Finite Group Databasebeta

← Group #10698732

Character table — Group #10698732

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
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
χ9222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-20000000000000000000000000000002200-2-20000
χ10222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000-2-200220000
χ11222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-2000000000000000000000000000000002200-2-200
χ12222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-200000000000000000000000000000000-2-2002200
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000002-222-2-20000000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000-22-2-2220000000000
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
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−33333−3−3−3−3000000002-2-1-1110000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−3−3−3−3−3333300000000-2211-1-10000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−333333333−3−3−3−300000000-2211-1-10000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−33333−3−3−3−33333000000002-2-1-1110000000000
χ232222-2-2-2-2222-2000-2022-22-2-2-20022-2000-2022−2−200000022−2−222−2−2000000002222−2−2−2−20000002-200000000
χ242222-2-2-2-2222-2000-2022-22-2-2-20022-2000-2022−2−200000022−2−222−2−200000000−2−2−2−22222000000-2200000000
χ252222-2-2-2-2222-2000-2022-22-2-2-20022-2000-20−2−222000000−2−222−2−222000000002222−2−2−2−2000000-2200000000
χ262222-2-2-2-2222-2000-2022-22-2-2-20022-2000-20−2−222000000−2−222−2−22200000000−2−2−2−222220000002-200000000
χ2722-2-22-2-22200022-20-22-2-2-22-220000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000002-200
χ2822-2-22-2-22200022-20-22-2-2-22-220000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000-2200
χ2922-2-22-2-22200022-20-22-2-2-22-220000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000-2200
χ3022-2-22-2-22200022-20-22-2-2-22-220000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000002-200
χ312-22-2-2-22220002-220-2-222-22-2-2000002-220-200002−22−200000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000002i−2i000000
χ322-22-2-2-22220002-220-2-222-22-2-2000002-220-200002−22−200000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000−2i2i000000
χ332-22-2-2-22220002-220-2-222-22-2-2000002-220-20000−22−220000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000−2i2i000000
χ342-22-2-2-22220002-220-2-222-22-2-2000002-220-20000−22−220000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000002i−2i000000
χ352-2-222-22-222-22000-20-2-222-2-22002-22000-20−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000002−2−22−222−200000000002i−2i0000
χ362-2-222-22-222-22000-20-2-222-2-22002-22000-20−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i200000000−222−22−2−220000000000−2i2i0000
χ372-2-222-22-222-22000-20-2-222-2-22002-22000-20i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000002−2−22−222−20000000000−2i2i0000
χ382-2-222-22-222-22000-20-2-222-2-22002-22000-20i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i200000000−222−22−2−2200000000002i−2i0000
χ392-2-22-22-2222-2-22-2-222-2-2-2222-2-222-2-22-2-222000000002-200000000000000002-2-222-2-220000000000000000
χ402-2-22-22-2222-2-22-2-222-2-2-2222-2-222-2-22-2-222000000002-20000000000000000-222-2-222-20000000000000000
χ412-2-22-22-2222-2-2-2222-2-2-2-2222-22-22-2-2-2222-22i−2i−2i2i0000-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ422-2-22-22-2222-2-2-2222-2-2-2-2222-22-22-2-2-2222-2−2i2i2i−2i0000-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ432-2-22-22-222-2222-2-2-22-2-2-2222-22-2-2222-2-2-2200002i−2i−2i2i-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ442-2-22-22-222-2222-2-2-22-2-2-2222-22-2-2222-2-2-220000−2i2i2i−2i-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ452-2-22-22-222-222-222-2-2-2-2-2222-2-22-222-222-2-2000000002-2000000000000000000000000000000000000002i−2i
χ462-2-22-22-222-222-222-2-2-2-2-2222-2-22-222-222-2-2000000002-200000000000000000000000000000000000000−2i2i
