Finite Group Databasebeta

← Group #10828773

Character table — Group #10828773

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666444444888812121212121212124444224446666881212121212122424242424242424222288884121212124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-111-1-1-11111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-111-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111111-1-1111-1-111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111-1-1-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1-11-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1111-1-111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-2000000000000-2-222000000000-2000000000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-200000000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-200002000000220000000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000022222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-10000-2-222-21111-2-211-1-1-1-1-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-211112211-1-1-1-11111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-2-2-22111122-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000-2-22221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-2-1-1-1-1221111111111-1-1-1-100000000-211-1-10000000000
χ2922-22-22-2-22-2-2222-2-22-22-22i2i−2i−2i0022-2-22-200002-20000002i−2i0000000002i2i−2i−2i22-2-20000000000000002i−2i0000000000
χ3022-22-22-2-22-2-2222-2-22-22-22i2i−2i−2i00-2-2222-200002-2000000−2i2i0000000002i2i−2i−2i-2-222000000000000000−2i2i0000000000
χ3122-22-22-2-22-2-2222-2-22-22-2−2i−2i2i2i0022-2-22-200002-2000000−2i2i000000000−2i−2i2i2i22-2-2000000000000000−2i2i0000000000
χ3222-22-22-2-22-2-2222-2-22-22-2−2i−2i2i2i00-2-2222-200002-20000002i−2i000000000−2i−2i2i2i-2-2220000000000000002i−2i0000000000
χ3322-22-22-2-2-1-2-222-111-11-112i2i−2i−2i0022-2-2-1133−3−3-110000002i−2i0−i3−i3i3i3003−3−i−iii-1-11133−3−3000000000−i3i3−ii0000000000
χ3422-22-22-2-2-1-2-222-111-11-112i2i−2i−2i0022-2-2-11−3−333-110000002i−2i0i3i3−i3−i300−33−i−iii-1-111−3−333000000000i3−i3−ii0000000000
χ3522-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-2-222-1133−3−3-11000000−2i2i0−i3−i3i3i3003−3−i−iii11-1-1−3−333000000000i3−i3i−i0000000000
χ3622-22-22-2-2-1-2-222-111-11-112i2i−2i−2i00-2-222-11−3−333-11000000−2i2i0i3i3−i3−i300−33−i−iii11-1-133−3−3000000000−i3i3i−i0000000000
χ3722-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i0022-2-2-1133−3−3-11000000−2i2i0i3i3−i3−i3003−3ii−i−i-1-11133−3−3000000000i3−i3i−i0000000000
χ3822-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i0022-2-2-11−3−333-11000000−2i2i0−i3−i3i3i300−33ii−i−i-1-111−3−333000000000−i3i3i−i0000000000
χ3922-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-2-222-1133−3−3-110000002i−2i0i3i3−i3−i3003−3ii−i−i11-1-1−3−333000000000−i3i3−ii0000000000
χ4022-22-22-2-2-1-2-222-111-11-11−2i−2i2i2i00-2-222-11−3−333-110000002i−2i0−i3−i3i3i300−33ii−i−i11-1-133−3−3000000000i3−i3−ii0000000000
χ412-222-2-2-2220000-22-2-222-200002i−2i2−22−2002i−2i2i−2i002i2i−2i−2i000000000−i2i20000002−22−2−i2i2−i2i2002-2−i2−i2i2i20000000000002−20
χ422-222-2-2-2220000-22-2-222-200002i−2i2−22−2002i−2i2i−2i00−2i−2i2i2i000000000−i2i20000002−22−2−i2i2−i2i200-22i2i2−i2−i2000000000000−220
χ432-222-2-2-2220000-22-2-222-200002i−2i−22−22002i−2i2i−2i002i2i−2i−2i000000000i2−i2000000−22−22i2−i2i2−i2002-2i2i2−i2−i2000000000000−220
χ442-222-2-2-2220000-22-2-222-200002i−2i−22−22002i−2i2i−2i00−2i−2i2i2i000000000i2−i2000000−22−22i2−i2i2−i200-22−i2−i2i2i20000000000002−20
χ452-222-2-2-2220000-22-2-222-20000−2i2i2−22−200−2i2i−2i2i002i2i−2i−2i000000000i2−i20000002−22−2i2−i2i2−i200-22−i2−i2i2i2000000000000−220
χ462-222-2-2-2220000-22-2-222-20000−2i2i2−22−200−2i2i−2i2i00−2i−2i2i2i000000000i2−i20000002−22−2i2−i2i2−i2002-2i2i2−i2−i20000000000002−20
χ472-222-2-2-2220000-22-2-222-20000−2i2i−22−2200−2i2i−2i2i002i2i−2i−2i000000000−i2i2000000−22−22−i2i2−i2i200-22i2i2−i2−i20000000000002−20
χ482-222-2-2-2220000-22-2-222-20000−2i2i−22−2200−2i2i−2i2i00−2i−2i2i2i000000000−i2i2000000−22−22−i2i2−i2i2002-2−i2−i2i2i2000000000000−220
χ492-22-222-2-22-22-22-2222-2-2-22i−2i2i−2i000000-2-2000022000000000000000002i−2i2i−2i0000000000002-22-200000000002i−2i000
