Finite Group Databasebeta

← Group #10698630

Character table — Group #10698630

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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111
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
χ13222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000000000000000000000000000-22
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
χ23222-2-2-22-222-2-20000222-2-22-2-20000000000−i2−i2−i2−i2i2i2i2i222-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22-20022-2-2−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000000000
χ24222-2-2-22-222-2-20000222-2-22-2-20000000000−i2−i2−i2−i2i2i2i2i222-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-2200-2-222i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000
χ25222-2-2-22-222-2-20000222-2-22-2-20000000000i2i2i2i2−i2−i2−i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22-20022-2-2i2i2−i2−i20000i2i2−i2−i2i2i2−i2−i2000000000000
χ26222-2-2-22-222-2-20000222-2-22-2-20000000000i2i2i2i2−i2−i2−i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2200-2-222−i2−i2i2i20000−i2−i2i2i2−i2−i2i2i2000000000000
χ27222-2-2-22-2-12-2-200002-1-111-111333−3−3−33−300−i2−i2−i2−i2i2i2i2i2-1-1113−33−3ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ232-200-1-111−i2−i2i2i233−3−3ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ28222-2-2-22-2-12-2-200002-1-111-111333−3−3−33−300−i2−i2−i2−i2i2i2i2i2-1-1113−33−3ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23-220011-1-1i2i2−i2−i2−3−333−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ29222-2-2-22-2-12-2-200002-1-111-111333−3−3−33−300i2i2i2i2−i2−i2−i2−i2-1-1113−33−3−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ232-200-1-111i2i2−i2−i233−3−3−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
χ30222-2-2-22-2-12-2-200002-1-111-111333−3−3−33−300i2i2i2i2−i2−i2−i2−i2-1-1113−33−3−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23-220011-1-1−i2−i2i2i2−3−333ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ31222-2-2-22-2-12-2-200002-1-111-111−3−3−3333−3300−i2−i2−i2−i2i2i2i2i2-1-111−33−33ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ72-200-1-111−i2−i2i2i2−3−333ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ32222-2-2-22-2-12-2-200002-1-111-111−3−3−3333−3300−i2−i2−i2−i2i2i2i2i2-1-111−33−33ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7-220011-1-1i2i2−i2−i233−3−3−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ33222-2-2-22-2-12-2-200002-1-111-111−3−3−3333−3300i2i2i2i2−i2−i2−i2−i2-1-111−33−33−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ72-200-1-111i2i2−i2−i2−3−333−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7000000000000
χ34222-2-2-22-2-12-2-200002-1-111-111−3−3−3333−3300i2i2i2i2−i2−i2−i2−i2-1-111−33−33−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7ζ5+ζ7-220011-1-1−i2−i2i2i233−3−3ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7000000000000
χ3522-2-22-2-22200022-2-202-22-2-2-2222-222-2-2-200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000002-2−i2−i2i2i20000
χ3622-2-22-2-22200022-2-202-22-2-2-2222-222-2-2-200−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000-22i2i2−i2−i20000
χ3722-2-22-2-22200022-2-202-22-2-2-2222-222-2-2-200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000002-2i2i2−i2−i20000
χ3822-2-22-2-22200022-2-202-22-2-2-2222-222-2-2-200i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000-22−i2−i2i2i20000
χ392-222-2-2-22222-22-22-2-2-2-2-2-22222-222-22-2-2-22000000002-22-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i0000
χ402-222-2-2-22222-22-22-2-2-2-2-2-22222-222-22-2-2-22000000002-22-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ412-222-2-2-22222-2-22-22-2-2-2-2-2222-22-2-22-2222-2000000002-22-222-2-20000000000000000000000000000000000000000000000002i−2i00
