Finite Group Databasebeta

← Group #10858337

Character table — Group #10858337

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ911111111111111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111111-1-1111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-111-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1111-1-111-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-2222200-20000-2-2000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-200-20000-2-20000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220020000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-200200002200000000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-222111111-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-1000022-2222211-1-1-1-111111111-1-1-1-100000000-211-1-10000000000
χ29222-2-22-2-2222-2-222-2-2-2-220022-2-222-2-200002-22-200002-20000000000022-2-222-2-20000000000000002-20000000000
χ30222-2-22-2-2222-2-222-2-2-2-220022-2-2-2-22200002-22-20000-220000000000022-2-2-2-222000000000000000-220000000000
χ31222-2-22-2-2222-2-222-2-2-2-2200-2-22222-2-200002-22-20000-2200000000000-2-22222-2-2000000000000000-220000000000
χ32222-2-22-2-2222-2-222-2-2-2-2200-2-222-2-22200002-22-200002-200000000000-2-222-2-2220000000000000002-20000000000
χ33222-2-22-2-2-122-2-2-1-11111-10022-2-222-2-233−3−3-11-1100002-2000003−333−3−3-1-111-1-11133−3−30000000003−3-110000000000
χ34222-2-22-2-2-122-2-2-1-11111-10022-2-222-2-2−3−333-11-1100002-200000−33−3−333-1-111-1-111−3−333000000000−33-110000000000
χ35222-2-22-2-2-122-2-2-1-11111-10022-2-2-2-22233−3−3-11-110000-22000003−333−3−3-1-11111-1-1−3−333000000000−331-10000000000
χ36222-2-22-2-2-122-2-2-1-11111-10022-2-2-2-222−3−333-11-110000-2200000−33−3−333-1-11111-1-133−3−30000000003−31-10000000000
χ37222-2-22-2-2-122-2-2-1-11111-100-2-22222-2-233−3−3-11-110000-22000003−3−3−33311-1-1-1-11133−3−3000000000−331-10000000000
χ38222-2-22-2-2-122-2-2-1-11111-100-2-22222-2-2−3−333-11-110000-2200000−3333−3−311-1-1-1-111−3−3330000000003−31-10000000000
χ39222-2-22-2-2-122-2-2-1-11111-100-2-222-2-22233−3−3-11-1100002-2000003−3−3−33311-1-111-1-1−3−3330000000003−3-110000000000
χ40222-2-22-2-2-122-2-2-1-11111-100-2-222-2-222−3−333-11-1100002-200000−3333−3−311-1-111-1-133−3−3000000000−33-110000000000
χ4122-222-2-2-2200002-222-2-2-22-200002−22−22-22-2000022-2-2000002−200000000002−22−22−22−22-20022−2−20000000000002−20
χ4222-222-2-2-2200002-222-2-2-22-200002−22−22-22-20000-2-222000002−200000000002−22−22−22−2-2200−2−222000000000000−220
χ4322-222-2-2-2200002-222-2-2-22-20000−22−222-22-2000022-2-200000−220000000000−22−22−22−222-200−2−222000000000000−220
χ4422-222-2-2-2200002-222-2-2-22-20000−22−222-22-20000-2-22200000−220000000000−22−22−22−22-220022−2−20000000000002−20
χ4522-222-2-2-2200002-222-2-2-2-2200002−22−2-22-22000022-2-200000−2200000000002−22−2−22−22-220022−2−2000000000000−220
χ4622-222-2-2-2200002-222-2-2-2-2200002−22−2-22-220000-2-22200000−2200000000002−22−2−22−222-200−2−2220000000000002−20
χ4722-222-2-2-2200002-222-2-2-2-220000−22−22-22-22000022-2-2000002−20000000000−22−222−22−2-2200−2−2220000000000002−20
χ4822-222-2-2-2200002-222-2-2-2-220000−22−22-22-220000-2-222000002−20000000000−22−222−22−22-20022−2−2000000000000−220
χ492-2-22-222-222-2-22-2-22-22-220000000000000022-2-22i−2i2i−2i0002i−2i00002i−2i2i−2i000000000000002i−2i00000000002-20000000
χ502-2-22-222-222-2-22-2-22-22-220000000000000022-2-22i−2i2i−2i000−2i2i0000−2i2i−2i2i000000000000002i−2i0000000000-220000000
χ512-2-22-222-222-2-22-2-22-22-220000000000000022-2-2−2i2i−2i2i0002i−2i00002i−2i2i−2i00000000000000−2i2i0000000000-220000000
χ522-2-22-222-222-2-22-2-22-22-220000000000000022-2-2−2i2i−2i2i000−2i2i0000−2i2i−2i2i00000000000000−2i2i00000000002-20000000
χ532-2-22-222-22-222-2-2-22-22-22002-22-200000000-2-2222i−2i2i−2i00000000000002-22-20000000000−2i2i0000000000002i−2i00000
