Finite Group Databasebeta

← Group #10830032

Character table — Group #10830032

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444422444881212121212121212121224242424242424244444888846612122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-11111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-111-111-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11-1-1111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-111-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-11111-1-1111-1-1-1
χ911111111111111111111-1-1-1-1111111111111111111-1-11-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1-1-1111-1-1-1-11
χ17222222222-2-2-2-2222222200002200002222-2-2-2-2222200-200000000-2-2000000000000-2-2220000000000000-200000
χ18222222222-2-2-2-2222222200002200002222-2-2-2-2-2-2-2-200-200000000-2-200000000000022-2-20000000000000200000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222220020000000022000000000000-2-2-2-20000000000000200000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-2002000000002200000000000022220000000000000-200000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-222221111-1-1-1-1000022-2-2-2-2-2-1-1-1-1111111-1-1-1-1111100000000-2-1-1110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-10000-2-2-2-2-222-1-1-1-11111111111-1-1-1-100000000211-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-10000-2-22-2-2221111-1-11111-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-21111-1-1111111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-1000022-22222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-22-2-22-2-22222-2-2-22-22i2i−2i−2i002i2i−2i−2i00002-22-200002-2000002i2i−2i−2i0000002i2i−2i−2i00000000000002-2000000000000
χ30222-2-22-2-22-2-22222-2-2-22-22i2i−2i−2i00−2i−2i2i2i00002-22-20000-22000002i2i−2i−2i000000−2i−2i2i2i0000000000000-22000000000000
χ31222-2-22-2-22-2-22222-2-2-22-2−2i−2i2i2i002i2i−2i−2i00002-22-20000-2200000−2i−2i2i2i0000002i2i−2i−2i0000000000000-22000000000000
χ32222-2-22-2-22-2-22222-2-2-22-2−2i−2i2i2i00−2i−2i2i2i00002-22-200002-200000−2i−2i2i2i000000−2i−2i2i2i00000000000002-2000000000000
χ33222-2-22-2-2-1-2-222-1-1111-112i2i−2i−2i002i2i−2i−2i33−3−3-11-1100002-200000−i−iii3−3−i3−i3i3i3−i−iii−i3−i3i3i3000000000-113−30000000000
χ34222-2-22-2-2-1-2-222-1-1111-112i2i−2i−2i002i2i−2i−2i−3−333-11-1100002-200000−i−iii−33i3i3−i3−i3−i−iiii3i3−i3−i3000000000-11−330000000000
χ35222-2-22-2-2-1-2-222-1-1111-112i2i−2i−2i00−2i−2i2i2i33−3−3-11-110000-2200000−i−iii3−3−i3−i3i3i3ii−i−ii3i3−i3−i30000000001-1−330000000000
χ36222-2-22-2-2-1-2-222-1-1111-112i2i−2i−2i00−2i−2i2i2i−3−333-11-110000-2200000−i−iii−33i3i3−i3−i3ii−i−i−i3−i3i3i30000000001-13−30000000000
χ37222-2-22-2-2-1-2-222-1-1111-11−2i−2i2i2i002i2i−2i−2i33−3−3-11-110000-2200000ii−i−i3−3i3i3−i3−i3−i−iii−i3−i3i3i30000000001-1−330000000000
χ38222-2-22-2-2-1-2-222-1-1111-11−2i−2i2i2i002i2i−2i−2i−3−333-11-110000-2200000ii−i−i−33−i3−i3i3i3−i−iiii3i3−i3−i30000000001-13−30000000000
χ39222-2-22-2-2-1-2-222-1-1111-11−2i−2i2i2i00−2i−2i2i2i33−3−3-11-1100002-200000ii−i−i3−3i3i3−i3−i3ii−i−ii3i3−i3−i3000000000-113−30000000000
χ40222-2-22-2-2-1-2-222-1-1111-11−2i−2i2i2i00−2i−2i2i2i−3−333-11-1100002-200000ii−i−i−33−i3−i3i3i3ii−i−i−i3−i3i3i3000000000-11−330000000000
χ4122-2-22-22-2200002-22-2-2-2200002i−2i2−22−22i−2i2i−2i00002i2i−2i−2i00000−i2i200000000002−22−2−i2i2−i2i2002-2−i2−i2i2i20000000000002−20
χ4222-2-22-22-2200002-22-2-2-2200002i−2i2−22−22i−2i2i−2i0000−2i−2i2i2i00000−i2i200000000002−22−2−i2i2−i2i200-22i2i2−i2−i2000000000000−220
χ4322-2-22-22-2200002-22-2-2-2200002i−2i−22−222i−2i2i−2i00002i2i−2i−2i00000i2−i20000000000−22−22i2−i2i2−i2002-2i2i2−i2−i2000000000000−220
χ4422-2-22-22-2200002-22-2-2-2200002i−2i−22−222i−2i2i−2i0000−2i−2i2i2i00000i2−i20000000000−22−22i2−i2i2−i200-22−i2−i2i2i20000000000002−20
χ4522-2-22-22-2200002-22-2-2-220000−2i2i2−22−2−2i2i−2i2i00002i2i−2i−2i00000i2−i200000000002−22−2i2−i2i2−i200-22−i2−i2i2i2000000000000−220
χ4622-2-22-22-2200002-22-2-2-220000−2i2i2−22−2−2i2i−2i2i0000−2i−2i2i2i00000i2−i200000000002−22−2i2−i2i2−i2002-2i2i2−i2−i20000000000002−20
χ4722-2-22-22-2200002-22-2-2-220000−2i2i−22−22−2i2i−2i2i00002i2i−2i−2i00000−i2i20000000000−22−22−i2i2−i2i200-22i2i2−i2−i20000000000002−20
χ4822-2-22-22-2200002-22-2-2-220000−2i2i−22−22−2i2i−2i2i0000−2i−2i2i2i00000−i2i20000000000−22−22−i2i2−i2i2002-2−i2−i2i2i2000000000000−220
χ492-2-2222-2-222-22-2-2-22-222-22i−2i2i−2i000000000022-2-2000000000002i−2i2i−2i0000000000000000002-22-200000000002i−2i000
