Finite Group Databasebeta

← Group #10692948

Character table — Group #10692948

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order122222222234466666664446666888888881212121222226666666612122424242424242424224444448888888844121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911111-1-1-11-11-1-111-1-11-1-111-111-1-1iiii−i−i−i−i11-1-111-1-11111-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ1011111-1-1-11-11-1-111-1-11-1-111-111-1-1iiii−i−i−i−i11-1-111-1-11111-1-1-1-11-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiiii−iii−i−i-11−ii
χ1111111-1-1-11-11-1-111-1-11-1-111-111-1-1iiii−i−i−i−i11-1-1-1-111-1-1-1-111111-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ1211111-1-1-11-11-1-111-1-11-1-111-111-1-1iiii−i−i−i−i11-1-1-1-111-1-1-1-111111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iii1-1i−i
χ1311111-1-1-11-11-1-111-1-11-1-111-111-1-1−i−i−i−iiiii11-1-111-1-11111-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ1411111-1-1-11-11-1-111-1-11-1-111-111-1-1−i−i−i−iiiii11-1-111-1-11111-1-1-1-11-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i−ii−i−iii-11i−i
χ1511111-1-1-11-11-1-111-1-11-1-111-111-1-1−i−i−i−iiiii11-1-1-1-111-1-1-1-111111-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ1611111-1-1-11-11-1-111-1-11-1-111-111-1-1−i−i−i−iiiii11-1-1-1-111-1-1-1-111111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i1-1−ii
χ1722222222222-2-22222222-2-2-2222200000000-2-2-2-2000000000000-2-20000000022-2-222-2-2000000000000000000
χ1822222222222-2-22222222-2-2-2222200000000-2-2-2-2000000000000-2-200000000-2-222-2-222000000000000000000
χ192222222222-122-1-1-1-1-1-1-1222-1-1-1-122222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ202222222222-122-1-1-1-1-1-1-1222-1-1-1-122222222-1-1-1-1-2-2-2-211111111-1-1-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ212222222222-122-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ222222222222-122-1-1-1-1-1-1-1222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-2-2-2-211111111-1-111111111000000000000000022-1-1-1-10000
χ2322222-2-2-22-222222-2-22-2-2-2-2222-2-200000000-2-222000000000000-220000000022-2-2-2-222000000000000000000
χ2422222-2-2-22-222222-2-22-2-2-2-2222-2-200000000-2-222000000000000-2200000000-2-22222-2-2000000000000000000
χ2522222-2-2-22-2-1-2-2-1-111-11122-2-1-1112i2i2i2i−2i−2i−2i−2i-1-11122-2-2-1-1-1-11111-11−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ2622222-2-2-22-2-1-2-2-1-111-11122-2-1-1112i2i2i2i−2i−2i−2i−2i-1-111-2-2221111-1-1-1-1-11−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ2722222-2-2-22-2-1-2-2-1-111-11122-2-1-111−2i−2i−2i−2i2i2i2i2i-1-11122-2-2-1-1-1-11111-11iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ2822222-2-2-22-2-1-2-2-1-111-11122-2-1-111−2i−2i−2i−2i2i2i2i2i-1-111-2-2221111-1-1-1-1-11iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-22-22-2-222222222222-2-2-2-2-2-222-2-222-2-22222000000000000-2-222-2-222-2-200000000000000000000000000
χ302222-22-22-2-222222222222-2-2-2-2-2-2-2-222-2-2222222000000000000-2-2-2-222-2-22200000000000000000000000000
χ312222-22-22-2-22-2-22222222-222-2-2-2-200000000-2-2-2-20000000000002200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ322222-22-22-2-22-2-22222222-222-2-2-2-200000000-2-2-2-2000000000000220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ332222-22-22-2-2-122-1-1-1-1-1-1-12-2-2111122-2-222-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i311-1-111-1-111000000000000000000−i3i3−i3i30000
