Finite Group Databasebeta

← Group #10697546

Character table — Group #10697546

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466612121212444661212121212124444888812121212121212121212242424242424242424661212224488882288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ92222222222-2-222222222-2-2-222-2-222-2-200000000-2-2000000000000000000000022-2-200000000
χ102222222222-2-222222222-2-2-222-2-222-2-200000000-2-20000000000000000000000-2-22200000000
χ112222222-2-2-222-2222-2-2-2-2-22-22222-2-2-2-2000000002-20000000000000000000000000000002-200
χ122222222-2-2-222-2222-2-2-2-2-22-22222-2-2-2-2000000002-2000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-22222-2-20000-222222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-222-2-2220000-22-2-2-2-2222200000000000000000000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-1-1-111112-22-1-11111-1-122-2-200001-1-1-1-1-11111−i3−i3−i3−i3i3i3i3i300−i3i3−i3i3000000000000
χ20222222-1-2-2-2-2-2-2-1-1-111112-22-1-11111-1-122-2-200001-1-1-1-1-11111i3i3i3i3−i3−i3−i3−i300i3−i3i3−i3000000000000
χ21222222-1-2-2-2-2-2-2-1-1-111112-22-1-11111-1-1-2-22200001-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i300i3−i3i3−i3000000000000
χ22222222-1-2-2-2-2-2-2-1-1-111112-22-1-11111-1-1-2-22200001-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i300−i3i3−i3i3000000000000
χ232222-2-2222-222-22222222-2-22-2-222-2-22200000000-2-20000000000000000000000000022-2-20000
χ242222-2-2222-222-22222222-2-22-2-222-2-22200000000-2-200000000000000000000000000-2-2220000
χ252222-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-200002i2i−2i−2i22000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ262222-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000−2i−2i2i2i2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ272222-2-22-2-22222222-2-2-2-22-2-2-2-22222-2-200000000-2200000000000000002-222-2-2000000000000
χ282222-2-22-2-22222222-2-2-2-22-2-2-2-22222-2-200000000-220000000000000000-22-2-222000000000000
χ292222-2-22-2-22-2-22222-2-2-2-2-222-2-2-2-22222000000002-2000000000000000000000000000000002-2
χ302222-2-22-2-22-2-22222-2-2-2-2-222-2-2-2-22222000000002-200000000000000000000000000000000-22
χ312222-2-2-122-2-2-2-2-1-1-1-1-1-1-122-21111111100002i2i−2i−2i-1-133−3−333−3−3−i−iii−i−iii00−i3i3i3−i3000000000000
χ322222-2-2-122-2-2-2-2-1-1-1-1-1-1-122-21111111100002i2i−2i−2i-1-1−3−333−3−333−i−iii−i−iii00i3−i3−i3i3000000000000
χ332222-2-2-122-2-2-2-2-1-1-1-1-1-1-122-2111111110000−2i−2i2i2i-1-133−3−333−3−3ii−i−iii−i−i00i3−i3−i3i3000000000000
χ342222-2-2-122-2-2-2-2-1-1-1-1-1-1-122-2111111110000−2i−2i2i2i-1-1−3−333−3−333ii−i−iii−i−i00−i3i3i3−i3000000000000
χ352222-2-2-1-2-22222-1-1-111112-2-211-1-1-1-111000000001-133−3−3−3−33333−3−3−3−3332-2-1-111000000000000
χ362222-2-2-1-2-22222-1-1-111112-2-211-1-1-1-111000000001-133−3−3−3−333−3−33333−3−3-2211-1-1000000000000
χ372222-2-2-1-2-22222-1-1-111112-2-211-1-1-1-111000000001-1−3−33333−3−333−3−3−3−333-2211-1-1000000000000
χ382222-2-2-1-2-22222-1-1-111112-2-211-1-1-1-111000000001-1−3−33333−3−3−3−33333−3−32-2-1-111000000000000
χ392-22-22-222-2200-2-2-2222-2-20002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000002i−2i2−22−20000
χ402-22-22-222-2200-2-2-2222-2-20002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200000000−2i2i−22−220000
χ412-22-22-222-2200-2-2-2222-2-20002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000002i−2i−22−220000
