Finite Group Databasebeta

← Group #10713913

Character table — Group #10713913

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1244222344466688881212121222446666668888881212121212122424242424242424242424242424242424446612121212121216161616161616162444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1
χ922222222222222-2-2-2-222222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222222-2-2-2-22-2-2-2-2-2-2-2-222222222000000000000000000000000
χ112222222-1222-1-1-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ122222222-1222-1-1-12222-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222-1222-1-1-12222-1-1-1-1-2-2-2-2-1-1111122-2-2-2-2-11111-1-1-1-1-1-1-1-1-11111111122-2-2-1-11111-1-1000000000000
χ142222222-1222-1-1-12222-1-1-1-1-2-2-2-2-1-1111122-2-2-2-2-11111-1-1-1-1-1-1-1-1-111111111-2-22211-1-1-1-111000000000000
χ152222222-1222-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000−i3i3−i3−i3i3i3−i3i3000000000000
χ162222222-1222-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000i3−i3i3i3−i3−i3i3−i3000000000000
χ172222222-1222-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-1-11111-2-22222-11111-111111111-1-1-1-1-1-1-1-10000−i3i3i3i3−i3−i3−i3i3000000000000
χ182222222-1222-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-1-11111-2-22222-11111-111111111-1-1-1-1-1-1-1-10000i3−i3−i3−i3i3i3i3−i3000000000000
χ1922222-2-22-2-22-2-22222222-2-200002-20000-2-20000-2000022222-2-2-2-20000000000000000000022-2-200000000
χ2022222-2-22-2-22-2-22222222-2-200002-20000-2-20000-2000022222-2-2-2-200000000000000000000-2-22200000000
χ2122222-2-22-2-22-2-22-2-2-2-222-2-200002-20000220000-200002-2-2-2-222220000000000000000000000002i2i−2i−2i0000
χ2222222-2-22-2-22-2-22-2-2-2-222-2-200002-20000220000-200002-2-2-2-22222000000000000000000000000−2i−2i2i2i0000
χ2322-2-22222-2-2-22220000-2-2-2-222-2-2222222000000-2-2-2-2-2-200000000000000000000000000002−22−22−22−20000
χ2422-2-22222-2-2-22220000-2-2-2-222-2-2222222000000-2-2-2-2-2-20000000000000000000000000000−22−22−22−220000
χ2522-2-22222-2-2-22220000-2-2-2-2-2-22222-2-2-2-2000000-22222-200000000000000000000000000002−22−2−22−220000
χ2622-2-22222-2-2-22220000-2-2-2-2-2-22222-2-2-2-2000000-22222-20000000000000000000000000000−22−222−22−20000
χ2722-2-22-2-2222-2-2-220000-2-22200002-20000002i2i−2i−2i20000-2000000002i2i2i2i−2i−2i−2i−2i0000000000002−2−22−i2i2i2−i20000
χ2822-2-22-2-2222-2-2-220000-2-22200002-20000002i2i−2i−2i20000-2000000002i2i2i2i−2i−2i−2i−2i000000000000−222−2i2−i2−i2i20000
χ2922-2-22-2-2222-2-2-220000-2-22200002-2000000−2i−2i2i2i20000-200000000−2i−2i−2i−2i2i2i2i2i0000000000002−2−22i2−i2−i2i20000
χ3022-2-22-2-2222-2-2-220000-2-22200002-2000000−2i−2i2i2i20000-200000000−2i−2i−2i−2i2i2i2i2i000000000000−222−2−i2i2i2−i20000
χ3122-2-2-22-222-2222222-2-2-2-2-2-20000-2-200002-2000020000222-2-222-2-200000000002-2002-22-200000000000000
χ3222-2-2-22-222-2222222-2-2-2-2-2-20000-2-200002-2000020000222-2-222-2-20000000000-2200-22-2200000000000000
χ3322-2-2-22-222-22222-2-222-2-2-2-20000-2-20000-220000200002-2-222-2-222000000002-200220000-2-2000000000000
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χ3622-2-2-22-2-12-22-1-1-122-2-21111000011−i3−i3i3i32-20000-1−i3−i3i3i3-1-1-111-1-111−i3−i3i3i3−i3−i3i3i300-22i3−i31-11-1−i3i3000000000000
χ3722-2-2-22-2-12-22-1-1-122-2-21111000011i3i3−i3−i32-20000-1i3i3−i3−i3-1-1-111-1-111i3i3−i3−i3i3i3−i3−i3002-2i3−i3-11-11−i3i3000000000000
χ3822-2-2-22-2-12-22-1-1-122-2-21111000011i3i3−i3−i32-20000-1i3i3−i3−i3-1-1-111-1-111i3i3−i3−i3i3i3−i3−i300-22−i3i31-11-1i3−i3000000000000
χ3922-2-2-22-2-12-22-1-1-1-2-2221111000011−i3−i3i3i3-220000-1−i3−i3i3i3-111-1-111-1-1i3i3−i3−i3i3i3−i3−i32-200-1-1−i3i3i3−i311000000000000
χ4022-2-2-22-2-12-22-1-1-1-2-2221111000011−i3−i3i3i3-220000-1−i3−i3i3i3-111-1-111-1-1i3i3−i3−i3i3i3−i3−i3-220011i3−i3−i3i3-1-1000000000000
χ4122-2-2-22-2-12-22-1-1-1-2-2221111000011i3i3−i3−i3-220000-1i3i3−i3−i3-111-1-111-1-1−i3−i3i3i3−i3−i3i3i32-200-1-1i3−i3−i3i311000000000000
χ4222-2-2-22-2-12-22-1-1-1-2-2221111000011i3i3−i3−i3-220000-1i3i3−i3−i3-111-1-111-1-1−i3−i3i3i3−i3−i3i3i3-220011−i3i3i3−i3-1-1000000000000
χ4322-2-2-2-222-222-2-2222-2-2-2-2220000-220000-220000-20000222-2-2-2-2220000000000000000000000000000002-2
χ4422-2-2-2-222-222-2-2222-2-2-2-2220000-220000-220000-20000222-2-2-2-222000000000000000000000000000000-22
χ4522-2-2-2-222-222-2-22-2-222-2-2220000-2200002-20000-200002-2-22222-2-200000000000000000000000000002-200