χ542-2-22-222-22-222-2-2-22-22-22002-22-200000000-2-222−2i2i−2i2i00000000000002-22-200000000002i−2i000000000000−2i2i00000
χ552-2-22-222-22-222-2-2-22-22-2200-22-2200000000-2-2222i−2i2i−2i0000000000000-22-220000000000−2i2i000000000000−2i2i00000
χ562-2-22-222-22-222-2-2-22-22-2200-22-2200000000-2-222−2i2i−2i2i0000000000000-22-2200000000002i−2i0000000000002i−2i00000
χ572-2-2-222-222-22-22-2-2-22-222002-2-2200000000-222-2000000000000000002-2-220000000000002-22-200000000002-2000
χ582-2-2-222-222-22-22-2-2-22-222002-2-2200000000-222-2000000000000000002-2-22000000000000-22-220000000000-22000
χ592-2-2-222-222-22-22-2-2-22-22200-222-200000000-222-200000000000000000-222-20000000000002-22-20000000000-22000
χ602-2-2-222-222-22-22-2-2-22-22200-222-200000000-222-200000000000000000-222-2000000000000-22-2200000000002-2000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-22222000000-4000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200000040000-2-2000000000000000000000000000000000000000
χ63444-4-44-4-44-4-44444-4-4-4-4400000000000000-44-440000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-2-4-444-2-22222-200000000002323−23−232-22-200000000000−2323000000000000000000000000000000000000000
χ65444-4-44-4-4-2-4-444-2-22222-20000000000−23−2323232-22-20000000000023−23000000000000000000000000000000000000000
χ6644-444-4-4-4-20000-22-2-22224-4000022−2222−22-22-22000000000000022−220000000000−22−22−22−2200000000000000000000000
χ6744-444-4-4-4-20000-22-2-22224-40000−2222−2222-22-220000000000000−222200000000002−22−22−22−200000000000000000000000
χ6844-444-4-4-4-20000-22-2-2222-44000022−2222−222-22-20000000000000−22220000000000−22−222−22−200000000000000000000000
χ6944-444-4-4-4-20000-22-2-2222-440000−2222−22222-22-2000000000000022−2200000000002−22−2−22−2200000000000000000000000
χ7044-4-4-4-444400004-4-4-444-400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ7144-4-4-4-444400004-4-4-444-4000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ7244-4-4-4-444-20000-2222-2-2200000022−22−222223−23−23230000000000000000000000000−222−26−6−6600000000000000000000000
χ7344-4-4-4-444-20000-2222-2-2200000022−22−2222−232323−230000000000000000000000000−222−2−666−600000000000000000000000
χ7444-4-4-4-444-20000-2222-2-22000000−222222−2223−23−232300000000000000000000000002−2−22−666−600000000000000000000000
χ7544-4-4-4-444-20000-2222-2-22000000−222222−22−232323−2300000000000000000000000002−2−226−6−6600000000000000000000000
χ764-444-4-4-4440000-444-4-44-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ774-444-4-4-4440000-444-4-44-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ784-44-44-44-440000-44-444-4-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ794-44-44-44-440000-44-444-4-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ804-4-44-444-4-24-4-4422-22-22-200000000000000-2-22200000004i−4i0000−2i2i−2i2i00000000000000000000000000000000000
χ814-4-44-444-4-24-4-4422-22-22-200000000000000-2-2220000000−4i4i00002i−2i2i−2i00000000000000000000000000000000000
χ824-4-44-444-4-2-444-422-22-22-2004-44-40000000022-2-200000000000000000-22-220000000000000000000000000000000
χ834-4-44-444-4-2-444-422-22-22-200-44-440000000022-2-2000000000000000002-22-20000000000000000000000000000000
χ844-4-4-444-4444-44-4-4-4-44-444000000000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-24-44-4222-22-2-200000000000000-222-20000000000000−2i32i32i3−2i300000000000000000000000000000000000
χ864-4-4-444-44-24-44-4222-22-2-200000000000000-222-200000000000002i3−2i3−2i32i300000000000000000000000000000000000
χ874-4-4-444-44-2-44-44222-22-2-2004-4-44000000002-2-2200000000000000000-222-20000000000000000000000000000000
χ884-4-4-444-44-2-44-44222-22-2-200-444-4000000002-2-22000000000000000002-2-220000000000000000000000000000000
χ898-888-8-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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