Finite Group Databasebeta

← Group #10689656

Character table — Group #10689656

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444444444444441212121212121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1
χ91-1111-1-1-1111-1-1-1-111-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−iii−i−ii−iii−i−i11-1-1i−ii−i11-1-111-1-1
χ101-1111-1-1-1111-1-1-1-111-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii−i−iiii−iii−i−i11-1-1−ii−ii-1-111-1-111
χ111-1111-1-1-1111-1-1-1-111-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i−i−iii−ii−i−iii-1-111i−i−ii11-1-1-1-111
χ121-1111-1-1-1111-1-1-1-111-1-1-111-111-1iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iiiii−i−i−ii−i−iii-1-111−iii−i-1-11111-1-1
χ131-1111-1-1-1111-1-1-1-111-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−iii−i−i−ii−i−iii11-1-1i−ii−i-1-111-1-111
χ141-1111-1-1-1111-1-1-1-111-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii−i−iii−ii−i−iii11-1-1−ii−ii11-1-111-1-1
χ151-1111-1-1-1111-1-1-1-111-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i−i−iiii−iii−i−i-1-111i−i−ii-1-11111-1-1
χ161-1111-1-1-1111-1-1-1-111-1-1-111-111-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iiiii−i−ii−iii−i−i-1-111−iii−i11-1-1-1-111
χ172222222222-222-2-22-22222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000002222000000000000-2-200000000
χ182222222222-222-2-22-22222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ19222222222-22-2-222-222222222-2-200000000-2-222-2-222-2-2-2-200000000000000000000222200000000000000-2-20000000000
χ20222222222-22-2-222-222222222-2-200000000-2-222-2-222-2-2-2-200000000000000000000-2-2-2-200000000000000220000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2222200000000000000002-22-2000000000000002-22-2000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-222220000000000000000-22-2200000000000000-22-22000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-21111-1-1-1-1000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000000022-1-1-1-11111000000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-20000000000−i3i3−i3i3-11-11000000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-220000000000i3−i3i3−i31-11-1000000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000000000i3−i3i3−i3-11-11000000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-220000000000−i3i3−i3i31-11-1000000000000
χ31222-2-22-2-2202002-20-222-22-2-2-20022−2−222−2−2002-2002-2000022−2−222−2−222−2−222−2−200002-22-20000000000000000002−22−20000
χ32222-2-22-2-2202002-20-222-22-2-2-20022−2−222−2−2002-2002-2000022−2−222−2−222−2−222−2−20000-22-22000000000000000000−22−220000
χ33222-2-22-2-2202002-20-222-22-2-2-200−2−222−2−222002-2002-20000−2−222−2−222−2−222−2−22200002-22-2000000000000000000−22−220000
χ34222-2-22-2-2202002-20-222-22-2-2-200−2−222−2−222002-2002-20000−2−222−2−222−2−222−2−2220000-22-220000000000000000002−22−20000
χ3522-22-2-22-22202-200-202-22-22-2-2002−22−22−22−22-2002-20000002−22−22−22−22−22−22−22−2000000002-22-20000000000000000002−22−2
χ3622-22-2-22-22202-200-202-22-22-2-2002−22−22−22−22-2002-20000002−22−22−22−22−22−22−22−200000000-22-22000000000000000000−22−22
χ3722-22-2-22-22202-200-202-22-22-2-200−22−22−22−222-2002-2000000−22−22−22−22−22−22−22−22000000002-22-2000000000000000000−22−22
χ3822-22-2-22-22202-200-202-22-22-2-200−22−22−22−222-2002-2000000−22−22−22−22−22−22−22−2200000000-22-220000000000000000002−22−2
χ392-2222-2-2-222-2-2-2222-2-2-2-222-22-220000000022-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i000000000000−2i2i00000000
χ402-2222-2-2-222-2-2-2222-2-2-2-222-22-220000000022-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i0000000000002i−2i00000000
