Finite Group Databasebeta

← Group #10868074

Character table — Group #10868074

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424444488884121212122444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-111111111111-1-1-1-111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-1-111-1-111-1-1-1
χ1011111111111111111111-1-111111111111-1-1-1-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-11-1-111-1-1111
χ1111111111111111111111-1-11111-1-1-1-1111-1-1-1-111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111111-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-1-11111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-11-1-1-1-111-1-11
χ17222222222-2-2-2-222222222200000000-2-2-22222-22222-2000000-2-2000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-222222222200000000-2-2-22222-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222222000000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-220000002200000000000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222222222-1-1-11111-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-11111-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-11111-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-1-1-11111-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-2-22-22-22-222-2-2222-2-2-2002i2i−2i−2i22-2-22-2-20000200000002i−2i00002i2i−2i−2i000022-2-200000000000002i−2i000000000000
χ3022-2-22-22-22-222-2-2222-2-2-2002i2i−2i−2i-2-2222-2-2000020000000−2i2i00002i2i−2i−2i0000-2-2220000000000000−2i2i000000000000
χ3122-2-22-22-22-222-2-2222-2-2-200−2i−2i2i2i22-2-22-2-2000020000000−2i2i0000−2i−2i2i2i000022-2-20000000000000−2i2i000000000000
χ3222-2-22-22-22-222-2-2222-2-2-200−2i−2i2i2i-2-2222-2-20000200000002i−2i0000−2i−2i2i2i0000-2-22200000000000002i−2i000000000000
χ3322-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i22-2-2-111−i3−i3i3i3-100000002i−2i00−i3i3−i−iii33−3−3-1-111−i3−i3i3i3000000000−ii3−30000000000
χ3422-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i22-2-2-111i3i3−i3−i3-100000002i−2i00i3−i3−i−iii−3−333-1-111i3i3−i3−i3000000000−ii−330000000000
χ3522-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-2-222-111−i3−i3i3i3-10000000−2i2i00−i3i3−i−iii33−3−311-1-1i3i3−i3−i3000000000i−i−330000000000
χ3622-2-22-22-2-1-222-21-1-1-1111002i2i−2i−2i-2-222-111i3i3−i3−i3-10000000−2i2i00i3−i3−i−iii−3−33311-1-1−i3−i3i3i3000000000i−i3−30000000000
χ3722-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i22-2-2-111−i3−i3i3i3-10000000−2i2i00−i3i3ii−i−i−3−333-1-111−i3−i3i3i3000000000i−i−330000000000
χ3822-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i22-2-2-111i3i3−i3−i3-10000000−2i2i00i3−i3ii−i−i33−3−3-1-111i3i3−i3−i3000000000i−i3−30000000000
χ3922-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-2-222-111−i3−i3i3i3-100000002i−2i00−i3i3ii−i−i−3−33311-1-1i3i3−i3−i3000000000−ii3−30000000000
χ4022-2-22-22-2-1-222-21-1-1-111100−2i−2i2i2i-2-222-111i3i3−i3−i3-100000002i−2i00i3−i3ii−i−i33−3−311-1-1−i3−i3i3i3000000000−ii−330000000000
χ412-222-2-22-2222-2-2-22-2-22-220000000000-22-2000022i2i−2i−2i02-200000000002-22-200000000002i−2i0000000000002i−2i00000
χ422-222-2-22-2222-2-2-22-2-22-220000000000-22-2000022i2i−2i−2i0-220000000000-22-2200000000002i−2i000000000000−2i2i00000
χ432-222-2-22-2222-2-2-22-2-22-220000000000-22-200002−2i−2i2i2i02-200000000002-22-20000000000−2i2i000000000000−2i2i00000
χ442-222-2-22-2222-2-2-22-2-22-220000000000-22-200002−2i−2i2i2i0-220000000000-22-220000000000−2i2i0000000000002i−2i00000
χ452-222-2-22-22-2-222-22-2-22-22002i−2i2i−2i00002-220000-22i2i−2i−2i0000000002i−2i2i−2i00000000000000−2i2i000000000000002-2000
χ462-222-2-22-22-2-222-22-2-22-22002i−2i2i−2i00002-220000-2−2i−2i2i2i0000000002i−2i2i−2i000000000000002i−2i00000000000000-22000
χ472-222-2-22-22-2-222-22-2-22-2200−2i2i−2i2i00002-220000-22i2i−2i−2i000000000−2i2i−2i2i00000000000000−2i2i00000000000000-22000
χ482-222-2-22-22-2-222-22-2-22-2200−2i2i−2i2i00002-220000-2−2i−2i2i2i000000000−2i2i−2i2i000000000000002i−2i000000000000002-2000
χ492-22-22-2-2220000-2-22-222-22-20000−i2i2−i2i20002-22-202i−2i2i−2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i0022−2−20000000000002−20
χ502-22-22-2-2220000-2-22-222-22-20000−i2i2−i2i20002-22-20−2i2i−2i2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i00−2−222000000000000−220
χ512-22-22-2-2220000-2-22-222-22-20000i2−i2i2−i20002-22-202i−2i2i−2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i00−2−222000000000000−220
