Finite Group Databasebeta

← Group #10828847

Character table — Group #10828847

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666664444448888121212121212121244444444488121212121212121212122424242424242424224488884121212122444444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111111111-1-11111-1-1-1-111111111-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-1-111-111-1-111-1-1-1
χ6111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-1111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-111-1-1-1-1111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1111111111-1-11-1-11111-1-1-1
χ911111111111111111111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ1011111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1111111111111111111111-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ1211111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-2222222200002200002222-2-2-2-22222-200000000000000-2-200000000-2-222000000000-2000000000
χ18222222222-2-2-2-2222222200002200002222-2-2-2-2-2-2-2-2-200000000000000-2-20000000022-2-20000000002000000000
χ19222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-222222000000000000002200000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-222222220000-2-20000-2-2-2-2-2-2-2-2-2-2-2-220000000000000022000000002222000000000-2000000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-222221111-1-1-1-10000-222-2-2-2-21111-1-1-1-111-1-1-1-1111100000000-211-1-10000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-21111-1-1-1-10000-2-2-2-2-2221111-1-1-1-1111111-1-1-1-1000000002-1-1110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2222222-1-1-1-1-1-1-1-100002-2-2-2-22211111111-1-1-1-1-1-1-1-1-1-100000000-211110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-10000222-2-2-2-211111111-1-111111111000000002-1-1-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-10000-2-2-222-2-2-1-1-1-1111111-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-10000-2222222-1-1-1-11111111111-1-1-1-100000000-211-1-10000000000
χ2922-22-2-22-22-2-2222-2-2-222-22i2i−2i−2i0022-2-200002-22-2000002i−2i000000002i2i−2i−2i0022-2-20000000000000002i−2i0000000000
χ3022-22-2-22-22-2-2222-2-2-222-22i2i−2i−2i00-2-22200002-22-200000−2i2i000000002i2i−2i−2i00-2-222000000000000000−2i2i0000000000
χ3122-22-2-22-22-2-2222-2-2-222-2−2i−2i2i2i0022-2-200002-22-200000−2i2i00000000−2i−2i2i2i0022-2-2000000000000000−2i2i0000000000
χ3222-22-2-22-22-2-2222-2-2-222-2−2i−2i2i2i00-2-22200002-22-2000002i−2i00000000−2i−2i2i2i00-2-2220000000000000002i−2i0000000000
χ3322-22-2-22-2-1-2-222-1111-1-112i2i−2i−2i0022-2-233−3−3-11-11000002i−2i0000−i3−i3i3i3−i−iii3−3-1-11133−3−3000000000−i3i3−ii0000000000
χ3422-22-2-22-2-1-2-222-1111-1-112i2i−2i−2i0022-2-2−3−333-11-11000002i−2i0000i3i3−i3−i3−i−iii−33-1-111−3−333000000000i3−i3−ii0000000000
χ3522-22-2-22-2-1-2-222-1111-1-112i2i−2i−2i00-2-22233−3−3-11-1100000−2i2i0000−i3−i3i3i3−i−iii3−311-1-1−3−333000000000i3−i3i−i0000000000
χ3622-22-2-22-2-1-2-222-1111-1-112i2i−2i−2i00-2-222−3−333-11-1100000−2i2i0000i3i3−i3−i3−i−iii−3311-1-133−3−3000000000−i3i3i−i0000000000
χ3722-22-2-22-2-1-2-222-1111-1-11−2i−2i2i2i0022-2-233−3−3-11-1100000−2i2i0000i3i3−i3−i3ii−i−i3−3-1-11133−3−3000000000i3−i3i−i0000000000
χ3822-22-2-22-2-1-2-222-1111-1-11−2i−2i2i2i0022-2-2−3−333-11-1100000−2i2i0000−i3−i3i3i3ii−i−i−33-1-111−3−333000000000−i3i3i−i0000000000
χ3922-22-2-22-2-1-2-222-1111-1-11−2i−2i2i2i00-2-22233−3−3-11-11000002i−2i0000i3i3−i3−i3ii−i−i3−311-1-1−3−333000000000−i3i3−ii0000000000
χ4022-22-2-22-2-1-2-222-1111-1-11−2i−2i2i2i00-2-222−3−333-11-11000002i−2i0000−i3−i3i3i3ii−i−i−3311-1-133−3−3000000000i3−i3−ii0000000000
χ4122-2-2-22-222000022-22-2-2-200002-22−22−22-22-200002i2i−2i−2i000002−200000000002−22−22−22−2002i−2i−i2−i2i2i2000000000000−i2i20
χ4222-2-2-22-222000022-22-2-2-200002-22−22−22-22-20000−2i−2i2i2i000002−200000000002−22−22−22−200−2i2ii2i2−i2−i2000000000000i2−i20
χ4322-2-2-22-222000022-22-2-2-200002-2−22−222-22-200002i2i−2i−2i00000−220000000000−22−22−22−22002i−2ii2i2−i2−i2000000000000i2−i20
χ4422-2-2-22-222000022-22-2-2-200002-2−22−222-22-20000−2i−2i2i2i00000−220000000000−22−22−22−2200−2i2i−i2−i2i2i2000000000000−i2i20
χ4522-2-2-22-222000022-22-2-2-20000-222−22−2-22-2200002i2i−2i−2i00000−2200000000002−22−2−22−2200−2i2i−i2−i2i2i2000000000000i2−i20
χ4622-2-2-22-222000022-22-2-2-20000-222−22−2-22-220000−2i−2i2i2i00000−2200000000002−22−2−22−22002i−2ii2i2−i2−i2000000000000−i2i20
χ4722-2-2-22-222000022-22-2-2-20000-22−22−22-22-2200002i2i−2i−2i000002−20000000000−22−222−22−200−2i2ii2i2−i2−i2000000000000−i2i20
χ4822-2-2-22-222000022-22-2-2-20000-22−22−22-22-220000−2i−2i2i2i000002−20000000000−22−222−22−2002i−2i−i2−i2i2i2000000000000i2−i20
