Finite Group Databasebeta

← Group #10828580

Character table — Group #10828580

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222244448888888888888888888888888812121212121212121616161616161616242424242424242424242424
order1222222234444666666612121212224444444488881212121224242424242424242244444466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ811111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-111-1-111-1-1
χ9111111111111111111111111-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-1-1-1
χ10111111111111111111111111-1-1111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111
χ11111111111111111111111111-1-111-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-111-1-111-1-1-1-111
χ12111111111111111111111111-1-111-111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1
χ13111111111111111111111111-1-1-1-11-1-11-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ14111111111111111111111111-1-1-1-11-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ15111111111111111111111111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ16111111111111111111111111-1-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ17222222222-2-2-2-22222222-2-2-2-20000200-200000022-2-20000000022-2-2-2-22200000000000000000000
χ18222222222-2-2-2-22222222-2-2-2-20000200-200000022-2-200000000-2-22222-2-200000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-20000-2002000000-2-222000000002222-2-2-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-20000-2002000000-2-22200000000-2-2-2-2222200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-222-2-21111-1-1-1-1111100000000-1-1-1-11111000000000000
χ2322222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-22222-2-2-2-2-2-2-1-1-1-11111111100000000-1-111-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-222-2-22211111111-1-1-1-100000000-1-11111-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2222-2-2222-2-2-2-2-1-1-1-1111111110000000011-1-111-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-222-2-2-2-2-22211111111-1-1-1-10000000011-1-1-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-2-22-2-22222-1-1-1-1-1-1-1-1-1-1-1-10000000011111111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-22222-2-21111-1-1-1-11111000000001111-1-1-1-1000000000000
χ292-2-22-222-2222-2-22-2-2-222-2-2-222002-20000000000000000000000002i−2i002i−2i002-200000000002i−2i0000
χ302-2-22-222-2222-2-22-2-2-222-2-2-222002-2000000000000000000000000−2i2i00−2i2i002-20000000000−2i2i0000
χ312-2-22-222-2222-2-22-2-2-222-2-2-22200-220000000000000000000000002i−2i002i−2i00-220000000000−2i2i0000
χ322-2-22-222-2222-2-22-2-2-222-2-2-22200-22000000000000000000000000−2i2i00−2i2i00-2200000000002i−2i0000
χ332-2-22-222-22-2-2222-2-2-222-222-2-2000000002i−2i0000000000000000002i−2i00−2i2i0000002i−2i2-20000000000
χ342-2-22-222-22-2-2222-2-2-222-222-2-2000000002i−2i000000000000000000−2i2i002i−2i0000002i−2i-220000000000
χ352-2-22-222-22-2-2222-2-2-222-222-2-200000000−2i2i0000000000000000002i−2i00−2i2i000000−2i2i-220000000000
χ362-2-22-222-22-2-2222-2-2-222-222-2-200000000−2i2i000000000000000000−2i2i002i−2i000000−2i2i2-20000000000
χ372-2-2-222-2222-22-2-2-2-22-2222-22-2000002-200000000000000000002-2002-20000002-20000002-2000000
χ382-2-2-222-2222-22-2-2-2-22-2222-22-2000002-20000000000000000000-2200-220000002-2000000-22000000
χ392-2-2-222-2222-22-2-2-2-22-2222-22-200000-2200000000000000000002-2002-2000000-22000000-22000000
χ402-2-2-222-2222-22-2-2-2-22-2222-22-200000-220000000000000000000-2200-22000000-220000002-2000000
χ412-2-2-222-222-22-22-2-2-22-222-22-222-20000000000000000000000002-200-22002-2000000002-200000000
