Finite Group Databasebeta

← Group #10702097

Character table — Group #10702097

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422222234444446661212121266666612121212121288888888888824242424242424242424242424242424242424242424242488888888222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−i1-11-1
χ101-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-11-11−i−iii-11-11
χ111-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1-11−i−iii1-1-11
χ121-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-111-1ii−i−i-111-1
χ131-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-111-1−i−iii-111-1
χ141-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1-11ii−i−i1-1-11
χ151-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-11-11ii−i−i-11-11
χ161-1-1111-1-1111-1-1-1111-11-1-1-1-1111-1-1111-1-1-111-11-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii1-11-1
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ21222222222-2-22-2-222-2-2-22-222222222-2-22-2-22-2-2-22-200002-22-200000000000022-2-222-2-20000000000000000000000000000
χ22222222222-2-22-2-222-2-2-22-222222222-2-22-2-22-2-2-22-20000-22-22000000000000-2-222-2-2220000000000000000000000000000
χ23222222222-2-22-2-2-12-2-2-22-2-1-1-1-1-1-1-1-111-111-1111-1100002-22-2000033−3−333−3−3-1-111-1-11133−3−333−3−300000000000000000000
χ24222222222-2-22-2-2-12-2-2-22-2-1-1-1-1-1-1-1-111-111-1111-1100002-22-20000−3−333−3−333-1-111-1-111−3−333−3−33300000000000000000000
χ25222222222-2-22-2-2-12-2-2-22-2-1-1-1-1-1-1-1-111-111-1111-110000-22-22000033−3−333−3−311-1-111-1-1−3−333−3−33300000000000000000000
χ26222222222-2-22-2-2-12-2-2-22-2-1-1-1-1-1-1-1-111-111-1111-110000-22-220000−3−333−3−33311-1-111-1-133−3−333−3−300000000000000000000
χ2722222222-22-2-22-22-22-2-2-222222222-22-2-22-2-22-2-2-222-22-2000000002-22-22-22-2000000000000000000000000000000000000
χ2822222222-22-2-22-22-22-2-2-222222222-22-2-22-2-22-2-2-22-22-2200000000-22-22-22-22000000000000000000000000000000000000
χ2922222222-22-2-22-2-1-22-2-2-22-1-1-1-1-1-1-11-111-111-1111-12-22-200000000-11-11-11-113−33−33−33−33−33−33−33−300000000000000000000
χ3022222222-22-2-22-2-1-22-2-2-22-1-1-1-1-1-1-11-111-111-1111-12-22-200000000-11-11-11-11−33−33−33−33−33−33−33−3300000000000000000000
χ3122222222-22-2-22-2-1-22-2-2-22-1-1-1-1-1-1-11-111-111-1111-1-22-22000000001-11-11-11-13−33−33−33−3−33−33−33−3300000000000000000000
χ3222222222-22-2-22-2-1-22-2-2-22-1-1-1-1-1-1-11-111-111-1111-1-22-22000000001-11-11-11-1−33−33−33−333−33−33−33−300000000000000000000
χ3322222222-2-22-2-222-2-222-2-22222222-2-22-2-22-2-222-2-2000000002-22-200000000000000002-2-222-2-2200000000000000000000
χ3422222222-2-22-2-222-2-222-2-22222222-2-22-2-22-2-222-2-200000000-22-220000000000000000-222-2-222-200000000000000000000
χ3522222222-2-22-2-22-1-2-222-2-2-1-1-1-1-1-1-111-111-111-1-111000000002-22-23−3−333−3−33−333−3−333−3-111-1-111-100000000000000000000
χ3622222222-2-22-2-22-1-2-222-2-2-1-1-1-1-1-1-111-111-111-1-111000000002-22-2−333−3−333−33−3−333−3−33-111-1-111-100000000000000000000
χ3722222222-2-22-2-22-1-2-222-2-2-1-1-1-1-1-1-111-111-111-1-11100000000-22-223−3−333−3−333−3−333−3−331-1-111-1-1100000000000000000000
χ3822222222-2-22-2-22-1-2-222-2-2-1-1-1-1-1-1-111-111-111-1-11100000000-22-22−333−3−333−3−333−3−333−31-1-111-1-1100000000000000000000
χ392222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ402222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ412222-2-2-2-22-2-22-2-22-2222-22222-2-2-2-22-2-22-2-2-2222-22000000000000000000000000000000000000000000000022000000-2-2