χ412-2222-2-2-22-2222-2-2-22-2-2-222-22-2200000000-2-22222-2-2-2-222000000000000000000002i2i−2i−2i00000000000000−2i2i0000000000
χ422-2222-2-2-22-2222-2-2-22-2-2-222-22-2200000000-2-22222-2-2-2-22200000000000000000000−2i−2i2i2i000000000000002i−2i0000000000
χ432-2222-2-2-22-2-22222-2-2-2-2-222-222-200000000-2-2-2-2222222-2-200000000000000002-2-22000000000000002-2-22000000000000
χ442-2222-2-2-22-2-22222-2-2-2-2-222-222-200000000-2-2-2-2222222-2-20000000000000000-222-200000000000000-222-2000000000000
χ452-2222-2-2-2-122-2-2-2-222111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-2000000002i−2i−i−iii-1-111000000000000
χ462-2222-2-2-2-122-2-2-2-222111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-22200000000−2i2iii−i−i11-1-1000000000000
χ472-2222-2-2-2-122-2-2-2-222111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-200000000−2i2iii−i−i-1-111000000000000
χ482-2222-2-2-2-122-2-2-2-222111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-222000000002i−2i−i−iii11-1-1000000000000
χ492-2222-2-2-2-1-2-22222-2-2111-1-11-12-2000000001111-1-1-1-1-1-1113333−3−3−3−3−3−3−3−333332-2-2200000000003−3−33-111-1000000000000
χ502-2222-2-2-2-1-2-22222-2-2111-1-11-12-2000000001111-1-1-1-1-1-1113333−3−3−3−3−3−3−3−33333-222-20000000000−333−31-1-11000000000000
χ512-2222-2-2-2-1-2-22222-2-2111-1-11-12-2000000001111-1-1-1-1-1-111−3−3−3−333333333−3−3−3−32-2-220000000000−333−3-111-1000000000000
χ522-2222-2-2-2-1-2-22222-2-2111-1-11-12-2000000001111-1-1-1-1-1-111−3−3−3−333333333−3−3−3−3-222-200000000003−3−331-1-11000000000000
χ532-22-2-2-22220200-220-2-2-222-22-200−i2−i2i2i2i2i2−i2−i2002-200-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002i−2i−2i2i000000000000000000−222−20000
χ542-22-2-2-22220200-220-2-2-222-22-200−i2−i2i2i2i2i2−i2−i2002-200-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000−2i2i2i−2i0000000000000000002−2−220000
χ552-22-2-2-22220200-220-2-2-222-22-200i2i2−i2−i2−i2−i2i2i2002-200-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002i−2i−2i2i0000000000000000002−2−220000
χ562-22-2-2-22220200-220-2-2-222-22-200i2i2−i2−i2−i2−i2i2i2002-200-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000−2i2i2i−2i000000000000000000−222−20000
χ572-2-22-22-22220-2200-20-22-2-222-200−i2i2−i2i2i2−i2i2−i22-200-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000002i−2i−2i2i000000000000000000−222−2
χ582-2-22-22-22220-2200-20-22-2-222-200−i2i2−i2i2i2−i2i2−i22-200-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000−2i2i2i−2i0000000000000000002−2−22
χ592-2-22-22-22220-2200-20-22-2-222-200i2−i2i2−i2−i2i2−i2i22-200-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000002i−2i−2i2i0000000000000000002−2−22
χ602-2-22-22-22220-2200-20-22-2-222-200i2−i2i2−i2−i2i2−i2i22-200-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000−2i2i2i−2i000000000000000000−222−2
χ6144444444-24-444-4-44-4-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000000000
χ6244444444-2-44-4-444-44-2-2-2-2-2-2-2-4-40000000022-2-222-2-2222200000000000000000000000000000000000000000000000000
χ63444-4-44-4-440-400-440444-44-4-4-4000000000000-4400-44000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-204004-40-4-2-22-2222002222−22−222222−22−2200-2200-220000−2−222−2−222−2−222−2−2220000000000000000000000000000000000
χ65444-4-44-4-4-204004-40-4-2-22-222200−22−222222−22−22222200-2200-22000022−2−222−2−222−2−222−2−20000000000000000000000000000000000
χ66444-4-44-4-4-20-400-4404-2-22-22220000000000002-2002-20000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ67444-4-44-4-4-20-400-4404-2-22-22220000000000002-2002-20000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ6844-44-4-44-44-40-4400404-44-44-4-40000000000-4400-4400000000000000000000000000000000000000000000000000000000
