Finite Group Databasebeta

← Group #10693701

Character table — Group #10693701

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12224444223444444666121212124466888888881212121212128888888844441212121212121212121224242424242424248888888888888824242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11111-1-1-1-111-1-111iiii−i−i−i−iii−i−i1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−iii−i−ii−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−iii1-1−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−iii−i−i−ii−i−iii-1-111-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11111-1-1-1-111-1-111−i−i−i−iiiiiii−i−i1-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−iii−i−iiii−iii−i−i-1-111-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11111-1-1-1-111-1-111−i−i−i−iiiii−i−iii1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii−i−iii−ii−i−iii11-1-11-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−iii−i−i1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iiiii−i−i−ii−i−iii11-1-1-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i−i−iii1-1−i−i−i−iiiii-1-1-1-11111−i−iii−i−iiiii−i−ii−iii−i−i-1-1111-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiiiii−i−i1-1iiii−i−i−i−i-1-1-1-11111ii−i−iii−i−i−i−iii−ii−i−iii-1-1111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii−i−iii1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i−i−iiii−iii−i−i11-1-1-11
χ17222222222222-2-2-2-222222222-2-2220000000022-2-2-2-2000000000000-2-200000000000000002222-2-2-2-20000000000000000
χ18222222222222-2-2-2-222222222-2-2220000000022-2-2-2-2000000000000-2-20000000000000000-2-2-2-222220000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-22-22222-22222222-2-2-2-200000000-2-22222222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ2422222222-2-22-22222-22222222-2-2-2-200000000-2-22222-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-200000000000022000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-20000000000002200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122112i2i−2i−2i2i2i−2i−2i111111000000000000-1-133−3−333−3−3−i−iii−i−iii00000000000000−i3i3−i3i3000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122112i2i−2i−2i2i2i−2i−2i111111000000000000-1-1−3−333−3−333−i−iii−i−iii00000000000000i3−i3i3−i3000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211−2i−2i2i2i−2i−2i2i2i111111000000000000-1-133−3−333−3−3ii−i−iii−i−i00000000000000i3−i3i3−i3000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-12211−2i−2i2i2i−2i−2i2i2i111111000000000000-1-1−3−333−3−333ii−i−iii−i−i00000000000000−i3i3−i3i3000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-222200000000-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000-22000000000000000000000000−2i−2i2i2i000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-222200000000-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000-220000000000000000000000002i2i−2i−2i000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-2222i2i−2i−2i−2i−2i2i2i-2-222-2-20000000000002-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-222−2i−2i2i2i2i2i−2i−2i-2-222-2-20000000000002-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-12i2i−2i−2i−2i−2i2i2i11-1-111000000000000-11−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i00000000000000−333−3000000
χ362222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-12i2i−2i−2i−2i−2i2i2i11-1-111000000000000-11i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i000000000000003−3−33000000
χ372222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-111000000000000-11−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii000000000000003−3−33000000
χ382222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-111000000000000-11i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii00000000000000−333−3000000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-2000000002222-2-2000000000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-2000000002222-2-2000000000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112222-2-2-2-2-1-111-1-1000000002i2i−2i−2i-11−i−i−i−iiiii-1-1-1-111110000000000002i−2i−i−iii000000
χ422222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112222-2-2-2-2-1-111-1-100000000−2i−2i2i2i-11iiii−i−i−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ432222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-2-2-2-22222-1-111-1-1000000002i2i−2i−2i-11−i−i−i−iiiii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ442222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-2-2-2-22222-1-111-1-100000000−2i−2i2i2i-11iiii−i−i−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ4522-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i000000000000002i−2i2-22ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ131+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000002−2−i2i200
χ4622-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i000000000000002i−2i2-22ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000−22i2−i200
