Finite Group Databasebeta

← Group #10697813

Character table — Group #10697813

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424248888888824242424242424242424242424242424444488884444
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
χ92222222222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ102222222222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ11222222222-222-2-222-2222222222222222-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-200000000
χ12222222222-222-2-222-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-2000000000000000000000000000000000000000000002i2i−2i−2i0000
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000000000000000000000000000−2i−2i2i2i0000
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
χ1922222222-12-2-222-2-22-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111000000003333−3−3−3−33333−3−3−3−3000000000000
χ2022222222-12-2-222-2-22-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000−3−3−3−33333−3−3−3−33333000000000000
χ2122222222-12-2-222-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1000000003333−3−3−3−3−3−3−3−33333000000000000
χ2222222222-12-2-222-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-100000000−3−3−3−333333333−3−3−3−3000000000000
χ23222-2-22-2-222002-200-222-2-22-2-20000000000000022-2-22-200002-2000000002222-2-2-2-222−2−222−2−222−2−222−2−222−2−222−2−2000000000000
χ24222-2-22-2-222002-200-222-2-22-2-20000000000000022-2-22-200002-2000000002222-2-2-2-2−2−222−2−222−2−222−2−222−2−222−2−222000000000000
χ25222-2-22-2-222002-200-222-2-22-2-200000000000000-2-2222-200002-200000000-2-2-2-2222222−2−2−2−22222−2−222−2−2−2−222−2−222000000000000
χ26222-2-22-2-222002-200-222-2-22-2-200000000000000-2-2222-200002-200000000-2-2-2-22222−2−22222−2−2−2−222−2−22222−2−222−2−2000000000000
χ27222-2-22-2-2-12002-200-2-1-111-11133−3−333−3−300000022-2-2-1133−3−3-113333−3−3−3−3-1-1-1-1111122−2−222−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ28222-2-22-2-2-12002-200-2-1-111-11133−3−333−3−300000022-2-2-1133−3−3-113333−3−3−3−3-1-1-1-11111−2−222−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ29222-2-22-2-2-12002-200-2-1-111-11133−3−333−3−3000000-2-222-1133−3−3-11−3−3−3−333331111-1-1-1-122−2−2−2−222ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ30222-2-22-2-2-12002-200-2-1-111-11133−3−333−3−3000000-2-222-1133−3−3-11−3−3−3−333331111-1-1-1-1−2−22222−2−2−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ31222-2-22-2-2-12002-200-2-1-111-111−3−333−3−33300000022-2-2-11−3−333-11−3−3−3−33333-1-1-1-1111122−2−222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ32222-2-22-2-2-12002-200-2-1-111-111−3−333−3−33300000022-2-2-11−3−333-11−3−3−3−33333-1-1-1-11111−2−222−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ33222-2-22-2-2-12002-200-2-1-111-111−3−333−3−333000000-2-222-11−3−333-113333−3−3−3−31111-1-1-1-122−2−2−2−222ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ34222-2-22-2-2-12002-200-2-1-111-111−3−333−3−333000000-2-222-11−3−333-113333−3−3−3−31111-1-1-1-1−2−22222−2−2−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3522-22-2-22-2202200-2-202-22-2-22-22222-2-2-2-20022−2−22−22−20000000022−2−222−2−222−2−222−2−20000000000000000000000002-2002−22−20000
χ3622-22-2-22-2202200-2-202-22-2-22-22222-2-2-2-20022−2−22−22−20000000022−2−222−2−222−2−222−2−2000000000000000000000000-2200−22−220000