χ492-22-2-222-22-22-22-222-2-22-22i−2i2i−2i0000000000-2-2220000000000000002i−2i2i−2i000000000000002-22-200000000002i−2i000
χ502-22-2-222-22-22-22-222-2-22-22i−2i2i−2i0000000000-2-2220000000000000002i−2i2i−2i00000000000000-22-220000000000−2i2i000
χ512-22-2-222-22-22-22-222-2-22-2−2i2i−2i2i0000000000-2-222000000000000000−2i2i−2i2i000000000000002-22-20000000000−2i2i000
χ522-22-2-222-22-22-22-222-2-22-2−2i2i−2i2i0000000000-2-222000000000000000−2i2i−2i2i00000000000000-22-2200000000002i−2i000
χ532-2-2-22-22222-2-22-2-2-22-2222-2-220000000000-222-22-22-2000000000002-2-2200000000002-20000000000002-20000000
χ542-2-2-22-22222-2-22-2-2-22-2222-2-220000000000-222-2-22-22000000000002-2-220000000000-22000000000000-220000000
χ552-2-2-22-22222-2-22-2-2-22-222-222-20000000000-222-22-22-200000000000-222-200000000002-2000000000000-220000000
χ562-2-2-22-22222-2-22-2-2-22-222-222-20000000000-222-2-22-2200000000000-222-20000000000-220000000000002-20000000
χ572-2-2-22-2222-222-2-2-2-22-222000000000000002-2-222-22-20002-2002-22-200000000000000-22000000000000002-200000
χ582-2-2-22-2222-222-2-2-2-22-222000000000000002-2-222-22-2000-2200-22-2200000000000000-2200000000000000-2200000
χ592-2-2-22-2222-222-2-2-2-22-222000000000000002-2-22-22-220002-2002-22-2000000000000002-200000000000000-2200000
χ602-2-2-22-2222-222-2-2-2-22-222000000000000002-2-22-22-22000-2200-22-22000000000000002-2000000000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000440000-2-2-2-222220000-400000000000000220000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-40000222222220000400000000000000-2-20000000000000000000000000000000
χ63444-44-4-4-4400004-44-4-4-4400000022−22−22220000000000000000000000000000022−22−2222000000000000000000000000000
χ64444-44-4-4-4400004-44-4-4-44000000−222222−2200000000000000000000000000000−222222−22000000000000000000000000000
χ65444-44-4-4-4-20000-22-2222-200000022−22−222223−23−23230000000000000000000000000−222−26−6−6600000000000000000000000
χ66444-44-4-4-4-20000-22-2222-200000022−22−2222−232323−230000000000000000000000000−222−2−666−600000000000000000000000
χ67444-44-4-4-4-20000-22-2222-2000000−222222−2223−23−232300000000000000000000000002−2−22−666−600000000000000000000000
χ68444-44-4-4-4-20000-22-2222-2000000−222222−22−232323−2300000000000000000000000002−2−226−6−6600000000000000000000000
χ6944-44-4-44-4444-4-44-4-4-444-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ7044-44-4-44-4-244-4-4-2222-2-2200000000002323−23−232-22-20000000000000000000−23230000000000000000000000000000000
χ7144-44-4-44-4-244-4-4-2222-2-220000000000−23−2323232-22-2000000000000000000023−230000000000000000000000000000000
χ7244-4-4-44-44-20000-2-22-222200004-422−2222−22-22-22000000000000022−220000000000−22−22−22−2200000000000000000000000
χ7344-4-4-44-44-20000-2-22-222200004-4−2222−2222-22-220000000000000−222200000000002−22−22−22−200000000000000000000000
χ7444-4-4-44-44-20000-2-22-22220000-4422−2222−222-22-20000000000000−22220000000000−22−222−22−200000000000000000000000
χ7544-4-4-44-44-20000-2-22-22220000-44−2222−22222-22-2000000000000022−2200000000002−22−2−22−2200000000000000000000000
χ764-444-4-4-4440000-4-4444-4-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ774-444-4-4-4440000-4-4444-4-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ784-44-4-444-444-44-4-444-4-44-40000000000000044-4-40000000000000000000000000000000000000000000000000000
χ794-44-4-444-4-24-44-42-2-222-2200000000000000-2-22200000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ804-44-4-444-4-24-44-42-2-222-2200000000000000-2-222000000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ814-44-4-444-4-2-44-442-2-222-224i−4i4i−4i000000000022-2-2000000000000000−2i2i−2i2i000000000000000000000000000000000
χ824-44-4-444-4-2-44-442-2-222-22−4i4i−4i4i000000000022-2-20000000000000002i−2i2i−2i000000000000000000000000000000000
χ834-4-4444-4-440000-44-4-44-44000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ844-4-4444-4-440000-44-4-44-440000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ854-4-4-44-444-24-4-44222-22-2-24-4-4400000000002-2-22000000000000000-222-2000000000000000000000000000000000
χ864-4-4-44-444-24-4-44222-22-2-2-444-400000000002-2-220000000000000002-2-22000000000000000000000000000000000
χ874-4-4-44-444-2-444-4222-22-2-200000000000000-222-200000004-400-22-220000000000000000000000000000000000000
χ884-4-4-44-444-2-444-4222-22-2-200000000000000-222-20000000-44002-22-20000000000000000000000000000000000000
χ898-888-8-8-88-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8888-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000000000

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