χ422222-2-2-2-22-2-22-2-22-2222-22222-2-2-2-22-2-22-2-2-2222-220000000000000000000000000000000000000000000000-2-200000022
χ432222-2-2-2-2-22-2-22-222-2222-2222-2-2-2-2-22-2-22-22-2222-20000000000000000000000000000000000000000000022000000-2-200
χ442222-2-2-2-2-22-2-22-222-2222-2222-2-2-2-2-22-2-22-22-2222-200000000000000000000000000000000000000000000-2-20000002200
χ452222-2-2-2-2-2-22-2-22222-2-222222-2-2-2-2-2-22-2-2222-2-2220000000000000000000000000000000000000000000000002-22-20000
χ462222-2-2-2-2-2-22-2-22222-2-222222-2-2-2-2-2-22-2-2222-2-222000000000000000000000000000000000000000000000000-22-220000
χ472-2-2222-2-2222-2-2-2-122-22-2-211-1-1-111-1-1-1111-1-11-1112i2i−2i−2i2i2i−2i−2i22-2-2−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1111100000000000000000000
χ482-2-2222-2-2222-2-2-2-122-22-2-211-1-1-111-1-1-1111-1-11-1112i2i−2i−2i−2i−2i2i2i-2-222−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-100000000000000000000
χ492-2-2222-2-2222-2-2-2-122-22-2-211-1-1-111-1-1-1111-1-11-111−2i−2i2i2i2i2i−2i−2i-2-222iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-100000000000000000000
χ502-2-2222-2-2222-2-2-2-122-22-2-211-1-1-111-1-1-1111-1-11-111−2i−2i2i2i−2i−2i2i2i22-2-2iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111100000000000000000000
χ512-2-2222-2-22-2-2-22222-22-2-22-2-2222-2-22-2-2-2222-22-2-2200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ522-2-2222-2-22-2-2-22222-22-2-22-2-2222-2-22-2-2-2222-22-2-220000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ532-2-2222-2-22-2-2-222-12-22-2-2211-1-1-111-1111-1-1-11-111-100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i−3−33333−3−300000000000000000000
χ542-2-2222-2-22-2-2-222-12-22-2-2211-1-1-111-1111-1-1-11-111-100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i33−3−3−3−33300000000000000000000
χ552-2-2222-2-22-2-2-222-12-22-2-2211-1-1-111-1111-1-1-11-111-10000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii33−3−3−3−33300000000000000000000
χ562-2-2222-2-22-2-2-222-12-22-2-2211-1-1-111-1111-1-1-11-111-10000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii−3−33333−3−300000000000000000000
χ572-2-2222-2-2-22-22-222-222-22-2-2-2222-2-2-22-22-22-222-22-22i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ582-2-2222-2-2-22-22-222-222-22-2-2-2222-2-2-22-22-22-222-22-2−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ592-2-2222-2-2-22-22-22-1-222-22-211-1-1-1111-11-11-11-1-11-112i−2i−2i2i00000000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i3−33−333−33−300000000000000000000
χ602-2-2222-2-2-22-22-22-1-222-22-211-1-1-1111-11-11-11-1-11-112i−2i−2i2i00000000−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i33−33−3−33−3300000000000000000000
χ612-2-2222-2-2-22-22-22-1-222-22-211-1-1-1111-11-11-11-1-11-11−2i2i2i−2i00000000i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i33−33−3−33−3300000000000000000000
χ622-2-2222-2-2-22-22-22-1-222-22-211-1-1-1111-11-11-11-1-11-11−2i2i2i−2i00000000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i3−33−333−33−300000000000000000000
χ632-2-2222-2-2-2-2222-22-2-2-2222-2-2222-2-2-2-2222-2-2-2-2222000000002-2-2200000000000000002-2-22-222-200000000000000000000
χ642-2-2222-2-2-2-2222-22-2-2-2222-2-2222-2-2-2-2222-2-2-2-222200000000-222-20000000000000000-222-22-2-2200000000000000000000
χ652-2-2222-2-2-2-2222-2-1-2-2-222211-1-1-11111-1-1-11111-1-1-1000000002-2-22−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-111-11-1-1100000000000000000000
