Finite Group Databasebeta

← Group #10698730

Character table — Group #10698730

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224466668888121212122424242424242424444488884444
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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ9222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-222220000-2-2-2-200000000000000000000
χ10222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-2-222-2-2-2-20000222200000000000000000000
χ11222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ12222222222-2-2-22222-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
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
χ1522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ1622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111000000000000
χ1722222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ1822222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ1922222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−322-2-2-1-1-1-1000011113333−3−3−3−3000000000000
χ2022222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-1111133333333−3−3−3−3−3−3−3−3-2-22211110000-1-1-1-1−3−3−3−33333000000000000
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−33333333322-2-2-1-1-1-100001111−3−3−3−33333000000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-111111111-2-200000000-1-1-1-11111−3−3−3−3−3−3−3−333333333-2-22211110000-1-1-1-13333−3−3−3−3000000000000
χ232222-2-2-2-2222-20000-222-2-22-2-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−22-20022-2-222−2−2000022−2−222−2−2000000000000
χ242222-2-2-2-2222-20000-222-2-22-2-200000000002222−2−2−2−222-2-200002222−2−2−2−22222−2−2−2−2-2200-2-222−2−2220000−2−222−2−222000000000000
χ252222-2-2-2-2222-20000-222-2-22-2-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−222222-20022-2-2−2−2220000−2−222−2−222000000000000
χ262222-2-2-2-2222-20000-222-2-22-2-20000000000−2−2−2−2222222-2-20000−2−2−2−22222−2−2−2−22222-2200-2-22222−2−2000022−2−222−2−2000000000000
χ272222-2-2-2-2-122-20000-2-1-111-111333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ232-200-1-11122−2−233−3−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ282222-2-2-2-2-122-20000-2-1-111-111333−3−3−33−3002222−2−2−2−2-1-1113−33−3ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23-220011-1-1−2−222−3−333−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ292222-2-2-2-2-122-20000-2-1-111-111333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ232-200-1-111−2−22233−3−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ302222-2-2-2-2-122-20000-2-1-111-111333−3−3−33−300−2−2−2−22222-1-1113−33−3−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23-220011-1-122−2−2−3−333ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ312222-2-2-2-2-122-20000-2-1-111-111−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ72-200-1-11122−2−2−3−333ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ322222-2-2-2-2-122-20000-2-1-111-111−3−3−3333−33002222−2−2−2−2-1-111−33−33ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7-220011-1-1−2−22233−3−3−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ332222-2-2-2-2-122-20000-2-1-111-111−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ72-200-1-111−2−222−3−333−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ342222-2-2-2-2-122-20000-2-1-111-111−3−3−3333−3300−2−2−2−22222-1-111−33−33−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7-220011-1-122−2−233−3−3ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ3522-2-2-222-2200022-2-202-22-2-2-2222-222-2-2-200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000002-2−i2−i2i2i20000
χ3622-2-2-222-2200022-2-202-22-2-2-2222-222-2-2-200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000-22i2i2−i2−i20000
χ3722-2-2-222-2200022-2-202-22-2-2-2222-222-2-2-200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000002-2i2i2−i2−i20000
χ3822-2-2-222-2200022-2-202-22-2-2-2222-222-2-2-200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000-22−i2−i2i2i20000
χ392-22-2-22-2220002-22-20-22-22-2-222-222-22-2-200−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000002i−2i002−22−20000
χ402-22-2-22-2220002-22-20-22-22-2-222-222-22-2-200−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000−2i2i00−22−220000