χ522-22-22-2-2220000-2-22-222-22-20000i2−i2i2−i20002-22-20−2i2i−2i2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i0022−2−20000000000002−20
χ532-22-22-2-2220000-2-22-222-2-220000−i2i2−i2i2000-22-2202i−2i2i−2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i0022−2−2000000000000−220
χ542-22-22-2-2220000-2-22-222-2-220000−i2i2−i2i2000-22-220−2i2i−2i2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i00−2−2220000000000002−20
χ552-22-22-2-2220000-2-22-222-2-220000i2−i2i2−i2000-22-2202i−2i2i−2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i00−2−2220000000000002−20
χ562-22-22-2-2220000-2-22-222-2-220000i2−i2i2−i2000-22-220−2i2i−2i2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i0022−2−2000000000000−220
χ572-2-2-2-222222-22-222-2-2-22-2002-2-22000022-20000-200000000000002-2-2200000000000000002i−2i2i−2i0000002i−2i0000000
χ582-2-2-2-222222-22-222-2-2-22-2002-2-22000022-20000-200000000000002-2-220000000000000000−2i2i−2i2i000000−2i2i0000000
χ592-2-2-2-222222-22-222-2-2-22-200-222-2000022-20000-20000000000000-222-200000000000000002i−2i2i−2i000000−2i2i0000000
χ602-2-2-2-222222-22-222-2-2-22-200-222-2000022-20000-20000000000000-222-20000000000000000−2i2i−2i2i0000002i−2i0000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000222-2-2-2-220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-44-4-4400004-4-444-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-4-44-4-4400004-4-444-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-44-4-4-4440000-4-4-44-444000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ6644-44-4-4-4440000-4-4-44-4440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ6744-4-44-44-444-4-44-4444-4-4-40000000000-4440000-40000000000000000000000000000000000000000000000000000
χ6844-4-44-44-4-24-4-442-2-2-222200000000002-2-2−2i3−2i32i32i32000000000002i3−2i3000000000000000000000000000000000000000
χ6944-4-44-44-4-24-4-442-2-2-222200000000002-2-22i32i3−2i3−2i3200000000000−2i32i3000000000000000000000000000000000000000
χ704-444-4-44-4-244-4-42-222-22-200000000002-220000-2000004-40000000000-22-220000000000000000000000000000000
χ714-444-4-44-4-244-4-42-222-22-200000000002-220000-200000-4400000000002-22-20000000000000000000000000000000
χ724-444-4-44-4-2-4-4442-222-22-2004i−4i4i−4i0000-22-2000020000000000000−2i2i−2i2i00000000000000000000000000000000000
χ734-444-4-44-4-2-4-4442-222-22-200−4i4i−4i4i0000-22-20000200000000000002i−2i2i−2i00000000000000000000000000000000000
χ744-44-44-4-44-2000022-22-2-224-40000−2i22i2−2i22i2000-22-220000000000−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ754-44-44-4-44-2000022-22-2-224-400002i2−2i22i2−2i2000-22-2200000000002i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ764-44-44-4-44-2000022-22-2-22-440000−2i22i2−2i22i20002-22-200000000002i2−2i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ774-44-44-4-44-2000022-22-2-22-4400002i2−2i22i2−2i20002-22-20000000000−2i22i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ784-4-4444-4-4400004-44-4-4-44000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ794-4-4444-4-4400004-44-4-4-440000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ804-4-4444-4-4-20000-22-2222-2000000−2i22i22i2−2i2000−2i32i32i3−2i30000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ814-4-4444-4-4-20000-22-2222-2000000−2i22i22i2−2i20002i3−2i3−2i32i30000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ824-4-4444-4-4-20000-22-2222-20000002i2−2i2−2i22i2000−2i32i32i3−2i30000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ834-4-4444-4-4-20000-22-2222-20000002i2−2i2−2i22i20002i3−2i3−2i32i30000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ844-4-4-4-44444-44-4444-4-4-44-40000000000-4-44000040000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-24-44-4-2-2222-22004-4-440000-2-22000020000000000000-222-200000000000000000000000000000000000
χ864-4-4-4-4444-24-44-4-2-2222-2200-444-40000-2-220000200000000000002-2-2200000000000000000000000000000000000
χ874-4-4-4-4444-2-44-44-2-2222-22000000000022-20000-20000000000000000023−23−23230000000000000000000000000000000
χ884-4-4-4-4444-2-44-44-2-2222-22000000000022-20000-200000000000000000−232323−230000000000000000000000000000000
χ89888-8-88-8-8-40000-444-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-8-88-40000444-44-4-40000000000000000000000000000000000000000000000000000000000000000000000

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