χ342222-22-22-2-2-122-1-1-1-1-1-1-12-2-2111122-2-222-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i311-1-111-1-111000000000000000000i3−i3i3−i30000
χ352222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-2-222-2-222-1-1-1-10000−i3−i3i3i3−i3−i3i3i31111-1-111-1-1000000000000000000i3−i3i3−i30000
χ362222-22-22-2-2-122-1-1-1-1-1-1-12-2-21111-2-222-2-222-1-1-1-10000i3i3−i3−i3i3i3−i3−i31111-1-111-1-1000000000000000000−i3i3−i3i30000
χ372222-2-22-2-2222222-2-22-2-2-22-2-2-22200000000-2-2220000000000002-2000000000000000022-2-2-2-2220000000000
χ382222-2-22-2-2222222-2-22-2-2-22-2-2-22200000000-2-2220000000000002-20000000000000000-2-22222-2-20000000000
χ392222-2-22-2-222-2-222-2-22-2-22-22-2-2222i2i−2i−2i−2i−2i2i2i22-2-2000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ402222-2-22-2-222-2-222-2-22-2-22-22-2-222−2i−2i2i2i2i2i−2i−2i22-2-2000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ412222-2-22-2-22-1-2-2-1-111-1112-2211-1-12i2i−2i−2i−2i−2i2i2i-1-1110000−i3−i3i3i3i3i3−i3−i31-1−i−iiiii−i−i0000000000000000003−3−330000
χ422222-2-22-2-22-1-2-2-1-111-1112-2211-1-12i2i−2i−2i−2i−2i2i2i-1-1110000i3i3−i3−i3−i3−i3i3i31-1−i−iiiii−i−i000000000000000000−333−30000
χ432222-2-22-2-22-1-2-2-1-111-1112-2211-1-1−2i−2i2i2i2i2i−2i−2i-1-1110000−i3−i3i3i3i3i3−i3−i31-1ii−i−i−i−iii000000000000000000−333−30000
χ442222-2-22-2-22-1-2-2-1-111-1112-2211-1-1−2i−2i2i2i2i2i−2i−2i-1-1110000i3i3−i3−i3−i3−i3i3i31-1ii−i−i−i−iii0000000000000000003−3−330000
χ4522-2-222-2-2-222002-222-2-2-20002-22-2−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i2−22−22−22−20000000000
χ4622-2-222-2-2-222002-222-2-2-20002-22-2−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i−22−22−22−220000000000
χ4722-2-222-2-2-222002-222-2-2-20002-22-2i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i−22−22−22−220000000000
χ4822-2-222-2-2-222002-222-2-2-20002-22-2i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i2−22−22−22−20000000000
χ4922-2-22-222-2-22002-2-2-2-2220002-2-222−22−2−22−220000000000000000002−22−2−22−22002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000
χ5022-2-22-222-2-22002-2-2-2-2220002-2-222−22−2−22−220000000000000000002−22−2−22−2200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000
χ5122-2-22-222-2-22002-2-2-2-2220002-2-22−22−222−22−2000000000000000000−22−222−22−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000
χ5222-2-22-222-2-22002-2-2-2-2220002-2-22−22−222−22−2000000000000000000−22−222−22−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000
χ5322-2-2-222-22-22002-222-2-2-2000-22-22−i2i2i2−i2−i2i2i2−i2000000000000000000−i2i2i2−i2−i2i2i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000
χ5422-2-2-222-22-22002-222-2-2-2000-22-22−i2i2i2−i2−i2i2i2−i2000000000000000000−i2i2i2−i2−i2i2i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000
χ5522-2-2-222-22-22002-222-2-2-2000-22-22i2−i2−i2i2i2−i2−i2i2000000000000000000i2−i2−i2i2i2−i2−i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000
χ5622-2-2-222-22-22002-222-2-2-2000-22-22i2−i2−i2i2i2−i2−i2i2000000000000000000i2−i2−i2i2i2−i2−i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000
χ5722-2-2-2-2-22222002-2-2-2-222000-222-22−2−22−222−20000000000000000002−2−22−222−22-200-22002−2−22−222−20000000000