χ412-22-2-22-2220002-22-20-22-22-2-222-222-22-2-200i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000000000002i−2i00−22−220000
χ422-22-2-22-2220002-22-20-22-22-2-222-222-22-2-200i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000−2i2i002−22−20000
χ432-2-2222-2-222-222-2-22-2-2-2-2-22222-2-22-2-2222-2000000002-22-222-2-2000000000000000000000000000000000000000000002i−2i−2i2i0000
χ442-2-2222-2-222-222-2-22-2-2-2-2-22222-2-22-2-2222-2000000002-22-222-2-200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ452-2-2222-2-222-22-222-2-2-2-2-2-2222-222-222-2-2-22000000002-22-2-2-222000000000000000000000000000000000000000000000000002i−2i
χ462-2-2222-2-222-22-222-2-2-2-2-2-2222-222-222-2-2-22000000002-22-2-2-22200000000000000000000000000000000000000000000000000−2i2i
χ472-2-2222-2-22-22-22-2-222-2-2-2-22222-2-22-2-222-222-2-222-2-22-22-22-2-2222-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ482-2-2222-2-22-22-22-2-222-2-2-2-22222-2-22-2-222-22-222-2-222-2-22-22-2-222-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ492-2-2222-2-22-22-2-222-22-2-2-2-2222-222-222-2-22-200000000-22-2222-2-20000000000000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000
χ502-2-2222-2-22-22-2-222-22-2-2-2-2222-222-222-2-22-200000000-22-2222-2-2000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000
χ512-2-2222-2-2-1-22-22-2-2221111-1-1-1-111-111-1-1-222-2-222-2-221-11-111-1-1-111-1-111-1-111-1-111-10000−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3000000000000
χ522-2-2222-2-2-1-22-22-2-2221111-1-1-1-111-111-1-1-222-2-222-2-221-11-111-1-1-111-1-111-1-111-1-111-10000i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3000000000000
χ532-2-2222-2-2-1-22-22-2-2221111-1-1-1-111-111-1-1-22-222-2-222-21-11-111-1-11-1-111-1-111-1-111-1-110000−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3000000000000
χ542-2-2222-2-2-1-22-22-2-2221111-1-1-1-111-111-1-1-22-222-2-222-21-11-111-1-11-1-111-1-111-1-111-1-110000i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3000000000000
χ552-2-2222-2-2-1-22-2-222-221111-1-1-11-1-11-1-1112-2000000001-11-1-1-1113−3−333−3−33−333−3−333−30000−i3i3−i3i32i−2i2i−2ii3−i3i3−i3−ii−ii−ii−ii000000000000
χ562-2-2222-2-2-1-22-2-222-221111-1-1-11-1-11-1-1112-2000000001-11-1-1-1113−3−333−3−33−333−3−333−30000i3−i3i3−i3−2i2i−2i2i−i3i3−i3i3i−ii−ii−ii−i000000000000
χ572-2-2222-2-2-1-22-2-222-221111-1-1-11-1-11-1-1112-2000000001-11-1-1-111−333−3−333−33−3−333−3−330000−i3i3−i3i3−2i2i−2i2ii3−i3i3−i3i−ii−ii−ii−i000000000000
χ582-2-2222-2-2-1-22-2-222-221111-1-1-11-1-11-1-1112-2000000001-11-1-1-111−333−3−333−33−3−333−3−330000i3−i3i3−i32i−2i2i−2i−i3i3−i3i3−ii−ii−ii−ii000000000000
χ592-2-22-2-2222-2220000-2-2-2222-2-200000000002−2−22−222−2-222-200002−2−22−222−22−2−22−222−2002i−2i0000−i2i2i2−i2−2i2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-22-2-2222-2220000-2-2-2222-2-200000000002−2−22−222−2-222-200002−2−22−222−22−2−22−222−200−2i2i0000i2−i2−i2i22i−2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ612-2-22-2-2222-2220000-2-2-2222-2-20000000000−222−22−2−22-222-20000−222−22−2−22−222−22−2−22002i−2i0000i2−i2−i2i2−2i2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ622-2-22-2-2222-2220000-2-2-2222-2-20000000000−222−22−2−22-222-20000−222−22−2−22−222−22−2−2200−2i2i0000−i2i2i2−i22i−2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ632-2-22-2-222-1-2220000-211-1-1-1113−3−3−3333−3002−2−22−222−21-1-11−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23002i−2ii3−i3−i3i3−i2i2i2−i2i−i−iiζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ642-2-22-2-222-1-2220000-211-1-1-1113−3−3−3333−3002−2−22−222−21-1-11−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ2300−2i2i−i3i3i3−i3i2−i2−i2i2−iii−i−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ652-2-22-2-222-1-2220000-211-1-1-1113−3−3−3333−300−222−22−2−221-1-11−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23002i−2ii3−i3−i3i3i2−i2−i2i2i−i−ii−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ662-2-22-2-222-1-2220000-211-1-1-1113−3−3−3333−300−222−22−2−221-1-11−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ2300−2i2i−i3i3i3−i3−i2i2i2−i2−iii−iζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.