χ472-2-22-22-22-12-2-2-2222-2111-1-1-112-2-1111-1-1-112i−2i−2i2i00001-1−iii−i−iii−i−i3i3i3−i3i3−i3−i3i300000000003−33−30000000000
χ482-2-22-22-22-12-2-2-2222-2111-1-1-112-2-1111-1-1-112i−2i−2i2i00001-1−iii−i−iii−ii3−i3−i3i3−i3i3i3−i30000000000−33−330000000000
χ492-2-22-22-22-12-2-2-2222-2111-1-1-112-2-1111-1-1-11−2i2i2i−2i00001-1i−i−iii−i−ii−i3i3i3−i3i3−i3−i3i30000000000−33−330000000000
χ502-2-22-22-22-12-2-2-2222-2111-1-1-112-2-1111-1-1-11−2i2i2i−2i00001-1i−i−iii−i−iii3−i3−i3i3−i3i3i3−i300000000003−33−30000000000
χ512-2-22-22-22-1-2222-2-2-22111-1-1-112-21-1-1-1111-100002i−2i−2i2i1-1−i3i3i3−i3i3−i3−i3i3−iii−i−iii−i0000000000−333−30000000000
χ522-2-22-22-22-1-2222-2-2-22111-1-1-112-21-1-1-1111-100002i−2i−2i2i1-1i3−i3−i3i3−i3i3i3−i3−iii−i−iii−i00000000003−3−330000000000
χ532-2-22-22-22-1-2222-2-2-22111-1-1-112-21-1-1-1111-10000−2i2i2i−2i1-1−i3i3i3−i3i3−i3−i3i3i−i−iii−i−ii00000000003−3−330000000000
χ542-2-22-22-22-1-2222-2-2-22111-1-1-112-21-1-1-1111-10000−2i2i2i−2i1-1i3−i3−i3i3−i3i3i3−i3i−i−iii−i−ii0000000000−333−30000000000
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ574444-4-4-4-44-4-440004044-44-4-4-400-4-440004000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4-244-4000-40-2-22-222200-2-22000202222−22−22000000−2−222−2−22200000000000000000000000000000000
χ594444-4-4-4-4-244-4000-40-2-22-222200-2-2200020−22−22222200000022−2−222−2−200000000000000000000000000000000
χ604444-4-4-4-4-2-4-4400040-2-22-22220022-2000-20000000000066−6−6−6−66600000000000000000000000000000000
χ614444-4-4-4-4-2-4-4400040-2-22-22220022-2000-200000000000−6−66666−6−600000000000000000000000000000000
χ6244-4-44-4-444000-4-44044-4-4-44-4400000-4-440400000000000000000000000000000000000000000000000000
χ6344-4-44-4-44-200044-40-4-2222-22-200000-2-22020000−2i2−2i22i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ6444-4-44-4-44-200044-40-4-2222-22-200000-2-220200002i22i2−2i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ6544-4-44-4-44-2000-4-4404-2222-22-20000022-20-2000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ6644-4-44-4-44-2000-4-4404-2222-22-20000022-20-2000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6744-4-4-444-44000000004-44-4-44-40000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ6844-4-4-444-44000000004-44-4-44-4000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ694-44-444-4-4400000000-44-4-4-4440000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ704-44-444-4-4400000000-44-4-4-444000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ714-44-4-4-4444000-44-404-444-44-4-400000-44-40400000000000000000000000000000000000000000000000000
χ724-44-4-4-444-20004-440-42-2-22-22200000-22-202000022−2222−220000000000−22−22−22−22000000000000000000000000
χ734-44-4-4-444-20004-440-42-2-22-22200000-22-2020000−2222−222200000000002−22−22−22−2000000000000000000000000
χ744-44-4-4-444-2000-44-4042-2-22-222000002-220-20000000000000000006−66−6−66−66000000000000000000000000
χ754-44-4-4-444-2000-44-4042-2-22-222000002-220-2000000000000000000−66−666−66−6000000000000000000000000
χ764-4-444-44-44-44-400040-4-444-4-4400-44-40004000000000000000000000000000000000000000000000000000
χ774-4-444-44-4-24-44000-4022-2-222-200-22-200020−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ784-4-444-44-4-24-44000-4022-2-222-200-22-2000202i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ794-4-444-44-4-2-44-40004022-2-222-2002-22000-200000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ804-4-444-44-4-2-44-40004022-2-222-2002-22000-200000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ814-4-44-44-44-24-4-44-4-444222-2-2-22-44-222-222-2-200000000-220000000000000000000000000000000000000000
χ824-4-44-44-44-2-444-444-4-4222-2-2-22-442-2-22-2-22200000000-220000000000000000000000000000000000000000
χ8388-8-8-888-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-8-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000

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