χ4622-2-2-2-222-222-2-22-2-222-2-2220000-2200002-20000-200002-2-22222-2-20000000000000000000000000000-2200
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χ5544-4-4444-2-4-4-4-2-2-20000222244-4-4-2-2-2-2-2-20000002222220000000000000000000000000000000000000000
χ5644-4-4444-2-4-4-4-2-2-200002222-4-444-2-222220000002-2-2-2-220000000000000000000000000000000000000000
χ5744-4-44-4-4-244-422-2000022-2-20000-220000004i4i−4i−4i-20000200000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ5844-4-44-4-4-244-422-2000022-2-20000-22000000−4i−4i4i4i-200002000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ5944-4-4-4-44-2-44422-244-4-422-2-200002-20000-44000020000-2-2-22222-2-200000000000000000000000000000000
χ6044-4-4-4-44-2-44422-2-4-44422-2-200002-200004-4000020000-222-2-2-2-22200000000000000000000000000000000
χ614-44i−4i000400000-4−2i22i222−224i−4i002-22i−2i002-22-2002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1302i−2i2i−2i0−2i22i222−2200002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
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χ634-44i−4i000400000-42i2−2i2−22224i−4i002-22i−2i002-22-200−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302i−2i2i−2i02i2−2i2−22220000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ644-44i−4i000400000-42i2−2i2−22224i−4i00-22−2i2i00-22-22002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2i2i−2i2i02i2−2i2−222200002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
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χ664-44i−4i000-2000−2i32i32−2i22i222−22−2i2i23−23-22−2i2i001+i3−1−i31−i3−1+i300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130−2ζ142ζ14−2ζ222ζ220i2−i2−226−6i6−i6−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23000000000000000000000000
χ674-44i−4i000-2000−2i32i322i2−2i2−2222−2i2i23−232-22i−2i00−1−i31+i3−1+i31−i300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ14−2ζ142ζ22−2ζ220−i2i22−2−66−i6i6−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23000000000000000000000000
χ684-44i−4i000-2000−2i32i322i2−2i2−2222−2i2i23−23-22−2i2i001+i3−1−i31−i3−1+i3002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ142ζ14−2ζ222ζ220−i2i22−2−66−i6i6ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23000000000000000000000000
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χ714-44i−4i000-20002i3−2i322i2−2i2−2222−2i2i−23232-22i−2i00−1+i31−i3−1−i31+i300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1302ζ22−2ζ222ζ14−2ζ140−i2i22−26−6i6−i6ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23000000000000000000000000
χ724-44i−4i000-20002i3−2i322i2−2i2−2222−2i2i−2323-22−2i2i001−i3−1+i31+i3−1−i3002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130−2ζ222ζ22−2ζ142ζ140−i2i22−26−6i6−i6−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23000000000000000000000000
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χ794-4−4i4i000-2000−2i32i322i2−2i222−222i−2i−23232-2−2i2i00−1−i31+i3−1+i31−i300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230−2ζ142ζ14−2ζ222ζ220−i2i2−22−66i6−i6ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23000000000000000000000000
χ804-4−4i4i000-2000−2i32i322i2−2i222−222i−2i−2323-222i−2i001+i3−1−i31−i3−1+i3002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2302ζ14−2ζ142ζ22−2ζ220−i2i2−22−66i6−i6−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23000000000000000000000000
χ814-4−4i4i000-20002i3−2i32−2i22i2−22222i−2i23−232-2−2i2i00−1+i31−i3−1−i31+i3002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230−2ζ222ζ22−2ζ142ζ140i2−i22−2−66i6−i6−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23000000000000000000000000
χ824-4−4i4i000-20002i3−2i32−2i22i2−22222i−2i23−23-222i−2i001−i3−1+i31+i3−1−i300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2302ζ22−2ζ222ζ14−2ζ140i2−i22−2−66i6−i6ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23000000000000000000000000
χ834-4−4i4i000-20002i3−2i322i2−2i222−222i−2i23−232-2−2i2i00−1+i31−i3−1−i31+i300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230−2ζ222ζ22−2ζ142ζ140−i2i2−226−6−i6i6ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23000000000000000000000000
χ844-4−4i4i000-20002i3−2i322i2−2i222−222i−2i23−23-222i−2i001−i3−1+i31+i3−1−i3002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2302ζ22−2ζ222ζ14−2ζ140−i2i2−226−6−i6i6−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23000000000000000000000000

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