Finite Group Databasebeta

← Group #10697532

Character table — Group #10697532

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212122244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-2-222222222-2-22222-2-2-2-2000000000000-2-20000000000000000000000000022-2-2000000
χ10222222222222-2-2-2-222222222-2-22222-2-2-2-2000000000000-2-200000000000000000000000000-2-222000000
χ11222222222-2-2-22222-22222222-2-2-2-2-2-2222222-2-20000-2-2-2-2-2-2222200000000000000000000000000000000
χ12222222222-2-2-22222-22222222-2-2-2-2-2-22222-2-22200002222-2-2-2-2-2-200000000000000000000000000000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111-1-11111111111110000000022-1-1-1-10000000000
χ1922222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-20000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-20000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2220000-1-1-1-1111111−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1-2-2-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2220000-1-1-1-1111111i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ23222-22-2-2-2222-20000-222-2-22-2-20022-2-20000000022−2−2000000000022−2−222−2−22222−2−2−2−20000002-200000000
χ24222-22-2-2-2222-20000-222-2-22-2-20022-2-20000000022−2−2000000000022−2−222−2−2−2−2−2−22222000000-2200000000
χ25222-22-2-2-2222-20000-222-2-22-2-20022-2-200000000−2−2220000000000−2−222−2−2222222−2−2−2−2000000-2200000000
χ26222-22-2-2-2222-20000-222-2-22-2-20022-2-200000000−2−2220000000000−2−222−2−222−2−2−2−222220000002-200000000
χ2722-22-2-22-220002-2-2202-22-2-22-20000002-2-222i−2i0000000000002i2i−2i−2i0000000022−2−222−2−20000000000−i2−i2i2i200
χ2822-22-2-22-220002-2-2202-22-2-22-20000002-2-222i−2i0000000000002i2i−2i−2i00000000−2−222−2−2220000000000i2i2−i2−i200
χ2922-22-2-22-220002-2-2202-22-2-22-20000002-2-22−2i2i000000000000−2i−2i2i2i0000000022−2−222−2−20000000000i2i2−i2−i200
χ3022-22-2-22-220002-2-2202-22-2-22-20000002-2-22−2i2i000000000000−2i−2i2i2i00000000−2−222−2−2220000000000−i2−i2i2i200
χ312-22-2-2-222200022-2-20-22-22-22-200000022-2-2002-2000022-2-200000000000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i200
χ322-22-2-2-222200022-2-20-22-22-22-200000022-2-2002-2000022-2-200000000000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i200
χ332-22-2-2-222200022-2-20-22-22-22-200000022-2-200-220000-2-22200000000000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i200
χ342-22-2-2-222200022-2-20-22-22-22-200000022-2-200-220000-2-22200000000000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i200
χ352-2-222-2-2222-2-200002-2-2222-2-2002-22-2000000002−22−200000000002−22−22−22−2−i2i2i2−i2i2−i2−i2i2000000002i−2i000000
χ362-2-222-2-2222-2-200002-2-2222-2-2002-22-2000000002−22−200000000002−22−22−22−2i2−i2−i2i2−i2i2i2−i200000000−2i2i000000
χ372-2-222-2-2222-2-200002-2-2222-2-2002-22-200000000−22−220000000000−22−22−22−22−i2i2i2−i2i2−i2−i2i200000000−2i2i000000
χ382-2-222-2-2222-2-200002-2-2222-2-2002-22-200000000−22−220000000000−22−22−22−22i2−i2−i2i2−i2i2i2−i2000000002i−2i000000
χ392-2-2-2222-222-222-22-2-2-2-2-2-22222-22-2-222-22-20000000000002-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ402-2-2-2222-222-222-22-2-2-2-2-2-22222-22-2-222-22-20000000000002-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ412-2-2-2222-222-22-22-22-2-2-2-2-2222-222-2-22-22-2200002-2-220000-2200002-2-222-2-22000000000000000000000000
χ422-2-2-2222-222-22-22-22-2-2-2-2-2222-222-2-22-22-220000-222-20000-220000-222-2-222-2000000000000000000000000
χ432-2-2-2222-22-22-22-22-22-2-2-2-2222-22-222-22-22-2000000000000-220000000000000000000000000000002-2-2200
χ442-2-2-2222-22-22-22-22-22-2-2-2-2222-22-222-22-22-2000000000000-22000000000000000000000000000000-222-200
χ452-2-2-2222-22-22-2-22-222-2-2-2-22222-2-222-2-22-220000000000002-2000000000000000000002-22-22-20000000000
χ462-2-2-2222-22-22-2-22-222-2-2-2-22222-2-222-2-22-220000000000002-200000000000000000000-22-22-220000000000
χ472-2-2-2222-2-12-22-22-22-21111-1-1-1-22-111-11-11-100002-2-22−i3i3−i3i31-1−i3i3−i3i3-111-1-111-10000000000−i3i3i3−i30000000000