χ5822-2-2-2-2-22222002-2-2-2-222000-222-22−2−22−222−20000000000000000002−2−22−222−2-22002-200−222−22−2−220000000000
χ5922-2-2-2-2-22222002-2-2-2-222000-222-2−222−22−2−22000000000000000000−222−22−2−222-200-2200−222−22−2−220000000000
χ6022-2-2-2-2-22222002-2-2-2-222000-222-2−222−22−2−22000000000000000000−222−22−2−22-22002-2002−2−22−222−20000000000
χ614444444444-2-4-4-2-2-2-2-2-2-2-4-4-4-2-2-2-2000000002222000000000000220000000000000000000000000000000000
χ6244444-4-4-44-4-244-2-222-222-4-44-2-2220000000022-2-20000000000002-20000000000000000000000000000000000
χ634444-44-44-4-4-2-4-4-2-2-2-2-2-2-2-4442222000000002222000000000000-2-20000000000000000000000000000000000
χ644444-4-44-4-44-244-2-222-222-44-422-2-20000000022-2-2000000000000-220000000000000000000000000000000000
χ6544-4-444-4-4-44-200-22-2-2222000-22-22−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ6644-4-444-4-4-44-200-22-2-2222000-22-222i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6744-4-44-444-4-4-200-22222-2-2000-222-222−2222−22−2222−2222000000000000000000−22−222−22−200000000000000000000000000
χ6844-4-44-444-4-4-200-22222-2-2000-222-2−2222−222222−2222−220000000000000000002−22−2−22−2200000000000000000000000000
χ6944-4-4-444-44-4-200-22-2-22220002-22-2−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000
χ7044-4-4-444-44-4-200-22-2-22220002-22-22i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000
χ7144-4-4-4-4-4444-200-22222-2-20002-2-2222−22−2222−222222−22000000000000000000−222−22−2−2200000000000000000000000000
χ7244-4-4-4-4-4444-200-22222-2-20002-2-22−222222−2222−22−22220000000000000000002−2−22−222−200000000000000000000000000
χ734-4-4400000044-4-4-400400000000000000000004-42-22-22-22-22-22-2000000000000000000000000000000000000
χ744-4-4400000044-4-4-400400000000000000000004-4-22-22-22-22-22-22000000000000000000000000000000000000
χ754-4-440000004-44-4-40040000000000000000000-442-2-222-22-2-22-22000000000000000000000000000000000000
χ764-4-440000004-44-4-40040000000000000000000-44-222-2-22-222-22-2000000000000000000000000000000000000
χ774-4-44000000-24-422−2i32i3-2−2i32i3000000000000000−2i32i3-222-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000
χ784-4-44000000-24-422−2i32i3-2−2i32i3000000000000000−2i32i3-22-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000
χ794-4-44000000-24-4222i3−2i3-22i3−2i30000000000000002i3−2i3-222-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000
χ804-4-44000000-24-4222i3−2i3-22i3−2i30000000000000002i3−2i3-22-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000
χ814-4-44000000-2-4422−2i32i3-2−2i32i30000000000000002i3−2i32-22-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000
χ824-4-44000000-2-4422−2i32i3-2−2i32i30000000000000002i3−2i32-2-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000
χ834-4-44000000-2-44222i3−2i3-22i3−2i3000000000000000−2i32i32-22-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000
χ844-4-44000000-2-44222i3−2i3-22i3−2i3000000000000000−2i32i32-2-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000
χ858-88-8000000800-8800-8000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-4004-4−4i34i344i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-4004-44i3−4i34−4i34i30000000000000000000000000000000000000000000000000000000000000000000

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