χ422-22-22-222-2200-2-2-2222-2-20002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200000000−2i2i2−22−20000
χ432-22-2-2222-2-2002-2-2222-2-2000-2200-220000002−2−2200000000002−2−222−2−220000002-2002−2−220000
χ442-22-2-2222-2-2002-2-2222-2-2000-2200-220000002−2−2200000000002−2−222−2−22000000-2200−222−20000
χ452-22-2-2222-2-2002-2-2222-2-2000-2200-22000000−222−20000000000−222−2−222−20000002-200−222−20000
χ462-22-2-2222-2-2002-2-2222-2-2000-2200-22000000−222−20000000000−222−2−222−2000000-22002−2−220000
χ47444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-222-2-22200000000220000000000000000000000000000000000
χ48444444-2-4-4-444-4-2-2-22222-44-4-2-2-2-2222200000000-220000000000000000000000000000000000
χ494444-4-4-244-444-4-2-2-2-2-2-2-2-4-4422-2-222-2-200000000220000000000000000000000000000000000
χ504444-4-4-2-4-44-4-44-2-2-22222-4442222-2-2-2-200000000-220000000000000000000000000000000000
χ514-44-44-44-44-4004-4-44-4-4440004-400-440000000000000000000000000000000000000000000000
χ524-44-44-4-24-4400-422-2-2-222000-2200-22000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000
χ534-44-44-4-24-4400-422-2-2-222000-2200-220000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000
χ544-44-44-4-2-44-400422-222-2-2000-22002-2000000000000000000006−66−6−66−66000000000000000000
χ554-44-44-4-2-44-400422-222-2-2000-22002-200000000000000000000−66−666−66−6000000000000000000
χ564-44-4-444-44400-4-4-44-4-444000-44004-40000000000000000000000000000000000000000000000
χ574-44-4-44-24-4-400422-2-2-2220002-2002-200000022−22−22220000000000−222−2−222−2000000000000000000
χ584-44-4-44-24-4-400422-2-2-2220002-2002-2000000−222222−2200000000002−2−222−2−22000000000000000000
χ594-44-4-44-2-44400-422-222-2-20002-200-2200000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ604-44-4-44-2-44400-422-222-2-20002-200-2200000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ614-4-440040004-404-4-40000000004-400002-22-20000002-22-22-22-200000000000000000000000000
χ624-4-440040004-404-4-40000000004-40000-22-22000000-22-22-22-2200000000000000000000000000
χ634-4-44004000-4404-4-4000000000-4400002-2-220000002-22-2-22-2200000000000000000000000000
χ644-4-44004000-4404-4-4000000000-440000-222-2000000-22-222-22-200000000000000000000000000
χ654-4-4400-20004-40-22223−2323−2300000-220023−232-22-2000000−1+31−3−1−31+3−1−31+3−1+31−300000000000000000000000000
χ664-4-4400-20004-40-22223−2323−2300000-220023−23-22-220000001−3−1+31+3−1−31+3−1−31−3−1+300000000000000000000000000
χ674-4-4400-20004-40-222−2323−232300000-2200−23232-22-2000000−1−31+3−1+31−3−1+31−3−1−31+300000000000000000000000000
χ684-4-4400-20004-40-222−2323−232300000-2200−2323-22-220000001+3−1−31−3−1+31−3−1+31+3−1−300000000000000000000000000
χ694-4-4400-2000-440-22223−2323−23000002-200−23232-2-22000000−1−31+3−1+31−31−3−1+31+3−1−300000000000000000000000000
χ704-4-4400-2000-440-22223−2323−23000002-200−2323-222-20000001+3−1−31−3−1+3−1+31−3−1−31+300000000000000000000000000
χ714-4-4400-2000-440-222−2323−2323000002-20023−232-2-22000000−1+31−3−1−31+31+3−1−31−3−1+300000000000000000000000000
χ724-4-4400-2000-440-222−2323−2323000002-20023−23-222-20000001−3−1+31+3−1−3−1−31+3−1+31−300000000000000000000000000
χ7388-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ7488-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000

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