χ482-2-2-2222-2-12-22-22-22-21111-1-1-1-22-111-11-11-100002-2-22i3−i3i3−i31-1i3−i3i3−i3-111-1-111-10000000000i3−i3−i3i30000000000
χ492-2-2-2222-2-12-22-22-22-21111-1-1-1-22-111-11-11-10000-222-2−i3i3−i3i31-1−i3i3−i3i31-1-111-1-110000000000i3−i3−i3i30000000000
χ502-2-2-2222-2-12-22-22-22-21111-1-1-1-22-111-11-11-10000-222-2i3−i3i3−i31-1i3−i3i3−i31-1-111-1-110000000000−i3i3i3−i30000000000
χ512-2-2-2222-2-1-22-2-22-2221111-1-1-12-21-1-111-11-100000000−i3i3−i3i3-11i3−i3i3−i3−i3i3i3−i3i3−i3−i3i300000000-221-11-10000000000
χ522-2-2-2222-2-1-22-2-22-2221111-1-1-12-21-1-111-11-100000000−i3i3−i3i3-11i3−i3i3−i3i3−i3−i3i3−i3i3i3−i3000000002-2-11-110000000000
χ532-2-2-2222-2-1-22-2-22-2221111-1-1-12-21-1-111-11-100000000i3−i3i3−i3-11−i3i3−i3i3−i3i3i3−i3i3−i3−i3i3000000002-2-11-110000000000
χ542-2-2-2222-2-1-22-2-22-2221111-1-1-12-21-1-111-11-100000000i3−i3i3−i3-11−i3i3−i3i3i3−i3−i3i3−i3i3i3−i300000000-221-11-10000000000
χ5544444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000022000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ57444-44-4-4-44-4-440000444-4-44-4-400-4-444000000000000000000000000000000000000000000000000000000
χ58444-44-4-4-4-244-40000-4-2-222-22200-2-222000000002222−22−220000000000−2−222−2−222000000000000000000000000
χ59444-44-4-4-4-244-40000-4-2-222-22200-2-22200000000−22−222222000000000022−2−222−2−2000000000000000000000000
χ60444-44-4-4-4-2-4-4400004-2-222-2220022-2-20000000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ61444-44-4-4-4-2-4-4400004-2-222-2220022-2-20000000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6244-44-4-44-44000-444-404-44-4-44-4000000-444-400000000000000000000000000000000000000000000000000
χ6344-44-4-44-4-20004-4-440-22-222-22000000-222-24i−4i000000000000−2i−2i2i2i00000000000000000000000000000000
χ6444-44-4-44-4-20004-4-440-22-222-22000000-222-2−4i4i0000000000002i2i−2i−2i00000000000000000000000000000000
χ6544-44-4-44-4-2000-444-40-22-222-220000002-2-2200000000−2i32i32i3−2i300000000000000000000000000000000000000
χ6644-44-4-44-4-2000-444-40-22-222-220000002-2-22000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ6744-4-4-44-444000000004-4-44-4-4400000000000000000000000000000000000022-2-2-2-2220000000000000000
χ6844-4-4-44-444000000004-4-44-4-44000000000000000000000000000000000000-2-22222-2-20000000000000000
χ694-444-44-4-4400000000-444-4-4-440000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ704-444-44-4-4400000000-444-4-4-44000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ714-44-4-4-4444000-4-4440-44-44-44-4000000-4-44400000000000000000000000000000000000000000000000000
χ724-44-4-4-444-200044-4-402-22-22-22000000-2-222004-40000-2-22200000000000000000000000000000000000000
χ734-44-4-4-444-200044-4-402-22-22-22000000-2-22200-44000022-2-200000000000000000000000000000000000000
χ744-44-4-4-444-2000-4-44402-22-22-2200000022-2-20000000000000023−23−232300000000000000000000000000000000
χ754-44-4-4-444-2000-4-44402-22-22-2200000022-2-200000000000000−232323−2300000000000000000000000000000000
χ764-4-444-4-444-4440000-4-4-4444-4-400-44-44000000000000000000000000000000000000000000000000000000
χ774-4-444-4-44-24-4-40000422-2-2-22200-22-220000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ784-4-444-4-44-24-4-40000422-2-2-22200-22-2200000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ794-4-444-4-44-2-4440000-422-2-2-222002-22-20000000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ804-4-444-4-44-2-4440000-422-2-2-222002-22-20000000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ814-4-4-4444-4-24-444-44-4-42222-2-2-24-4-222-2-22-22000000000000-22000000000000000000000000000000000000
χ824-4-4-4444-4-2-44-44-44-442222-2-2-2-442-2-22-22-220000000000002-2000000000000000000000000000000000000
χ8388-8-8-88-88-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-888-88-8-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000

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