χ3722-22-2-22-2202200-2-202-22-2-22-22222-2-2-2-200−2−222−22−2200000000−2−222−2−222−2−222−2−2220000000000000000000000002-200−22−220000
χ3822-22-2-22-2202200-2-202-22-2-22-22222-2-2-2-200−2−222−22−2200000000−2−222−2−222−2−222−2−222000000000000000000000000-22002−22−20000
χ3922-22-2-22-220-2-2002202-22-2-22-2-2-2-2-222220022−2−2−22−220000000022−2−222−2−2−2−222−2−222000000000000000000000000002i−2i−i2i2i2−i20000
χ4022-22-2-22-220-2-2002202-22-2-22-2-2-2-2-222220022−2−2−22−220000000022−2−222−2−2−2−222−2−22200000000000000000000000000−2i2ii2−i2−i2i20000
χ4122-22-2-22-220-2-2002202-22-2-22-2-2-2-2-2222200−2−2222−22−200000000−2−222−2−22222−2−222−2−2000000000000000000000000002i−2ii2−i2−i2i20000
χ4222-22-2-22-220-2-2002202-22-2-22-2-2-2-2-2222200−2−2222−22−200000000−2−222−2−22222−2−222−2−200000000000000000000000000−2i2i−i2i2i2−i20000
χ432-2-2222-2-22200-2200-2-2-2222-2-200000000002-22-200002-20000-222-22-22-22-2000000002−22−22−22−22−22−22−22−22−22−22−22−2000000000000
χ442-2-2222-2-22200-2200-2-2-2222-2-200000000002-22-200002-20000-222-22-22-22-200000000−22−22−22−22−22−22−22−22−22−22−22−22000000000000
χ452-2-2222-2-22200-2200-2-2-2222-2-20000000000-22-2200002-20000-22-22-22-22-22000000002−22−2−22−222−22−22−22−2−22−22−22−22000000000000
χ462-2-2222-2-22200-2200-2-2-2222-2-20000000000-22-2200002-20000-22-22-22-22-2200000000−22−222−22−2−22−22−22−222−22−22−22−2000000000000
χ472-2-2222-2-2-1200-2200-211-1-1-1113−33−33−33−3002-22-20000-113−33−31-1-11-11-11-113−33−33−33−32−22−22−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ482-2-2222-2-2-1200-2200-211-1-1-1113−33−33−33−3002-22-20000-113−33−31-1-11-11-11-113−33−33−33−3−22−22−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ492-2-2222-2-2-1200-2200-211-1-1-1113−33−33−33−300-22-220000-113−33−31-11-11-11-11-1−33−33−33−332−22−2−22−22ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ502-2-2222-2-2-1200-2200-211-1-1-1113−33−33−33−300-22-220000-113−33−31-11-11-11-11-1−33−33−33−33−22−222−22−2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ512-2-2222-2-2-1200-2200-211-1-1-111−33−33−33−33002-22-20000-11−33−331-1-11-11-11-11−33−33−33−332−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ522-2-2222-2-2-1200-2200-211-1-1-111−33−33−33−33002-22-20000-11−33−331-1-11-11-11-11−33−33−33−33−22−22−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ532-2-2222-2-2-1200-2200-211-1-1-111−33−33−33−3300-22-220000-11−33−331-11-11-11-11-13−33−33−33−32−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ542-2-2222-2-2-1200-2200-211-1-1-111−33−33−33−3300-22-220000-11−33−331-11-11-11-11-13−33−33−33−3−22−222−22−2−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ552-2-2-2-2222222-2-2-22-22-2-2-2-22222-2-222-2-222-200000000222-2-22-2-200000000000000002-2-2200002-2-222-2-2200000000000000000000
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χ582-2-2-2-222222-22-2-2-222-2-2-2-2222-222-2-222-2-220000000022-222-2-2-200000000000000000000-222-200000000-222-2-222-2000000000000
χ592-2-2-2-22222-22-2222-2-2-2-2-2-22222-2-222-2-22-2200000000-2-2-222-2220000000000000000000000000000000000000000000000002-200
χ602-2-2-2-22222-22-2222-2-2-2-2-2-22222-2-222-2-22-2200000000-2-2-222-222000000000000000000000000000000000000000000000000-2200
χ612-2-2-2-22222-2-2222-22-2-2-2-2-2222-222-2-222-22-200000000-2-22-2-2222000000000000000000000000000000000000000000000000002-2