χ422-222-2-2-22222-2-22-22-2-2-2-2-2222-22-2-22-2222-2000000002-22-222-2-2000000000000000000000000000000000000000000000000−2i2i00
χ432-222-2-2-222-2-222-22-22-2-2-2-22222-222-22-2-22-22i−2i2i−2i2i−2i2i−2i-22-2222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ442-222-2-2-222-2-222-22-22-2-2-2-22222-222-22-2-22-2−2i2i−2i2i−2i2i−2i2i-22-2222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ452-222-2-2-222-2-22-22-222-2-2-2-2222-22-2-22-222-2200000000-22-22-2-2220000000000000000000000002-22-200002-22-22-22-2000000000000
χ462-222-2-2-222-2-22-22-222-2-2-2-2222-22-2-22-222-2200000000-22-22-2-222000000000000000000000000-22-220000-22-22-22-22000000000000
χ472-222-2-2-22-1-2-222-22-221111-1-1-1-11-1-11-1112-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000−i3i3−i3i30000−i3i3−i3i33−33−3−33−33000000000000
χ482-222-2-2-22-1-2-222-22-221111-1-1-1-11-1-11-1112-22i−2i2i−2i2i−2i2i−2i1-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000i3−i3i3−i30000i3−i3i3−i3−33−333−33−3000000000000
χ492-222-2-2-22-1-2-222-22-221111-1-1-1-11-1-11-1112-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000−i3i3−i3i30000−i3i3−i3i3−33−333−33−3000000000000
χ502-222-2-2-22-1-2-222-22-221111-1-1-1-11-1-11-1112-2−2i2i−2i2i−2i2i−2i2i1-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000i3−i3i3−i30000i3−i3i3−i33−33−3−33−33000000000000
χ512-222-2-2-22-1-2-22-22-2221111-1-1-11-111-11-1-1-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000−i3i3−i3i32-22-2i3−i3i3−i3-11-11-11-11000000000000
χ522-222-2-2-22-1-2-22-22-2221111-1-1-11-111-11-1-1-22000000001-11-111-1-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000i3−i3i3−i3-22-22−i3i3−i3i31-11-11-11-1000000000000
χ532-222-2-2-22-1-2-22-22-2221111-1-1-11-111-11-1-1-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000−i3i3−i3i3-22-22i3−i3i3−i31-11-11-11-1000000000000
χ542-222-2-2-22-1-2-22-22-2221111-1-1-11-111-11-1-1-22000000001-11-111-1-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000i3−i3i3−i32-22-2−i3i3−i3i3-11-11-11-11000000000000
χ552-22-222-2-22-22-200002-2-2222-2-200000000002−22−2−22−22-222-200002−22−2−22−222−22−2−22−22002i−2i0000−i2i2i2−i22i−2i−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ562-22-222-2-22-22-200002-2-2222-2-200000000002−22−2−22−22-222-200002−22−2−22−222−22−2−22−2200−2i2i0000i2−i2−i2i2−2i2i2i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ572-22-222-2-22-22-200002-2-2222-2-20000000000−22−222−22−2-222-20000−22−222−22−2−22−222−22−2002i−2i0000i2−i2−i2i22i−2i−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ582-22-222-2-22-22-200002-2-2222-2-20000000000−22−222−22−2-222-20000−22−222−22−2−22−222−22−200−2i2i0000−i2i2i2−i2−2i2i2i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ592-22-222-2-2-1-22-20000211-1-1-1113−33−33−3−33002−22−2−22−221-1-113−3−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7002i−2i−i3i3i3−i3−i2i2i2−i2−iii−iζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ602-22-222-2-2-1-22-20000211-1-1-1113−33−33−3−33002−22−2−22−221-1-113−3−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700−2i2ii3−i3−i3i3i2−i2−i2i2i−i−ii−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ612-22-222-2-2-1-22-20000211-1-1-1113−33−33−3−3300−22−222−22−21-1-113−3−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7002i−2i−i3i3i3−i3i2−i2−i2i2−iii−i−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ622-22-222-2-2-1-22-20000211-1-1-1113−33−33−3−3300−22−222−22−21-1-113−3−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700−2i2ii3−i3−i3i3−i2i2i2−i2i−i−iiζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.