Finite Group Databasebeta

← Group #10698225

Character table — Group #10698225

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424244444888812121212121212122424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9222222222222-2-2-22-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ10222222222222-2-2-22-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ11222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-200002222-2-2-2-200000000000000000000
χ12222222222-2-2-2222-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-2220000-2-2-2-2222200000000000000000000
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000000000000000000000002-200
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000-2200
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-20000-1-1-1-111113333−3−3−3−3000000000000
χ2022222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22200001111-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-20000-1-1-1-11111−3−3−3−33333000000000000
χ2222222222-1-2-2-2222-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22200001111-1-1-1-13333−3−3−3−3000000000000
χ23222-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-2-2-22-20000000022-2-222-2-2000000000000000000000000000000000000000000000000002-2
χ24222-2-2-2-22222-222-2-2-2-2-2222-2-22222-2-2-2-22-20000000022-2-222-2-200000000000000000000000000000000000000000000000000-22
χ25222-2-2-2-22222-2-2-22-22-2-2222-2-22222-2-2-2-2-2200000000-2-222-2-222000000000000000000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000
χ26222-2-2-2-22222-2-2-22-22-2-2222-2-22222-2-2-2-2-2200000000-2-222-2-22200000000000000000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000
χ27222-2-2-2-222-2-2222-22-2-2-2222-2-2-2-2-2-22222-220000000022-2-2-2-222000000000000000000000000000000000000000000002i2i−2i−2i0000
χ28222-2-2-2-222-2-2222-22-2-2-2222-2-2-2-2-2-22222-220000000022-2-2-2-22200000000000000000000000000000000000000000000−2i−2i2i2i0000
χ29222-2-2-2-222-2-22-2-2222-2-2222-2-2-2-2-2-222222-22i2i2i2i−2i−2i−2i−2i-2-22222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ30222-2-2-2-222-2-22-2-2222-2-2222-2-2-2-2-2-222222-2−2i−2i−2i−2i2i2i2i2i-2-22222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ31222-2-2-2-22-122-2-2-22-2211-1-1-111-1-1-1-11111-220000000011-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300002i2i−2i−2i33−3−333−3−3−i−iii−i−iii000000000000
χ32222-2-2-2-22-122-2-2-22-2211-1-1-111-1-1-1-11111-220000000011-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i30000−2i−2i2i2i−3−333−3−333ii−i−iii−i−i000000000000
χ33222-2-2-2-22-122-2-2-22-2211-1-1-111-1-1-1-11111-220000000011-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300002i2i−2i−2i−3−333−3−333−i−iii−i−iii000000000000
χ34222-2-2-2-22-122-2-2-22-2211-1-1-111-1-1-1-11111-220000000011-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i30000−2i−2i2i2i33−3−333−3−3ii−i−iii−i−i000000000000
χ35222-2-2-2-22-1-2-22-2-222211-1-1-1111111-1-1-1-12-22i2i2i2i−2i−2i−2i−2i11-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ36222-2-2-2-22-1-2-22-2-222211-1-1-1111111-1-1-1-12-22i2i2i2i−2i−2i−2i−2i11-1-1-1-111−i−i−i−iiiii−i−i−i−iiiii00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ37222-2-2-2-22-1-2-22-2-222211-1-1-1111111-1-1-1-12-2−2i−2i−2i−2i2i2i2i2i11-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ38222-2-2-2-22-1-2-22-2-222211-1-1-1111111-1-1-1-12-2−2i−2i−2i−2i2i2i2i2i11-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ3922-22-22-2-222-2-200020-2-22-2-22222-2-2-2-2220022−2−222−2−20000000022−2−222−2−222−2−222−2−20000000000000000000000002i−2i00−i2i2−i2i20000
χ4022-22-22-2-222-2-200020-2-22-2-22222-2-2-2-2220022−2−222−2−20000000022−2−222−2−222−2−222−2−2000000000000000000000000−2i2i00i2−i2i2−i20000
χ4122-22-22-2-222-2-200020-2-22-2-22222-2-2-2-22200−2−222−2−22200000000−2−222−2−222−2−222−2−2220000000000000000000000002i−2i00i2−i2i2−i20000
χ4222-22-22-2-222-2-200020-2-22-2-22222-2-2-2-22200−2−222−2−22200000000−2−222−2−222−2−222−2−222000000000000000000000000−2i2i00−i2i2−i2i20000
χ4322-2-22-22-22-22-200020222-2-2-2-2-2-222-2-22200−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000002i−2i2−2−220000