χ502-22-222-2-22-22-22-2222-2-2-22i−2i2i−2i000000-2-2000022000000000000000002i−2i2i−2i000000000000-22-220000000000−2i2i000
χ512-22-222-2-22-22-22-2222-2-2-2−2i2i−2i2i000000-2-200002200000000000000000−2i2i−2i2i0000000000002-22-20000000000−2i2i000
χ522-22-222-2-22-22-22-2222-2-2-2−2i2i−2i2i000000-2-200002200000000000000000−2i2i−2i2i000000000000-22-2200000000002i−2i000
χ532-2-2-2-222222-2-22-2-2-222-222-2-22000000-2200002-22-22-200000000000002-2-22000000002-2000000000000002-200000
χ542-2-2-2-222222-2-22-2-2-222-222-2-22000000-2200002-2-22-2200000000000002-2-2200000000-2200000000000000-2200000
χ552-2-2-2-222222-2-22-2-2-222-22-222-2000000-2200002-22-22-20000000000000-222-2000000002-200000000000000-2200000
χ562-2-2-2-222222-2-22-2-2-222-22-222-2000000-2200002-2-22-220000000000000-222-200000000-22000000000000002-200000
χ572-2-2-2-22222-222-2-2-2-222-2200000000002-20000-222-22-22-20002-22-20000000000000000-220000000000002-20000000
χ582-2-2-2-22222-222-2-2-2-222-2200000000002-20000-222-22-2-22000-22-220000000000000000-22000000000000-220000000
χ592-2-2-2-22222-222-2-2-2-222-2200000000002-20000-22-22-222-20002-22-200000000000000002-2000000000000-220000000
χ602-2-2-2-22222-222-2-2-2-222-2200000000002-20000-22-22-22-22000-22-2200000000000000002-20000000000002-20000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2000044000022-2-2-2-22200000000-40000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000004000000-2-200000000000000000000000000000000000
χ63444-4-4-44-44000044-4-4-4-44000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ64444-4-4-44-44000044-4-4-4-440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ6544-44-44-4-4444-4-44-4-44-44-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-244-4-4-222-22-2200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ6744-44-44-4-4-244-4-4-222-22-2200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6844-4-44-4-44400004-44-44-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ6944-4-44-4-44400004-44-44-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ704-444-4-4-44-200002-222-2-2200004i−4i22−2222−2200−2i2i−2i2i000000000000000−2i22i2000000−22−22i2−i2i2−i200000000000000000000000
χ714-444-4-4-44-200002-222-2-2200004i−4i−2222−222200−2i2i−2i2i0000000000000002i2−2i20000002−22−2−i2i2−i2i200000000000000000000000
χ724-444-4-4-44-200002-222-2-220000−4i4i22−2222−22002i−2i2i−2i0000000000000002i2−2i2000000−22−22−i2i2−i2i200000000000000000000000
χ734-444-4-4-44-200002-222-2-220000−4i4i−2222−2222002i−2i2i−2i000000000000000−2i22i20000002−22−2i2−i2i2−i200000000000000000000000
χ744-44-444-4-444-44-4-4444-4-4-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ754-44-444-4-4-24-44-42-2-2-22220000000000-2-2000022000000000−2i32i32i3−2i3000000000000000000000000000000000000000
χ764-44-444-4-4-24-44-42-2-2-22220000000000-2-20000220000000002i3−2i3−2i32i3000000000000000000000000000000000000000
χ774-44-444-4-4-2-44-442-2-2-22224i−4i4i−4i000000220000-2-200000000000000000−2i2i−2i2i0000000000000000000000000000000
χ784-44-444-4-4-2-44-442-2-2-2222−4i4i−4i4i000000220000-2-2000000000000000002i−2i2i−2i0000000000000000000000000000000
χ794-4-444-44-440000-4-44-4-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ804-4-444-44-440000-4-44-4-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ814-4-444-44-4-2000022-222-2-200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ824-4-444-44-4-2000022-222-2-200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ834-4-444-44-4-2000022-222-2-2000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ844-4-444-44-4-2000022-222-2-2000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ854-4-4-4-4444-24-4-44222-2-22-24-4-440000002-20000-2200000000000000000-222-20000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-2-22-2-444-40000002-20000-22000000000000000002-2-220000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-2-22-20000000000-2200002-200004-4000-22-22000000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-2-22-20000000000-2200002-20000-440002-22-2000000000000000000000000000000000000000
χ89888-8-8-88-8-40000-4-44444-40000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-88-8-88-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000

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