Finite Group Databasebeta

← Group #10690026

Character table — Group #10690026

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444488888888121224242424242424242424242424242424444444448888888812121212224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ91-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1ii−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1iiii−i−i−i−iii−i−i1-1i−i1-1
χ101-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1ii−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−i−i−i−iiiiiii−i−i-11−ii-11
χ111-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1ii−i−i-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−i−i−i−iiiiiii−i−i1-1i−i-11
χ121-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1ii−i−i-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii−i−iii-1-111iiii−i−i−i−iii−i−i-11−ii1-1
χ131-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1−i−iii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111iiii−i−i−i−i−i−iii-11i−i-11
χ141-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1−i−iii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−i−i−i−iiiii−i−iii1-1−ii1-1
χ151-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1−i−iii-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−i−i−i−iiiii−i−iii-11i−i1-1
χ161-11-1-1-111111-11-1-1-11-1-1-1111-11-1111-1-1-11-1−i−iii-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1iiii−i−i−i−i−i−iii1-1−ii-11
χ17222222222222-2-2-22-22222222-2-222-22-2-2-22000000000000-2-200000000000000002222000000000000000000-2-200
χ18222222222222-2-2-22-22222222-2-222-22-2-2-22000000000000-2-20000000000000000-2-2-2-20000000000000000002200
χ19222222222-2-2-2222-222222222-2-2-2-22-2222-2000000000000-2-2000000000000000000002222000000000000-2-20000
χ20222222222-2-2-2222-222222222-2-2-2-22-2222-2000000000000-2-200000000000000000000-2-2-2-2000000000000220000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22-22-20000000022000000000000000000000000000000002-22-2000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-22-22000000002200000000000000000000000000000000-22-22000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112-22-200000000-1-133−3−333−3−333−3−333−3−30000000000000000-11-11000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112-22-200000000-1-1−3−333−3−333−3−333−3−3330000000000000000-11-11000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-22-2200000000-1-133−3−333−3−3−3−333−3−33300000000000000001-11-1000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111-22-2200000000-1-1−3−333−3−33333−3−333−3−300000000000000001-11-1000000
χ3122-22-2-2-22200022-20-22-2-22-2-220000202-2-2000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i22−2−222−2−20000000000
χ3222-22-2-2-22200022-20-22-2-22-2-220000202-2-2000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i−2−222−2−2220000000000
χ3322-22-2-2-22200022-20-22-2-22-2-220000202-2-2000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i−2−222−2−2220000000000
χ3422-22-2-2-22200022-20-22-2-22-2-220000202-2-2000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i22−2−222−2−20000000000
χ3522-2-22-22-222-2-20002022-2-22-2-2002-20-200020000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000002i−2i2i−2i00002−22−22−22−20000000000
χ3622-2-22-22-222-2-20002022-2-22-2-2002-20-200020000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i200000000−2i2i−2i2i0000−22−22−22−220000000000
χ3722-2-22-22-222-2-20002022-2-22-2-2002-20-200020000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000002i−2i2i−2i0000−22−22−22−220000000000
χ3822-2-22-22-222-2-20002022-2-22-2-2002-20-200020000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i200000000−2i2i−2i2i00002−22−22−22−20000000000
χ392-22-2-2-222222-2-222-2-2-2-2-2222-2-2222-2-222-2-2000000000000-2200000000000000002i2i−2i−2i000000000000000000−2i2i00
χ402-22-2-2-222222-2-222-2-2-2-2-2222-2-2222-2-222-2-2000000000000-220000000000000000−2i−2i2i2i0000000000000000002i−2i00
χ412-22-2-2-2222-2-222-2-222-2-2-2222-2-22-2-222-2-222000000000000-220000000000000000000022-2-2000000000000-220000
χ422-22-2-2-2222-2-222-2-222-2-2-2222-2-22-2-222-2-222000000000000-2200000000000000000000-2-2220000000000002-20000
χ432-22-2-2-2222-2-22-2222-2-2-2-2222-22-2-2-2-2222-222i−2i−2i2i000000002-2000000000000000000000000000000002i−2i−2i2i000000
χ442-22-2-2-2222-2-22-2222-2-2-2-2222-22-2-2-2-2222-22−2i2i2i−2i000000002-200000000000000000000000000000000−2i2i2i−2i000000
χ452-22-2-2-222-122-22-2-2-22111-1-1-112-2-1-1-1111-112i2i−2i−2i22-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii0000000000000000−i−iii000000
χ462-22-2-2-222-122-22-2-2-22111-1-1-112-2-1-1-1111-112i2i−2i−2i-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i0000000000000000−i−iii000000
χ472-22-2-2-222-122-22-2-2-22111-1-1-112-2-1-1-1111-11−2i−2i2i2i22-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000000000000000ii−i−i000000
χ482-22-2-2-222-122-22-2-2-22111-1-1-112-2-1-1-1111-11−2i−2i2i2i-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000000000000000ii−i−i000000
