Finite Group Databasebeta

← Group #10698601

Character table — Group #10698601

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222446666888812121212121224242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-2-222222222-2-2-2-2-22222-2000000000000-2-20000000000000000000000000022-2-2000000
χ10222222222222-2-2-2-222222222-2-2-2-2-22222-2000000000000-2-200000000000000000000000000-2-222000000
χ11222222222-2-2-22222-22222222-2-2222-2-2-2-2222-2-222220000-2-2-2-2-2-200000000000000000000000000000000
χ12222222222-2-2-22222-22222222-2-2222-2-2-2-22-2-222-2-2-2-20000-2-2222200000000000000000000000000000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ1922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ23222-2-2-2-2220002-2-22022-22-2-2-2002-2-200002002i−2i00000000002i2i−2i−2i00000000−i2−i2−i2−i2i2i2i2i2000000000022−2−200
χ24222-2-2-2-2220002-2-22022-22-2-2-2002-2-200002002i−2i00000000002i2i−2i−2i00000000i2i2i2i2−i2−i2−i2−i20000000000−2−22200
χ25222-2-2-2-2220002-2-22022-22-2-2-2002-2-20000200−2i2i0000000000−2i−2i2i2i00000000−i2−i2−i2−i2i2i2i2i20000000000−2−22200
χ26222-2-2-2-2220002-2-22022-22-2-2-2002-2-20000200−2i2i0000000000−2i−2i2i2i00000000i2i2i2i2−i2−i2−i2−i2000000000022−2−200
χ2722-2-222-2-222-2-2000022-22-2-22-20000022-2-2000000000−i2−i2i2i2000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000002i−2i000000
χ2822-2-222-2-222-2-2000022-22-2-22-20000022-2-2000000000−i2−i2i2i2000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000−2i2i000000
χ2922-2-222-2-222-2-2000022-22-2-22-20000022-2-2000000000i2i2−i2−i2000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000−2i2i000000
χ3022-2-222-2-222-2-2000022-22-2-22-20000022-2-2000000000i2i2−i2−i2000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000002i−2i000000
χ312-22-22-22-2222-20000-2-22-2-2-222000002-22-20000000002−22−20000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000002i−2i00000000
χ322-22-22-22-2222-20000-2-22-2-2-222000002-22-20000000002−22−20000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000−2i2i00000000
χ332-22-22-22-2222-20000-2-22-2-2-222000002-22-2000000000−22−22000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000−2i2i00000000
χ342-22-22-22-2222-20000-2-22-2-2-222000002-22-2000000000−22−22000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000002i−2i00000000
χ352-2-222-2-2222-2222-2-2-2-2-2-2222-2-2222-22-2-22-2000000002i−2i−2i2i2-200002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ362-2-222-2-2222-2222-2-2-2-2-2-2222-2-2222-22-2-22-200000000−2i2i2i−2i2-20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ372-2-222-2-2222-22-2-222-2-2-2-2222-22-2-2-222-2-222000000000000-220000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382-2-222-2-2222-22-2-222-2-2-2-2222-22-2-2-222-2-222000000000000-22000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-2-222-2-222-22-222-2-22-2-2-2222-22-222-2-222-2-2000000000000-22000000000000000000002i−2i2i−2i2i−2i0000000000
χ402-2-222-2-222-22-222-2-22-2-2-2222-22-222-2-222-2-2000000000000-2200000000000000000000−2i2i−2i2i−2i2i0000000000
χ412-2-222-2-222-22-2-2-2222-2-2-2222-2-22-2-22-222-220000000000002-20000000000000000000000000000002-22-200
χ422-2-222-2-222-22-2-2-2222-2-2-2222-2-22-2-22-222-220000000000002-2000000000000000000000000000000-22-2200
χ432-2-222-2-22-12-2222-2-2-2111-1-1-11-22-1-11-111-110000−i3−i3i3i32i−2i−2i2i-11−i3i3−i3i3−iii−i−iii−i00000000003−3−330000000000
χ442-2-222-2-22-12-2222-2-2-2111-1-1-11-22-1-11-111-110000−i3−i3i3i3−2i2i2i−2i-11−i3i3−i3i3i−i−iii−i−ii0000000000−333−30000000000
χ452-2-222-2-22-12-2222-2-2-2111-1-1-11-22-1-11-111-110000i3i3−i3−i32i−2i−2i2i-11i3−i3i3−i3−iii−i−iii−i0000000000−333−30000000000
χ462-2-222-2-22-12-2222-2-2-2111-1-1-11-22-1-11-111-110000i3i3−i3−i3−2i2i2i−2i-11i3−i3i3−i3i−i−iii−i−ii00000000003−3−330000000000