χ422-2-2-222-222-22-22-2-2-22-222-22-222-2000000000000000000000000-22002-2002-200000000-2200000000
χ432-2-2-222-222-22-22-2-2-22-222-22-22-220000000000000000000000002-200-2200-2200000000-2200000000
χ442-2-2-222-222-22-22-2-2-22-222-22-22-22000000000000000000000000-22002-200-22000000002-200000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-222220000400-4000000-2-222000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-222220000-400400000022-2-2000000000000000000000000000000000000
χ47444-4-44-4-444-4-44-444-4-44-4-444-4000000000000000000000000000000000000000000000000000000
χ48444-4-44-4-44-444-4-444-4-44-44-4-44000000000000000000000000000000000000000000000000000000
χ49444-4-44-4-4-24-4-442-2-222-222-2-2200000000000000000000002323−23−230000000000000000000000000000
χ50444-4-44-4-4-24-4-442-2-222-222-2-220000000000000000000000−23−2323230000000000000000000000000000
χ51444-4-44-4-4-2-444-42-2-222-22-222-20000000000000000002323−23−2300000000000000000000000000000000
χ52444-4-44-4-4-2-444-42-2-222-22-222-2000000000000000000−23−23232300000000000000000000000000000000
χ5344-444-4-4-440000-44-444-4-40000000000000022−2200000022−2222−2200000000000000000000000000000000
χ5444-444-4-4-440000-44-444-4-400000000000000−2222000000−2222−222200000000000000000000000000000000
χ5544-444-4-4-4-200002-22-2-2220000000000000022−22000023−23−22−226−66−60000000000000000000000000000
χ5644-444-4-4-4-200002-22-2-2220000000000000022−220000−2323−22−22−66−660000000000000000000000000000
χ5744-444-4-4-4-200002-22-2-22200000000000000−2222000023−232−22−2−66−660000000000000000000000000000
χ5844-444-4-4-4-200002-22-2-22200000000000000−22220000−23232−22−26−66−60000000000000000000000000000
χ5944-4-4-4-4444000044-4-4-4-44000000000000000022−220000000022−22−22220000000000000000000000000000
χ6044-4-4-4-4444000044-4-4-4-440000000000000000−222200000000−222222−220000000000000000000000000000
χ6144-4-4-4-444-20000-2-22222-2000000000000000022−2223−23006−6−66−222−20000000000000000000000000000
χ6244-4-4-4-444-20000-2-22222-2000000000000000022−22−232300−666−6−222−20000000000000000000000000000
χ6344-4-4-4-444-20000-2-22222-20000000000000000−222223−2300−666−62−2−220000000000000000000000000000
χ6444-4-4-4-444-20000-2-22222-20000000000000000−2222−2323006−6−662−2−220000000000000000000000000000
χ654-444-4-4-4440000-4-44-44-440000000000000000000000000000000000000000000000000000000022−22
χ664-444-4-4-4440000-4-44-44-4400000000000000000000000000000000000000000000000000000000−2222
χ674-44-44-44-4400004-444-4-4-400000000000000000000000000000000000000000000000000000022−2200
χ684-44-44-44-4400004-444-4-4-4000000000000000000000000000000000000000000000000000000−222200
χ694-4-44-444-4-244-4-4-2222-2-2222-2-2004-400000000000000000000000000000000-220000000000000000
χ704-4-44-444-4-244-4-4-2222-2-2222-2-200-44000000000000000000000000000000002-20000000000000000
χ714-4-44-444-4-2-4-444-2222-2-22-2-222000000004i−4i000000000000000000000000000000−2i2i000000000000
χ724-4-44-444-4-2-4-444-2222-2-22-2-22200000000−4i4i0000000000000000000000000000002i−2i000000000000
χ734-4-4-444-44-24-44-4222-22-2-2-22-22000004-40000000000000000000000000000000-2200000000000000
χ744-4-4-444-44-24-44-4222-22-2-2-22-2200000-4400000000000000000000000000000002-200000000000000
χ754-4-4-444-44-2-44-44222-22-2-22-22-24-400000000000000000000000000000000-22000000000000000000
χ764-4-4-444-44-2-44-44222-22-2-22-22-2-44000000000000000000000000000000002-2000000000000000000
χ778-888-8-8-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000
χ788-88-88-88-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000

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