2200000000022−2222−220000000000−22−22−22−2200000000000000000000000000
χ864-4-4-4-4444-2004-44-400222-22-2-200000-22-22000000000−2222−222200000000002−22−22−22−200000000000000000000000000
χ874-4-4-4-4444-200-44-4400222-22-2-2000002-22-200000000022−22−22220000000000−22−222−22−200000000000000000000000000
χ884-4-4-4-4444-200-44-4400222-22-2-2000002-22-2000000000−222222−2200000000002−22−2−22−2200000000000000000000000000
χ8988-88-8-88-8-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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