χ662-2-2222-2-2-2-2222-2-1-2-2-222211-1-1-11111-1-1-11111-1-1-1000000002-2-22i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-111-11-1-1100000000000000000000
χ672-2-2222-2-2-2-2222-2-1-2-2-222211-1-1-11111-1-1-11111-1-1-100000000-222-2−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i31-1-11-111-100000000000000000000
χ682-2-2222-2-2-2-2222-2-1-2-2-222211-1-1-11111-1-1-11111-1-1-100000000-222-2i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i31-1-11-111-100000000000000000000
χ692-2-22-2-222222-2-2-22-2-22-222-2-22-2-222222-2-2-2-2-22-22200000000000000000000000000000000000022-2-2-2-222000000000000
χ702-2-22-2-222222-2-2-22-2-22-222-2-22-2-222222-2-2-2-2-22-222000000000000000000000000000000000000-2-22222-2-2000000000000
χ712-2-22-2-2222-2-2-2222-22-222-2-2-22-2-2222-2-2-222-22-222-200000000000000000000000000000000000000000000002-2000000-22
χ722-2-22-2-2222-2-2-2222-22-222-2-2-22-2-2222-2-2-222-22-222-20000000000000000000000000000000000000000000000-220000002-2
χ732-2-22-2-222-22-22-2222-2-22-22-2-22-2-222-22-22-222-2-22-22000000000000000000000000000000000000000000002-2000000-2200
χ742-2-22-2-222-22-22-2222-2-22-22-2-22-2-222-22-22-222-2-22-2200000000000000000000000000000000000000000000-220000002-200
χ752-2-22-2-222-2-2222-22222-2-2-2-2-22-2-222-2-2222-2222-2-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ762-2-22-2-222-2-2222-22222-2-2-2-2-22-2-222-2-2222-2222-2-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ774444-4-4-4-4444444-2-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-222222200000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-44-4-44-4-4-2-4444-44-2-2-22222-222-2222-2-2-22-200000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-44-4-44-4-24-4444-4-2-2-222222-222-22-22-2-2-2200000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-4-44-4-44-244-4-444-2-2-2222222-222-2-2-222-2-200000000000000000000000000000000000000000000000000000000
χ8144-4-44i−4i4i−4i00000040000004-4-44i−4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ8244-4-44i−4i4i−4i00000040000004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ8344-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ8444-4-4−4i4i−4i4i00000040000004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ854-44-44i−4i−4i4i0000004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ864-44-44i−4i−4i4i0000004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ874-44-4−4i4i4i−4i0000004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ884-44-4−4i4i4i−4i0000004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ894-4-44-4-444444-4-4-4-2-4-44-44422-222-2-2-2-2-222222-22-2-200000000000000000000000000000000000000000000000000000000
χ904-4-44-4-4444-4-4-444-2-44-444-422-222-2-2-2222-2-22-22-2-2200000000000000000000000000000000000000000000000000000000
χ914-4-44-4-444-44-44-44-24-4-44-4422-222-2-22-22-22-2-222-22-200000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-4-4444-4-2444-4-4-422-222-2-222-2-2-22-2-2-222200000000000000000000000000000000000000000000000000000000
χ9388-8-88i−8i8i−8i000000-4000000-444−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8−8i8i−8i8i000000-4000000-4444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-88-88i−8i−8i8i000000-40000004-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i000000-40000004-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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