χ6944-44-4-44-4-2404-400-40-22-22-2220022−2222−2222−2222−22-2200-22000000−22−22−22−22−22−22−22−220000000000000000000000000000000000
χ7044-44-4-44-4-2404-400-40-22-22-22200−2222−2222−2222−2222-2200-220000002−22−22−22−22−22−22−22−20000000000000000000000000000000000
χ7144-44-4-44-4-2-40-440040-22-22-22200000000002-2002-2000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000
χ7244-44-4-44-4-2-40-440040-22-22-22200000000002-2002-2000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ7344-4-44-4-444000000004-4-4-4-444002-2-222-2-220000000000002-2-222-2-222-2-222-2-220000000000000000000000000000000000
χ7444-4-44-4-444000000004-4-4-4-44400-222-2-222-2000000000000-222-2-222-2-222-2-222-20000000000000000000000000000000000
χ7544-4-44-4-44-200000000-22222-2-2002-2-222-2-2200000000−2i32i3−2i32i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ7644-4-44-4-44-200000000-22222-2-2002-2-222-2-22000000002i3−2i32i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ7744-4-44-4-44-200000000-22222-2-200-222-2-222-200000000−2i32i3−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ7844-4-44-4-44-200000000-22222-2-200-222-2-222-2000000002i3−2i32i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ794-4444-4-4-4-24-4-4-4444-4222-2-22-2-4400000000-2-22222-2-222-2-200000000000000000000000000000000000000000000000000
χ804-4444-4-4-4-2-4444-4-4-44222-2-22-2-440000000022-2-2-2-22222-2-200000000000000000000000000000000000000000000000000
χ814-44-4-4-44440-4004-404-4-444-44-4000000000000-44004-4000000000000000000000000000000000000000000000000000000
χ824-44-4-4-444-20400-440-422-2-22-2200−2i2−2i22i22i22i22i2−2i2−2i200-22002-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ834-44-4-4-444-20400-440-422-2-22-22002i22i2−2i2−2i2−2i2−2i22i22i200-22002-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ844-44-4-4-444-20-4004-40422-2-22-220000000000002-200-22000066−6−6−6−666−6−66666−6−60000000000000000000000000000000000
χ854-44-4-4-444-20-4004-40422-2-22-220000000000002-200-220000−6−66666−6−666−6−6−6−6660000000000000000000000000000000000
χ864-4-44-44-444-404-40040-44-4-444-40000000000-44004-400000000000000000000000000000000000000000000000000000000
χ874-4-44-44-44-240-4400-402-222-2-2200−2i22i2−2i22i22i2−2i22i2−2i2-22002-2000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ884-4-44-44-44-240-4400-402-222-2-22002i2−2i22i2−2i2−2i22i2−2i22i2-22002-2000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ894-4-44-44-44-2-404-400402-222-2-2200000000002-200-220000006−66−6−66−66−66−666−66−60000000000000000000000000000000000
χ904-4-44-44-44-2-404-400402-222-2-2200000000002-200-22000000−66−666−66−66−66−6−66−660000000000000000000000000000000000
χ914-4-4-4444-4400000000-444-4-4-44002i−2i−2i2i−2i2i2i−2i0000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ924-4-4-4444-4400000000-444-4-4-4400−2i2i2i−2i2i−2i−2i2i000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ934-4-4-4444-4-2000000002-2-2222-2002i−2i−2i2i−2i2i2i−2i00000000−2i32i32i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ140000000000000000000000000000000000
χ944-4-4-4444-4-2000000002-2-2222-2002i−2i−2i2i−2i2i2i−2i000000002i3−2i3−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ220000000000000000000000000000000000
χ954-4-4-4444-4-2000000002-2-2222-200−2i2i2i−2i2i−2i−2i2i00000000−2i32i32i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ140000000000000000000000000000000000
χ964-4-4-4444-4-2000000002-2-2222-200−2i2i2i−2i2i−2i−2i2i000000002i3−2i3−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ220000000000000000000000000000000000

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