χ622-2-2-2-22222-2-2222-22-2-2-2-2-2222-222-2-222-22-200000000-2-22-2-222200000000000000000000000000000000000000000000000000-22
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χ642-2-2-2-2222-122-2-2-22-221111-1-1-1-111-1-111-12-200000000-1-1-111-1113−33−3−33−33−33−333−33−3-222-200001-1-111-1-113−3−33−333−3000000000000
χ652-2-2-2-2222-122-2-2-22-221111-1-1-1-111-1-111-12-200000000-1-1-111-111−33−333−33−33−33−3−33−332-2-220000-111-1-111-13−3−33−333−3000000000000
χ662-2-2-2-2222-122-2-2-22-221111-1-1-1-111-1-111-12-200000000-1-1-111-111−33−333−33−33−33−3−33−33-222-200001-1-111-1-11−333−33−3−33000000000000
χ672-2-2-2-2222-12-22-2-2-2221111-1-1-11-1-111-1-11-2200000000-1-11-1-11113−33−3−33−333−33−3−33−3300002-2-223−3−33−333−3-111-1-111-1000000000000
χ682-2-2-2-2222-12-22-2-2-2221111-1-1-11-1-111-1-11-2200000000-1-11-1-11113−33−3−33−333−33−3−33−330000-222-2−333−33−3−331-1-111-1-11000000000000
χ692-2-2-2-2222-12-22-2-2-2221111-1-1-11-1-111-1-11-2200000000-1-11-1-1111−33−333−33−3−33−333−33−300002-2-22−333−33−3−33-111-1-111-1000000000000
χ702-2-2-2-2222-12-22-2-2-2221111-1-1-11-1-111-1-11-2200000000-1-11-1-1111−33−333−33−3−33−333−33−30000-222-23−3−33−333−31-1-111-1-11000000000000
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χ7944-44-4-44-4-20-4-400440-22-222-222222-2-2-2-200−22−22222222−2222−220000000022−2−222−2−2−2−222−2−222000000000000000000000000000000000000
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χ884-444-4-4-44-2000000002-2-2222-223−2323−23−2323−23230022−22−2222000000000000−222−2−222−26−6−666−6−66000000000000000000000000000000000000
χ894-444-4-4-44-2000000002-2-2222-223−2323−23−2323−232300−222222−220000000000002−2−222−2−22−666−6−666−6000000000000000000000000000000000000
χ904-444-4-4-44-2000000002-2-2222-2−2323−232323−2323−230022−22−2222000000000000−222−2−222−2−666−6−666−6000000000000000000000000000000000000
χ914-444-4-4-44-2000000002-2-2222-2−2323−232323−2323−2300−222222−220000000000002−2−222−2−226−6−666−6−66000000000000000000000000000000000000
χ924-44-44-44-4404-400-440-44-44-44-44-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-440-44004-40-44-44-44-4-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-4-204-400-4402-22-22-22-222-22-2-220000000000000000006−6−66−666−6−666−66−6−66000000000000000000000000000000000000
χ954-44-44-44-4-204-400-4402-22-22-22-222-22-2-22000000000000000000−666−66−6−666−6−66−666−6000000000000000000000000000000000000
χ964-44-44-44-4-20-44004-402-22-22-222-2-22-222-20000000000000000006−6−66−666−66−6−66−666−6000000000000000000000000000000000000
χ974-44-44-44-4-20-44004-402-22-22-222-2-22-222-2000000000000000000−666−66−6−66−666−66−6−66000000000000000000000000000000000000
χ984-4-4444-4-44-4004-4004-4-4444-4-4000000000000000000-4400004-40000000000000000000000000000000000000000000000000000
χ994-4-4444-4-4-2-4004-400422-2-2-22223−2323−2323−2323−2300000000002-2−2323−2323-220000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-4-2-4004-400422-2-2-222−2323−2323−2323−232300000000002-223−2323−23-220000000000000000000000000000000000000000000000000000
χ1014-4-4-4-4444-2-44-4444-4-42222-2-2-2-222-2-222-2-4400000000222-2-22-2-20000000000000000000000000000000000000000000000000000
χ1024-4-4-4-4444-2-4-4444-44-42222-2-2-22-2-222-2-224-40000000022-222-2-2-20000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.