χ502-2-2222-2-222-22-2-2-22-222-22i−2i2i−2i000000000022-2-2000000000002i−2i2i−2i000000000000000000-22-220000000000−2i2i000
χ512-2-2222-2-222-22-2-2-22-222-2−2i2i−2i2i000000000022-2-200000000000−2i2i−2i2i0000000000000000002-22-20000000000−2i2i000
χ522-2-2222-2-222-22-2-2-22-222-2−2i2i−2i2i000000000022-2-200000000000−2i2i−2i2i000000000000000000-22-2200000000002i−2i000
χ532-2-2-2-222222-2-22-2-2-22-22200000000000000-222-22-22-20002-2000000002-22-2000000002-2000000000002-200000000
χ542-2-2-2-222222-2-22-2-2-22-22200000000000000-222-22-22-2000-2200000000-22-22000000002-200000000000-2200000000
χ552-2-2-2-222222-2-22-2-2-22-22200000000000000-222-2-22-220002-2000000002-22-200000000-2200000000000-2200000000
χ562-2-2-2-222222-2-22-2-2-22-22200000000000000-222-2-22-22000-2200000000-22-2200000000-22000000000002-200000000
χ572-2-2-2-22222-222-2-2-2-22-2222-2-2200000000002-2-222-22-200000002-2-2200000000000000-2200000000000002-2000000
χ582-2-2-2-22222-222-2-2-2-22-2222-2-2200000000002-2-22-22-2200000002-2-22000000000000002-20000000000000-22000000
χ592-2-2-2-22222-222-2-2-2-22-222-222-200000000002-2-222-22-20000000-222-200000000000000-220000000000000-22000000
χ602-2-2-2-22222-222-2-2-2-22-222-222-200000000002-2-22-22-220000000-222-2000000000000002-200000000000002-2000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000-2-2-2-22222000000-4000000002200000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-4000022222222000000400000000-2-200000000000000000000000000000000000
χ63444-4-44-4-4444-4-444-4-4-44-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-244-4-4-2-2222-2200000000002323−23−232-22-2000000000000000−232300000000000000000000000000000000000
χ65444-4-44-4-4-244-4-4-2-2222-220000000000−23−2323232-22-200000000000000023−2300000000000000000000000000000000000
χ6644-44-4-4-44400004-4-444-4-4000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ6744-44-4-4-44400004-4-444-4-40000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ6844-44-4-4-44-20000-222-2-222000000−2i22i22i2−2i2−2i32i32i3−2i30000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ6944-44-4-4-44-20000-222-2-222000000−2i22i22i2−2i22i3−2i3−2i32i30000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ7044-44-4-4-44-20000-222-2-2220000002i2−2i2−2i22i2−2i32i32i3−2i30000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ7144-44-4-4-44-20000-222-2-2220000002i2−2i2−2i22i22i3−2i3−2i32i30000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ7244-4-44-44-4-20000-22-2222-200004i−4i22−2222−22−2i2i−2i2i0000000000000−2i22i20000000000−22−22i2−i2i2−i200000000000000000000000
χ7344-4-44-44-4-20000-22-2222-200004i−4i−2222−2222−2i2i−2i2i00000000000002i2−2i200000000002−22−2−i2i2−i2i200000000000000000000000
χ7444-4-44-44-4-20000-22-2222-20000−4i4i22−2222−222i−2i2i−2i00000000000002i2−2i20000000000−22−22−i2i2−i2i200000000000000000000000
χ7544-4-44-44-4-20000-22-2222-20000−4i4i−2222−22222i−2i2i−2i0000000000000−2i22i200000000002−22−2i2−i2i2−i200000000000000000000000
χ764-444-4-44-440000-44-4-44-440000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ774-444-4-44-440000-44-4-44-44000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ784-44-44-4-4440000-4444-4-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ794-44-44-4-4440000-4444-4-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ804-4-4444-4-44-44-44-4-44-444-400000000000000-4-4440000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-24-44-422-22-2-224i−4i4i−4i0000000000-2-22200000000000−2i2i−2i2i0000000000000000000000000000000000000
χ824-4-4444-4-4-24-44-422-22-2-22−4i4i−4i4i0000000000-2-222000000000002i−2i2i−2i0000000000000000000000000000000000000
χ834-4-4444-4-4-2-44-4422-22-2-220000000000000022-2-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ844-4-4444-4-4-2-44-4422-22-2-220000000000000022-2-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ854-4-4-4-4444-24-4-44222-22-2-2000000000000002-2-2200000004-400000000-22-220000000000000000000000000000000
χ864-4-4-4-4444-24-4-44222-22-2-2000000000000002-2-220000000-44000000002-22-20000000000000000000000000000000
χ874-4-4-4-4444-2-444-4222-22-2-24-4-440000000000-222-200000000000-222-20000000000000000000000000000000000000
χ884-4-4-4-4444-2-444-4222-22-2-2-444-40000000000-222-2000000000002-2-220000000000000000000000000000000000000
χ898-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-8-88-400004-4-4-44440000000000000000000000000000000000000000000000000000000000000000000000

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