Finite Group Databasebeta

← Group #10858324

Character table — Group #10858324

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666662222448888121212121212121244442244466668812121212121224242424242424244444888846612124444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-11111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-1111111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-111-111-1-1-1
χ6111111111111111111111111-1-1111111-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-11111-1-1111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-222222220000220000-2-22222-2-222220000-2000000-2-2000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-222222220000220000-2-22222-2-2-2-2-2-20000-2000000-2-200000000000022-2-20000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220000200000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2000020000002200000000000022220000000000000-200000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-1-1-1-1-2-2-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-22222-1-11111-1-1000022-2-2-2-1-1-1-1-2-2111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-11111-1-10000-2-2-2-2-2-1-1-1-1221111111111-1-1-1-100000000211-1-10000000000
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
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-221111-2-2-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-11111-1-10000-2-222-21111-2-211-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-11111-1-100002222-211112211-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ292222-2-2-2-2222-2-222-22-2-2-222-2-20022-2-22-200002-200002-200022-2-20000000022-2-200000000000002-2000000000000
χ302222-2-2-2-2222-2-222-22-2-2-222-2-200-2-2222-200002-20000-2200022-2-200000000-2-2220000000000000-22000000000000
χ312222-2-2-2-2222-2-222-22-2-2-2-2-2220022-2-22-200002-20000-22000-2-2220000000022-2-20000000000000-22000000000000
χ322222-2-2-2-2222-2-222-22-2-2-2-2-22200-2-2222-200002-200002-2000-2-22200000000-2-22200000000000002-2000000000000
χ332222-2-2-2-2-122-2-2-1-11-111122-2-20022-2-2-1133−3−3-1100002-2000-1-111003−333−3−3-1-11133−3−3000000000-113−30000000000
χ342222-2-2-2-2-122-2-2-1-11-111122-2-20022-2-2-11−3−333-1100002-2000-1-11100−33−3−333-1-111−3−333000000000-11−330000000000
χ352222-2-2-2-2-122-2-2-1-11-111122-2-200-2-222-1133−3−3-110000-22000-1-111003−333−3−311-1-1−3−3330000000001-1−330000000000
χ362222-2-2-2-2-122-2-2-1-11-111122-2-200-2-222-11−3−333-110000-22000-1-11100−33−3−33311-1-133−3−30000000001-13−30000000000
χ372222-2-2-2-2-122-2-2-1-11-1111-2-2220022-2-2-1133−3−3-110000-2200011-1-1003−3−3−333-1-11133−3−30000000001-1−330000000000
χ382222-2-2-2-2-122-2-2-1-11-1111-2-2220022-2-2-11−3−333-110000-2200011-1-100−3333−3−3-1-111−3−3330000000001-13−30000000000
χ392222-2-2-2-2-122-2-2-1-11-1111-2-22200-2-222-1133−3−3-1100002-200011-1-1003−3−3−33311-1-1−3−333000000000-113−30000000000
χ402222-2-2-2-2-122-2-2-1-11-1111-2-22200-2-222-11−3−333-1100002-200011-1-100−3333−3−311-1-133−3−3000000000-11−330000000000
χ4122-2-2-222-2200002-22-22-2-200002i−2i2−22−2002i−2i2i−2i002i2i−2i−2i000000000−i2i20000002−22−2−i2i2−i2i2002-2−i2−i2i2i20000000000002−20
χ4222-2-2-222-2200002-22-22-2-200002i−2i2−22−2002i−2i2i−2i00−2i−2i2i2i000000000−i2i20000002−22−2−i2i2−i2i200-22i2i2−i2−i2000000000000−220
χ4322-2-2-222-2200002-22-22-2-200002i−2i−22−22002i−2i2i−2i002i2i−2i−2i000000000i2−i2000000−22−22i2−i2i2−i2002-2i2i2−i2−i2000000000000−220
χ4422-2-2-222-2200002-22-22-2-200002i−2i−22−22002i−2i2i−2i00−2i−2i2i2i000000000i2−i2000000−22−22i2−i2i2−i200-22−i2−i2i2i20000000000002−20
χ4522-2-2-222-2200002-22-22-2-20000−2i2i2−22−200−2i2i−2i2i002i2i−2i−2i000000000i2−i20000002−22−2i2−i2i2−i200-22−i2−i2i2i2000000000000−220
χ4622-2-2-222-2200002-22-22-2-20000−2i2i2−22−200−2i2i−2i2i00−2i−2i2i2i000000000i2−i20000002−22−2i2−i2i2−i2002-2i2i2−i2−i20000000000002−20
χ4722-2-2-222-2200002-22-22-2-20000−2i2i−22−2200−2i2i−2i2i002i2i−2i−2i000000000−i2i2000000−22−22−i2i2−i2i200-22i2i2−i2−i20000000000002−20
χ4822-2-2-222-2200002-22-22-2-20000−2i2i−22−2200−2i2i−2i2i00−2i−2i2i2i000000000−i2i2000000−22−22−i2i2−i2i2002-2−i2−i2i2i2000000000000−220
χ492-2-2222-2-222-2-22-2-2-222-2200000000002-20000-222i−2i2i−2i002-20000000002-22-2000000002i−2i000000000002i−2i00000000
