Finite Group Databasebeta

← Group #10868086

Character table — Group #10868086

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666444444441212121212121212226666888812121212121224242424242424242244441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111
χ911111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-11-1-1111-1-1-111-1-111-1-111
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-11-1-111-1111-1-111-1-111-1-1
χ1111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-11-111-1-11-11111-1-1-1-111-1-1
χ1211111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111-111-1-1-11-1-1-1-11111-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-111-1-11-111-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-1-11-1-111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1111-1-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-111-111111-1-1-1-1-1-111
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000-22000000000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000000022000000000000-2-2220000002-2000000000000
χ19222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-20000000000002222000000-2-2000000000000
χ20222222222-2-2-2-22222222-2-2220000-2-22222-2-20000000000-2-2000000000000-2-2-2-200000022000000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-1111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-2111122-2-211-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-11111-1-1-2-21111-2-22211-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-1-1-1-122-2-2111111-1-1-1-1111100002-2-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-1-1-1-1-2-2221111111111-1-1-1-10000-2211-1-100000000000000
χ2922-2-22-22-2222-2-2-2-2-222-22000022-2-22-200002-200000000000022-2-2000000000000000000002i−2i0000002i−2i00
χ3022-2-22-22-2222-2-2-2-2-222-22000022-2-22-200002-200000000000022-2-200000000000000000000−2i2i000000−2i2i00
χ3122-2-22-22-2222-2-2-2-2-222-220000-2-2222-200002-2000000000000-2-222000000000000000000002i−2i000000−2i2i00
χ3222-2-22-22-2222-2-2-2-2-222-220000-2-2222-200002-2000000000000-2-22200000000000000000000−2i2i0000002i−2i00
χ332-22-22-2-2222-2-222-2-22-22-22i−2i2i−2i00002-22i2i−2i−2i-2200000000002i−2i000000000000000000000000002i−2i2-2000000
χ342-22-22-2-2222-2-222-2-22-22-22i−2i2i−2i00002-22i2i−2i−2i-2200000000002i−2i00000000000000000000000000−2i2i-22000000
χ352-22-22-2-2222-2-222-2-22-22-2−2i2i−2i2i00002-2−2i−2i2i2i-220000000000−2i2i000000000000000000000000002i−2i-22000000
χ362-22-22-2-2222-2-222-2-22-22-2−2i2i−2i2i00002-2−2i−2i2i2i-220000000000−2i2i00000000000000000000000000−2i2i2-2000000
χ372-22-22-2-222-222-22-2-22-22-22i−2i−2i2i2i−2i2i−2i-22−2i−2i2i2i2-22-222-2-200002i−2i2i−2i2i−2i00000000000000000000000000000000
χ382-22-22-2-222-222-22-2-22-22-22i−2i−2i2i−2i2i−2i2i-22−2i−2i2i2i2-2-22-2-22200002i−2i−2i2i−2i2i00000000000000000000000000000000
χ392-22-22-2-222-222-22-2-22-22-2−2i2i2i−2i2i−2i2i−2i-222i2i−2i−2i2-2-22-2-2220000−2i2i2i−2i2i−2i00000000000000000000000000000000
χ402-22-22-2-222-222-22-2-22-22-2−2i2i2i−2i−2i2i−2i2i-222i2i−2i−2i2-22-222-2-20000−2i2i−2i2i−2i2i00000000000000000000000000000000
χ412-22-22-2-22-1-222-2-111-11-112i−2i−2i2i2i−2i2i−2i1-1ii−i−i-112-2-1-1110000−ii−ii−ii−i3−i3i3i333−3−3000000−i3i33−300000000000000
χ422-22-22-2-22-1-222-2-111-11-112i−2i−2i2i2i−2i2i−2i1-1ii−i−i-112-2-1-1110000−ii−ii−iii3i3−i3−i3−3−333000000i3−i3−3300000000000000
χ432-22-22-2-22-1-222-2-111-11-112i−2i−2i2i−2i2i−2i2i1-1ii−i−i-11-2211-1-10000−iii−ii−i−i3−i3i3i333−3−3000000i3−i3−3300000000000000
χ442-22-22-2-22-1-222-2-111-11-112i−2i−2i2i−2i2i−2i2i1-1ii−i−i-11-2211-1-10000−iii−ii−ii3i3−i3−i3−3−333000000−i3i33−300000000000000
χ452-22-22-2-22-1-222-2-111-11-11−2i2i2i−2i2i−2i2i−2i1-1−i−iii-11-2211-1-10000i−i−ii−ii−i3−i3i3i3−3−333000000i3−i33−300000000000000
χ462-22-22-2-22-1-222-2-111-11-11−2i2i2i−2i2i−2i2i−2i1-1−i−iii-11-2211-1-10000i−i−ii−iii3i3−i3−i333−3−3000000−i3i3−3300000000000000
χ472-22-22-2-22-1-222-2-111-11-11−2i2i2i−2i−2i2i−2i2i1-1−i−iii-112-2-1-1110000i−ii−ii−i−i3−i3i3i3−3−333000000−i3i3−3300000000000000
