Finite Group Databasebeta

← Group #10698617

Character table — Group #10698617

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-22-22222222-2-2222-2-2-2-2222-2-20000-2-22222-2-2-2-200000000000000000000000000000000
χ10222222222222-2-2-22-22222222-2-2222-2-2-2-22-2-2220000-2-2-2-2-2-2222200000000000000000000000000000000
χ11222222222-2-2-2222-222222222-2-2-2-2-22222-200000000-2-200000000000000000000000000000022-2-2000000
χ12222222222-2-2-2222-222222222-2-2-2-2-22222-200000000-2-2000000000000000000000000000000-2-222000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ1922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ232222-2-2-2-2222-2000-2022-2-22-2-20022-20000-2002-2000000000022-2-2000000002222−2−2−2−2000000000022−2−200
χ242222-2-2-2-2222-2000-2022-2-22-2-20022-20000-2002-2000000000022-2-200000000−2−2−2−222220000000000−2−22200
χ252222-2-2-2-2222-2000-2022-2-22-2-20022-20000-200-220000000000-2-222000000002222−2−2−2−20000000000−2−22200
χ262222-2-2-2-2222-2000-2022-2-22-2-20022-20000-200-220000000000-2-22200000000−2−2−2−22222000000000022−2−200
χ2722-2-2-22-22200022-20-22-22-2-2-220000022-2-200000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000002i−2i00000000
χ2822-2-2-22-22200022-20-22-22-2-2-220000022-2-200000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000−2i2i00000000
χ2922-2-2-22-22200022-20-22-22-2-2-220000022-2-200000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000−2i2i00000000
χ3022-2-2-22-22200022-20-22-22-2-2-220000022-2-200000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000002i−2i00000000
χ312-22-222-2-222-2-200020-22-2-2-222002-2-2000022-20000000022-2-2000000000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i200
χ322-22-222-2-222-2-200020-22-2-2-222002-2-2000022-20000000022-2-2000000000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i200
χ332-22-222-2-222-2-200020-22-2-2-222002-2-200002-2200000000-2-222000000000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i200
χ342-22-222-2-222-2-200020-22-2-2-222002-2-200002-2200000000-2-222000000000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i200
χ352-22-2-2-22222-222-22-2-2-2222-2-2-2-222-222-22-2-2000000002-200000000000000000000000000000000002i−2i−2i2i00
χ362-22-2-2-22222-222-22-2-2-2222-2-2-2-222-222-22-2-2000000002-20000000000000000000000000000000000−2i2i2i−2i00
χ372-22-2-2-22222-22-22-2-22-2222-2-2-22-22-22-22-22-200000000-2200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ382-22-2-2-22222-22-22-2-22-2222-2-2-22-22-22-22-22-200000000-220000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ392-22-2-2-2222-22-22-222-2-2222-2-2-22-2-22-22-22-2200000000-220000000000000000000000002i−2i2i−2i2i−2i0000000000
χ402-22-2-2-2222-22-22-222-2-2222-2-2-22-2-22-22-22-2200000000-22000000000000000000000000−2i2i−2i2i−2i2i0000000000
χ412-22-2-2-2222-22-2-22-222-2222-2-2-2-22-22-2-22-22200002-22-22-2000000002-22-22-22-2000000000000000000000000
χ422-22-2-2-2222-22-2-22-222-2222-2-2-2-22-22-2-22-2220000-22-222-200000000-22-22-22-22000000000000000000000000
χ432-22-2-2-222-1-22-22-222-21-1-1-11112-21-11-11-11-1000000001-13−33−33−33−3−i3i3−i3i3i3−i3i3−i3000000002i−2i−ii−ii0000000000
χ442-22-2-2-222-1-22-22-222-21-1-1-11112-21-11-11-11-1000000001-13−33−33−33−3i3−i3i3−i3−i3i3−i3i300000000−2i2ii−ii−i0000000000
χ452-22-2-2-222-1-22-22-222-21-1-1-11112-21-11-11-11-1000000001-1−33−33−33−33−i3i3−i3i3i3−i3i3−i300000000−2i2ii−ii−i0000000000
χ462-22-2-2-222-1-22-22-222-21-1-1-11112-21-11-11-11-1000000001-1−33−33−33−33i3−i3i3−i3−i3i3−i3i3000000002i−2i−ii−ii0000000000
χ472-22-2-2-222-1-22-2-22-2221-1-1-1111-221-111-11-1-100002-22-2-113−33−3−33−33-11-11-11-1100000000003−3−330000000000
χ482-22-2-2-222-1-22-2-22-2221-1-1-1111-221-111-11-1-100002-22-2-11−33−333−33−3-11-11-11-110000000000−333−30000000000