χ492-22-2-2-222-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i00000000-1133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000−iii−i000000
χ502-22-2-2-222-1-2-22-2222-2111-1-1-112-2111-1-1-11-12i−2i−2i2i00000000-11−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000−iii−i000000
χ512-22-2-2-222-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i00000000-1133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000i−i−ii000000
χ522-22-2-2-222-1-2-22-2222-2111-1-1-112-2111-1-1-11-1−2i2i2i−2i00000000-11−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000i−i−ii000000
χ532-2-22-222-222-22000-20-2-22-22-22002-202000-20000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2000000002-2-220000−i2i2−i2i2i2−i2i2−i20000000000
χ542-2-22-222-222-22000-20-2-22-22-22002-202000-20000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i200000000-222-20000i2−i2i2−i2−i2i2−i2i20000000000
χ552-2-22-222-222-22000-20-2-22-22-22002-202000-20000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2000000002-2-220000i2−i2i2−i2−i2i2−i2i20000000000
χ562-2-22-222-222-22000-20-2-22-22-22002-202000-20000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i200000000-222-20000−i2i2−i2i2i2−i2i2−i20000000000
χ572-2-2-222-2220002-220-2-2222-2-2-2000020-22-20000000002−2−2200000000002−22−2−22−2200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000
χ582-2-2-222-2220002-220-2-2222-2-2-2000020-22-20000000002−2−2200000000002−22−2−22−220000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000
χ592-2-2-222-2220002-220-2-2222-2-2-2000020-22-2000000000−222−20000000000−22−222−22−200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000
χ602-2-2-222-2220002-220-2-2222-2-2-2000020-22-2000000000−222−20000000000−22−222−22−20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000
χ6144444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-4-2-22-2222-200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-422-22-2-2-2200000000000022000000000000000000000000000000000000000000
χ63444-4-44-4-44000000004-44-4-44-40000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ64444-4-44-4-44000000004-44-4-44-4000000000000000000000000000000000000000000000000-222-2-222-20000000000
χ6544-44-4-4-444000-4-44044-4-44-4-440000-40-444000000000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-200044-40-4-222-222-20000-20-222000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ6744-44-4-4-44-200044-40-4-222-222-20000-20-2220000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6844-44-4-4-44-2000-4-4404-222-222-20000202-2-200000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ6944-44-4-4-44-2000-4-4404-222-222-20000202-2-200000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ7044-4-44-44-44-444000-4044-4-44-4-400-4404000-400000000000000000000000000000000000000000000000000000000
χ7144-4-44-44-4-24-4-400040-2-222-22200-2202000-20000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ7244-4-44-44-4-24-4-400040-2-222-22200-2202000-200002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ7344-4-44-44-4-2-444000-40-2-222-222002-20-2000200000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000000000
χ7444-4-44-44-4-2-444000-40-2-222-222002-20-2000200000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000000000
χ754-4444-4-4-4400000000-44-4-4-4440000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ764-4444-4-4-4400000000-44-4-4-444000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ774-44-4-4-444-244-4-444-4-4222-2-2-22-44-2-222-2-2220000000000002-2000000000000000000000000000000000000000000
χ784-44-4-4-444-2-4-444-4-444222-2-2-22-4422-2-222-2-20000000000002-2000000000000000000000000000000000000000000
χ794-4-44-444-44-44-400040-4-44-44-4400-440-4000400000000000000000000000000000000000000000000000000000000
χ804-4-44-444-4-24-44000-4022-22-22-200-220-200020000−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000000000
χ814-4-44-444-4-24-44000-4022-22-22-200-220-2000200002i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000000000
χ824-4-44-444-4-2-44-40004022-22-22-2002-202000-200000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ834-4-44-444-4-2-44-40004022-22-22-2002-202000-200000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ844-4-4-444-444000-44-404-4444-4-4-40000-404-44000000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-20004-440-42-2-2-22220000-202-2200000000022−22−22220000000000−22−222−22−200000000000000000000000000
χ864-4-4-444-44-20004-440-42-2-2-22220000-202-22000000000−222222−2200000000002−22−2−22−2200000000000000000000000000
χ874-4-4-444-44-2000-44-4042-2-2-2222000020-22-2000000000000000000000006−6−66−666−600000000000000000000000000
χ884-4-4-444-44-2000-44-4042-2-2-2222000020-22-200000000000000000000000−666−66−6−6600000000000000000000000000
χ89888-8-88-8-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8888-8-8-8-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000

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