χ482-22-22-2-22-1-222-2-111-11-11−2i2i2i−2i−2i2i−2i2i1-1−i−iii-112-2-1-1110000i−ii−ii−ii3i3−i3−i333−3−3000000i3−i33−300000000000000
χ492-2-2222-2-22-22-22-2222-2-2-200002i−2i−2i2i-2-20000220000000000002i−2i−2i2i000000000000000000000000002i−2i002-2
χ502-2-2222-2-22-22-22-2222-2-2-200002i−2i−2i2i-2-20000220000000000002i−2i−2i2i00000000000000000000000000−2i2i00-22
χ512-2-2222-2-22-22-22-2222-2-2-20000−2i2i2i−2i-2-2000022000000000000−2i2i2i−2i000000000000000000000000002i−2i00-22
χ522-2-2222-2-22-22-22-2222-2-2-20000−2i2i2i−2i-2-2000022000000000000−2i2i2i−2i00000000000000000000000000−2i2i002-2
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000222222220000000000-2-2000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000022-2-2-2-222000000000022000000000000000000000000000000000000
χ554444-4-4-4-440000-44-4-444-4000000000000000000000022−220000000022−2222−220000000000000000000000000000
χ564444-4-4-4-440000-44-4-444-40000000000000000000000−222200000000−2222−22220000000000000000000000000000
χ574444-4-4-4-4-200002-222-2-22000000000023−2323−230000000022−2200000000−22−226−66−6000000000000000000000000
χ584444-4-4-4-4-200002-222-2-22000000000023−2323−2300000000−2222000000002−22−2−66−66000000000000000000000000
χ594444-4-4-4-4-200002-222-2-220000000000−2323−23230000000022−2200000000−22−22−66−66000000000000000000000000
χ604444-4-4-4-4-200002-222-2-220000000000−2323−232300000000−2222000000002−22−26−66−6000000000000000000000000
χ6144-4-44-44-44-4-444-4-4-444-4400000000-440000-44000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-244-4-4222-2-22-2000044-4-4-220000-22000000000000-2-22200000000000000000000000000000000
χ6344-4-44-44-4-244-4-4222-2-22-20000-4-444-220000-2200000000000022-2-200000000000000000000000000000000
χ6444-4-44-44-4-2-4-444222-2-22-2000000002-200002-200−2i32i3−2i32i3000000000000000000000000000000000000000000
χ6544-4-44-44-4-2-4-444222-2-22-2000000002-200002-2002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ6644-4-4-44-44400004-44-44-4-40000000000000000000000000000000000000000004i−4i00000000000000000000
χ6744-4-4-44-44400004-44-44-4-4000000000000000000000000000000000000000000−4i4i00000000000000000000
χ684-44-44-4-44-24-4-44-222-22-224i−4i4i−4i0000-22−2i−2i2i2i2-20000000000−2i2i000000000000000000000000000000000000
χ694-44-44-4-44-24-4-44-222-22-22−4i4i−4i4i0000-222i2i−2i−2i2-200000000002i−2i000000000000000000000000000000000000
χ704-44-4-444-440000-4-44-4-44400000000000000000000000022−22000000000022−22−2222000000000000000000000000
χ714-44-4-444-440000-4-44-4-444000000000000000000000000−22220000000000−222222−22000000000000000000000000
χ724-44-4-444-4-2000022-222-2-20000000000−2i32i32i3−2i3000000000022−22000000i6−i6−i6i6−222−2000000000000000000000000
χ734-44-4-444-4-2000022-222-2-20000000000−2i32i32i3−2i30000000000−2222000000−i6i6i6−i62−2−22000000000000000000000000
χ744-44-4-444-4-2000022-222-2-200000000002i3−2i3−2i32i3000000000022−22000000−i6i6i6−i6−222−2000000000000000000000000
χ754-44-4-444-4-2000022-222-2-200000000002i3−2i3−2i32i30000000000−2222000000i6−i6−i6i62−2−22000000000000000000000000
χ764-4-4444-4-444-44-4-4444-4-4-400000000440000-4-4000000000000000000000000000000000000000000000000
χ774-4-4444-4-4-24-44-42-2-2-222200000000-2-200002200−2i32i32i3−2i3000000000000000000000000000000000000000000
χ784-4-4444-4-4-24-44-42-2-2-222200000000-2-2000022002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ794-4-4444-4-4-2-44-442-2-2-222200004i−4i−4i4i220000-2-2000000000000−2i2i2i−2i00000000000000000000000000000000
χ804-4-4444-4-4-2-44-442-2-2-22220000−4i4i4i−4i220000-2-20000000000002i−2i−2i2i00000000000000000000000000000000
χ814-4-44-4-4444000044-4-4-4-4400000000000000000000000000000000000000004-40000000000000000000000
χ824-4-44-4-4444000044-4-4-4-440000000000000000000000000000000000000000-440000000000000000000000
χ8388-8-8-88-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000

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