χ4722-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i000000000000002i−2i2-2−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ131+i−1−i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000−22i2−i200
χ4822-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i000000000000002i−2i2-2−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−1−i1+i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000002−2−i2i200
χ4922-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i00000000000000−2i2i2-2−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ231−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000002−2i2−i200
χ5022-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i00000000000000−2i2i2-2−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000−22−i2i200
χ5122-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i00000000000000−2i2i2-22ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ231−i−1+i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000−22−i2i200
χ5222-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i00000000000000−2i2i2-22ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−1+i1−i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000002−2i2−i200
χ532-2-2222-2-22-22-200002-22-222-2-2002-22−22−22−22−22-20000−i2i2−i2i2−i2i2−i2i2000000000000002−22−22−22−200002i−2i2i−2i−i2i2−i2i2000000000000
χ542-2-2222-2-22-22-200002-22-222-2-2002-22−22−22−22−22-20000i2−i2i2−i2i2−i2i2−i2000000000000002−22−22−22−20000−2i2i−2i2ii2−i2i2−i2000000000000
χ552-2-2222-2-22-22-200002-22-222-2-2002-2−22−22−22−222-20000−i2i2−i2i2−i2i2−i2i200000000000000−22−22−22−220000−2i2i−2i2i−i2i2−i2i2000000000000
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χ572-2-2222-2-2-22220000-2-22-222-2-200-22−i2i2i2−i2−i2i2i2−i2-220000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2i2−i2−i2i2i2−i22-22-20000i2−i2i2−i2000000000000
χ582-2-2222-2-2-22220000-2-22-222-2-200-22−i2i2i2−i2−i2i2i2−i2-220000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2i2−i2−i2i2i2−i2-22-220000−i2i2−i2i2000000000000
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χ622-2-22-2-2222-2220000-2-22-2-2-222002-2−i2i2i2−i2i2−i2−i2i2-220000−22−222−22−200000000000000−i2i2i2−i2i2−i2−i2i2−2i2i2i−2i00002−2−22000000000000
χ632-2-22-2-2222-2220000-2-22-2-2-222002-2i2−i2−i2i2−i2i2i2−i2-2200002−22−2−22−2200000000000000i2−i2−i2i2−i2i2i2−i2−2i2i2i−2i0000−222−2000000000000
χ642-2-22-2-2222-2220000-2-22-2-2-222002-2i2−i2−i2i2−i2i2i2−i2-220000−22−222−22−200000000000000i2−i2−i2i2−i2i2i2−i22i−2i−2i2i00002−2−22000000000000
χ652-2-22-2-222-222-200002-22-2-2-22200-222−22−2−22−222-200002−22−2−22−22000000000000002−22−2−22−220000-222-22−2−22000000000000
χ662-2-22-2-222-222-200002-22-2-2-22200-222−22−2−22−222-20000−22−222−22−2000000000000002−22−2−22−2200002-2-22−222−2000000000000
χ672-2-22-2-222-222-200002-22-2-2-22200-22−22−222−22−22-200002−22−2−22−2200000000000000−22−222−22−200002-2-222−2−22000000000000
χ682-2-22-2-222-222-200002-22-2-2-22200-22−22−222−22−22-20000−22−222−22−200000000000000−22−222−22−20000-222-2−222−2000000000000
χ694444444444-24-4-4-4-44-2-2-2-2-2-2-2-4-4-2-200000000-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-4-4-2-44444-4-2-2-2-2-2-2-2-4-4220000000022-2-2-2-2000000000000220000000000000000000000000000000000000000
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χ8044-4-4−4i4i−4i4i00-204-4−4i4i0-2222i−2i2i−2i000000000000002i−2i-2200000000−2+2i2−2i−2−2i2+2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ8144-4-4−4i4i−4i4i00-20-444i−4i0-2222i−2i2i−2i00000000000000−2i2i2-200000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ8244-4-4−4i4i−4i4i00-20-444i−4i0-2222i−2i2i−2i00000000000000−2i2i2-200000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ834-44-44i−4i−4i4i004000000-4-444i−4i−4i4i0000000000000000002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000000000
χ874-4-4444-4-44-4-2-4000042-22-2-22200-2222−2222−2222−2222−22-2200000000000000000000000000−22−22−22−22000000000000000000000000
χ884-4-4444-4-44-4-2-4000042-22-2-22200-22−2222−2222−2222−2222-22000000000000000000000000002−22−22−22−2000000000000000000000000
χ894-4-4444-4-4-44-240000-42-22-2-222002-2−2i22i22i2−2i2−2i22i22i2−2i22-200000000000000000000000000i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ904-4-4444-4-4-44-240000-42-22-2-222002-22i2−2i2−2i22i22i2−2i2−2i22i22-200000000000000000000000000−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ914-4-44-4-4444-4-240000-42-2222-2-200-22−2i22i22i2−2i22i2−2i2−2i22i22-200000000000000000000000000i2−i2−i2i2−i2i2i2−i2000000000000000000000000
χ924-4-44-4-4444-4-240000-42-2222-2-200-222i2−2i2−2i22i2−2i22i22i2−2i22-200000000000000000000000000−i2i2i2−i2i2−i2−i2i2000000000000000000000000
χ934-4-44-4-444-44-2-4000042-2222-2-2002-222−2222−22−2222−2222-2200000000000000000000000000−22−222−22−2000000000000000000000000
χ944-4-44-4-444-44-2-4000042-2222-2-2002-2−2222−222222−2222−22-22000000000000000000000000002−22−2−22−22000000000000000000000000
χ958-88-88i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000

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