χ4422-2-22-22-22-22-200020222-2-2-2-2-2-222-2-22200−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000−2i2i−222−20000
χ4522-2-22-22-22-22-200020222-2-2-2-2-2-222-2-22200i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000002i−2i−222−20000
χ4622-2-22-22-22-22-200020222-2-2-2-2-2-222-2-22200i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000−2i2i2−2−220000
χ472-2-22-2-22220002-220-22-2-22-22-200000000002−22−22−22−22-22-200002−22−22−22−22−22−22−22−2002i−2i−i2i2−i2i200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ482-2-22-2-22220002-220-22-2-22-22-200000000002−22−22−22−22-22-200002−22−22−22−22−22−22−22−200−2i2ii2−i2i2−i20000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-22-2-22220002-220-22-2-22-22-20000000000−22−22−22−222-22-20000−22−22−22−22−22−22−22−22002i−2ii2−i2i2−i200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ502-2-22-2-22220002-220-22-2-22-22-20000000000−22−22−22−222-22-20000−22−22−22−22−22−22−22−2200−2i2i−i2i2−i2i20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ512-2-22-2-222-10002-220-2-111-11-113−33−33−33−3002−22−22−22−2-11-113−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23002i−2i−i2i2−i2i2−i3i3−i3i3−ii−iiζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ522-2-22-2-222-10002-220-2-111-11-113−33−33−33−3002−22−22−22−2-11-113−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300−2i2ii2−i2i2−i2i3−i3i3−i3i−ii−i−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ532-2-22-2-222-10002-220-2-111-11-113−33−33−33−300−22−22−22−22-11-113−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23002i−2ii2−i2i2−i2−i3i3−i3i3−ii−ii−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ542-2-22-2-222-10002-220-2-111-11-113−33−33−33−300−22−22−22−22-11-113−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300−2i2i−i2i2−i2i2i3−i3i3−i3i−ii−iζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ552-2-22-2-222-10002-220-2-111-11-11−33−33−33−33002−22−22−22−2-11-11−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7002i−2i−i2i2−i2i2i3−i3i3−i3−ii−iiζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ562-2-22-2-222-10002-220-2-111-11-11−33−33−33−33002−22−22−22−2-11-11−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700−2i2ii2−i2i2−i2−i3i3−i3i3i−ii−i−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ572-2-22-2-222-10002-220-2-111-11-11−33−33−33−3300−22−22−22−22-11-11−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7002i−2ii2−i2i2−i2i3−i3i3−i3−ii−ii−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ582-2-22-2-222-10002-220-2-111-11-11−33−33−33−3300−22−22−22−22-11-11−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700−2i2i−i2i2−i2i2−i3i3−i3i3i−ii−iζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ592-2-2-222-222000-2220-2-22-22-2-220000000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22i−2i002−2−22−2i2i2i−2i00002−2−222−2−22000000000000
χ602-2-2-222-222000-2220-2-22-22-2-220000000000−i2i2−i2i2i2−i2i2−i2-222-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−2i2i00−222−22i−2i−2i2i0000−222−2−222−2000000000000
χ612-2-2-222-222000-2220-2-22-22-2-220000000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22i−2i00−222−2−2i2i2i−2i0000−222−2−222−2000000000000
χ622-2-2-222-222000-2220-2-22-22-2-220000000000i2−i2i2−i2−i2i2−i2i2-222-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−2i2i002−2−222i−2i−2i2i00002−2−222−2−22000000000000
χ632-2-2-222-22-1000-2220-21-11-111-13−33−3−33−3300−i2i2−i2i2i2−i2i2−i21-1-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232i−2i002−2−22i−i−ii−i3i3i3−i3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ642-2-2-222-22-1000-2220-21-11-111-13−33−3−33−3300−i2i2−i2i2i2−i2i2−i21-1-11−333−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−2i2i00−222−2−iii−ii3−i3−i3i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ652-2-2-222-22-1000-2220-21-11-111-13−33−3−33−3300i2−i2i2−i2−i2i2−i2i21-1-11−333−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232i−2i00−222−2i−i−ii−i3i3i3−i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.