χ502-2-2222-2-222-2-22-2-2-222-2200000000002-20000-222i−2i2i−2i00-22000000000-22-22000000002i−2i00000000000−2i2i00000000
χ512-2-2222-2-222-2-22-2-2-222-2200000000002-20000-22−2i2i−2i2i002-20000000002-22-200000000−2i2i00000000000−2i2i00000000
χ522-2-2222-2-222-2-22-2-2-222-2200000000002-20000-22−2i2i−2i2i00-22000000000-22-2200000000−2i2i000000000002i−2i00000000
χ532-2-2222-2-22-222-2-2-2-222-222-22-2000000-2200002-22i−2i2i−2i000002-22-20000000000000000−2i2i00000000000002i−2i000000
χ542-2-2222-2-22-222-2-2-2-222-222-22-2000000-2200002-2−2i2i−2i2i000002-22-200000000000000002i−2i0000000000000−2i2i000000
χ552-2-2222-2-22-222-2-2-2-222-22-22-22000000-2200002-22i−2i2i−2i00000-22-220000000000000000−2i2i0000000000000−2i2i000000
χ562-2-2222-2-22-222-2-2-2-222-22-22-22000000-2200002-2−2i2i−2i2i00000-22-2200000000000000002i−2i00000000000002i−2i000000
χ572-2-22-2-2222-22-22-2-222-22-22-2-22000000-2-20000220000000002-2-22000000000000000000002-22-200000000002-2000
χ582-2-22-2-2222-22-22-2-222-22-22-2-22000000-2-20000220000000002-2-2200000000000000000000-22-220000000000-22000
χ592-2-22-2-2222-22-22-2-222-22-2-222-2000000-2-2000022000000000-222-2000000000000000000002-22-20000000000-22000
χ602-2-22-2-2222-22-22-2-222-22-2-222-2000000-2-2000022000000000-222-200000000000000000000-22-2200000000002-2000
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
χ634444-4-4-4-44-4-44444-44-4-4-40000000000-440000-440000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-2-22-222200000000002-22323−23−232-2000000000000000−232300000000000000000000000000000000000
χ654444-4-4-4-4-2-4-444-2-22-222200000000002-2−23−2323232-200000000000000023−2300000000000000000000000000000000000
χ6644-4-44-4-44400004-4-4-4-44400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ6744-4-44-4-44400004-4-4-4-444000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ6844-4-44-4-44-20000-22222-2-200000022−22−222200−2i32i32i3−2i300000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ6944-4-44-4-44-20000-22222-2-200000022−22−2222002i3−2i3−2i32i300000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ7044-4-44-4-44-20000-22222-2-2000000−222222−2200−2i32i32i3−2i3000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ7144-4-44-4-44-20000-22222-2-2000000−222222−22002i3−2i3−2i32i3000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ7244-4-4-444-4-20000-22-22-22200004i−4i22−2222−2200−2i2i−2i2i000000000000000−2i22i2000000−22−22i2−i2i2−i200000000000000000000000
χ7344-4-4-444-4-20000-22-22-22200004i−4i−2222−222200−2i2i−2i2i0000000000000002i2−2i20000002−22−2−i2i2−i2i200000000000000000000000
χ7444-4-4-444-4-20000-22-22-2220000−4i4i22−2222−22002i−2i2i−2i0000000000000002i2−2i2000000−22−22−i2i2−i2i200000000000000000000000
χ7544-4-4-444-4-20000-22-22-2220000−4i4i−2222−2222002i−2i2i−2i000000000000000−2i22i20000002−22−2i2−i2i2−i200000000000000000000000
χ764-44-44-44-440000-444-4-4-44000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ774-44-44-44-440000-444-4-4-440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ784-44-4-44-4440000-44-4-444-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ794-44-4-44-4440000-44-4-444-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-24-4-44222-2-22-20000000000-2200002-20000004-4000000000-22-220000000000000000000000000000000
χ814-4-4444-4-4-24-4-44222-2-22-20000000000-2200002-2000000-440000000002-22-20000000000000000000000000000000
χ824-4-4444-4-4-2-444-4222-2-22-24-44-40000002-20000-22000000000-22-22000000000000000000000000000000000000000
χ834-4-4444-4-4-2-444-4222-2-22-2-44-440000002-20000-220000000002-22-2000000000000000000000000000000000000000
χ844-4-44-4-44444-44-4-4-444-44-40000000000440000-4-40000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-24-44-422-2-22-220000000000-2-20000220000000000000000023−23−23230000000000000000000000000000000
χ864-4-44-4-444-24-44-422-2-22-220000000000-2-200002200000000000000000−232323−230000000000000000000000000000000
χ874-4-44-4-444-2-44-4422-2-22-224-4-44000000220000-2-2000000000-222-2000000000000000000000000000000000000000
χ884-4-44-4-444-2-44-4422-2-22-22-444-4000000220000-2-20000000002-2-22000000000000000000000000000000000000000
χ898-88-88-88-8-400004-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-88-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000000000

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