χ472-2-222-2-22-1-22-222-2-22111-1-1-112-2-1-111-1-1110000−i3−i3i3i300001-1i3−i3i3−i33−3−33−333−3000000002i−2i−ii−ii0000000000
χ482-2-222-2-22-1-22-222-2-22111-1-1-112-2-1-111-1-1110000−i3−i3i3i300001-1i3−i3i3−i3−333−33−3−3300000000−2i2ii−ii−i0000000000
χ492-2-222-2-22-1-22-222-2-22111-1-1-112-2-1-111-1-1110000i3i3−i3−i300001-1−i3i3−i3i33−3−33−333−300000000−2i2ii−ii−i0000000000
χ502-2-222-2-22-1-22-222-2-22111-1-1-112-2-1-111-1-1110000i3i3−i3−i300001-1−i3i3−i3i3−333−33−3−33000000002i−2i−ii−ii0000000000
χ512-2-2-2-22222000-22-220-2-222-2-2200-22-2000022-2002-22-20000000000000000002−2−22−222−200000000002−2−2200
χ522-2-2-2-22222000-22-220-2-222-2-2200-22-2000022-2002-22-2000000000000000000−222−22−2−220000000000−222−200
χ532-2-2-2-22222000-22-220-2-222-2-2200-22-200002-2200-22-220000000000000000002−2−22−222−20000000000−222−200
χ542-2-2-2-22222000-22-220-2-222-2-2200-22-200002-2200-22-22000000000000000000−222−22−2−2200000000002−2−2200
χ5544444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ57444-4-4-4-444000-444-4044-44-4-4-400-4440000-400000000000000000000000000000000000000000000000000
χ58444-4-4-4-44-20004-4-440-2-22-222200-2220000-2004i−4i0000000000−2i−2i2i2i00000000000000000000000000000000
χ59444-4-4-4-44-20004-4-440-2-22-222200-2220000-200−4i4i00000000002i2i−2i−2i00000000000000000000000000000000
χ60444-4-4-4-44-2000-444-40-2-22-2222002-2-2000020000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ61444-4-4-4-44-2000-444-40-2-22-2222002-2-20000200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ6244-44-4-44-44000000004-4-4-44-440000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ6344-44-4-44-44000000004-4-4-44-44000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ6444-4-444-4-44-4440000-44-44-4-44-400000-4-444000000000000000000000000000000000000000000000000000
χ6544-4-444-4-4-24-4-400004-22-222-2200000-2-222000000000−2i2−2i22i22i2000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ6644-4-444-4-4-24-4-400004-22-222-2200000-2-2220000000002i22i2−2i2−2i2000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ6744-4-444-4-4-2-4440000-4-22-222-220000022-2-2000000000000000000066−6−6−6−666000000000000000000000000
χ6844-4-444-4-4-2-4440000-4-22-222-220000022-2-20000000000000000000−6−66666−6−6000000000000000000000000
χ694-444-44-4-4400000000-444-44-4-40000000000000000000000000000000000002-22-2-22-220000000000000000
χ704-444-44-4-4400000000-444-44-4-4000000000000000000000000000000000000-22-222-22-20000000000000000
χ714-44-44-44-44-4-4400004-44-4-4-44400000-44-44000000000000000000000000000000000000000000000000000
χ724-44-44-44-4-244-40000-42-2222-2-200000-22-2200000000022−2222−22000000−22−22−22−22000000000000000000000000
χ734-44-44-44-4-244-40000-42-2222-2-200000-22-22000000000−2222−22220000002−22−22−22−2000000000000000000000000
χ744-44-44-44-4-2-4-44000042-2222-2-2000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ754-44-44-44-4-2-4-44000042-2222-2-2000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ764-4-444-4-44-24-44-4-444-4222-2-2-224-422-2-222-2-20000000000002-2000000000000000000000000000000000000
χ774-4-444-4-44-2-44-4-4-4444222-2-2-22-4422-22-2-22-2000000000000-22000000000000000000000000000000000000
χ784-4-4-4-444440004-44-40-4-444-4-44004-440000-400000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-20004-44-4022-2-222-200-22-2000020000000000000023−23−232300000000000000000000000000000000
χ804-4-4-4-4444-20004-44-4022-2-222-200-22-20000200000000000000−232323−2300000000000000000000000000000000
χ814-4-4-4-4444-2000-44-44022-2-222-2002-220000-24-400-22-22000000000000000000000000000000000000000000
χ824-4-4-4-4444-2000-44-44022-2-222-2002-220000-2-44002-22-2000000000000000000000000000000000000000000
χ8388-88-8-88-8-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000

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