χ492-22-2-2-222-1-22-2-22-2221-1-1-1111-221-111-11-1-10000-22-22-113−33−3−33−331-11-11-11-10000000000−333−30000000000
χ502-22-2-2-222-1-22-2-22-2221-1-1-1111-221-111-11-1-10000-22-22-11−33−333−33−31-11-11-11-100000000003−3−330000000000
χ512-2-222-2-222000-2220-2-2-22-222-200000-222-200000−i2i2i2−i20000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000002-2000000
χ522-2-222-2-222000-2220-2-2-22-222-200000-222-200000−i2i2i2−i20000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000-22000000
χ532-2-222-2-222000-2220-2-2-22-222-200000-222-200000i2−i2−i2i20000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000-22000000
χ542-2-222-2-222000-2220-2-2-22-222-200000-222-200000i2−i2−i2i20000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000002-2000000
χ5544444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ574444-4-4-4-44-4-440004044-4-44-4-400-4-440000400000000000000000000000000000000000000000000000000
χ584444-4-4-4-4-244-4000-40-2-222-22200-2-2200002004-40000000000-2-22200000000000000000000000000000000
χ594444-4-4-4-4-244-4000-40-2-222-22200-2-220000200-44000000000022-2-200000000000000000000000000000000
χ604444-4-4-4-4-2-4-4400040-2-222-2220022-20000-2000000000023−23−2323000000000000000000000000000000000000
χ614444-4-4-4-4-2-4-4400040-2-222-2220022-20000-20000000000−232323−23000000000000000000000000000000000000
χ6244-4-44-44-44000000004-4-44-44-400000000000000000000000000000000000022-2-2-2-2220000000000000000
χ6344-4-44-44-44000000004-4-44-44-4000000000000000000000000000000000000-2-22222-2-20000000000000000
χ6444-4-4-44-444000-4-44044-44-4-4-4400000-4-444000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44-200044-40-4-22-2222-200000-2-22200000−2i2−2i22i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ6644-4-4-44-44-200044-40-4-22-2222-200000-2-222000002i22i2−2i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ6744-4-4-44-44-2000-4-4404-22-2222-20000022-2-2000000000000000000066−6−6−6−666000000000000000000000000
χ6844-4-4-44-44-2000-4-4404-22-2222-20000022-2-20000000000000000000−6−66666−6−6000000000000000000000000
χ694-44-444-4-44-444000-40-44-4-4-44400-4440000-400000000000000000000000000000000000000000000000000
χ704-44-444-4-4-24-4-4000402-2222-2-200-2220000-24-400000000-2-222000000000000000000000000000000000000
χ714-44-444-4-4-24-4-4000402-2222-2-200-2220000-2-440000000022-2-2000000000000000000000000000000000000
χ724-44-444-4-4-2-444000-402-2222-2-2002-2-2000020000000000000023−23−232300000000000000000000000000000000
χ734-44-444-4-4-2-444000-402-2222-2-2002-2-20000200000000000000−232323−2300000000000000000000000000000000
χ744-44-4-4-444-24-444-44-4-42-2-2-2222-44-22-2-22-22200000000-220000000000000000000000000000000000000000
χ754-44-4-4-444-24-44-44-4-442-2-2-22224-4-22-22-22-22000000002-20000000000000000000000000000000000000000
χ764-4-444-4-4440004-4-404-4-44-444-4000004-4-44000000000000000000000000000000000000000000000000000
χ774-4-444-4-44-20004-4-40422-22-2-2200000-222-200000000000000000006−6−66−666−6000000000000000000000000
χ784-4-444-4-44-20004-4-40422-22-2-2200000-222-20000000000000000000−666−66−6−66000000000000000000000000
χ794-4-444-4-44-2000-4440-422-22-2-22000002-2-2200000−2i22i22i2−2i20000000000i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ804-4-444-4-44-2000-4440-422-22-2-22000002-2-22000002i2−2i2−2i22i20000000000−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ814-4-44-444-4400000000-4-4-444-440000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ824-4-44-444-4400000000-4-4-444-44000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ8388-8-88-88-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000

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