Finite Group Databasebeta

← Group #10691580

Character table — Group #10691580

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888812121212161616161616242424242424242424244848
order12222234444446666666224444412121212121212122466668888121212121212242424242424242488884412121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111-1-111-1-1111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1
χ911111111-11-1-1-11111111111-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i1-111-1-1i−iii−i−iii−i−ii−i
χ1011111111-11-1-1-11111111111-1-1-1-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii1-111-1-1−ii−i−iii−i−iii−ii
χ1111111111-11-1-1-11111111111-1-1-1-1111-1-1-1-111-11111-1-111-1-1-1-1-1-1-1-1-1-11111ii−i−i-11-1-111i−iii−i−i−i−iii−ii
χ1211111111-11-1-1-11111111111-1-1-1-1111-1-1-1-111-11111-1-111-1-1-1-1-1-1-1-1-1-11111−i−iii-11-1-111−ii−i−iiiii−i−ii−i
χ1311111111-11-1-1-11111111-1-11-111-1111-1-1-1-11-11-1-1-1-111-1-1-1-111111111-1-1-1-1ii−i−i-11-1-111i−i−i−iiiii−i−i−ii
χ1411111111-11-1-1-11111111-1-11-111-1111-1-1-1-11-11-1-1-1-111-1-1-1-111111111-1-1-1-1−i−iii-11-1-111−iiii−i−i−i−iiii−i
χ1511111111-11-1-1-11111111-1-11-111-1111-1-1-1-11-11-1-1-1-1-1-111-1-11111-1-1-1-11111ii−i−i1-111-1-1i−i−i−iii−i−iiii−i
χ1611111111-11-1-1-11111111-1-11-111-1111-1-1-1-11-11-1-1-1-1-1-111-1-11111-1-1-1-11111−i−iii1-111-1-1−iiii−i−iii−i−i−ii
χ172222222-22-2222222222200-2-200-2-2-2-22222-20000000000-2-20000000000002222000000-2-20000000000
χ182222222-22-2222222222200-2-200-2-2-2-22222-20000000000-2-2000000000000-2-2-2-2000000220000000000
χ192222222-2-2-2-2-2-2222222200-22002-2-2-2-2-2-2-2-20000000000220000000000002i2i−2i−2i000000−2i2i0000000000
χ202222222-2-2-2-2-2-2222222200-22002-2-2-2-2-2-2-2-2000000000022000000000000−2i−2i2i2i0000002i−2i0000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-10000-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-1111111111111000022-1-1-1-1000000000000
χ25222222-12-22-2-2-2-1-1-1-1-1-1-1222-2-2-2-2-1-1-11111-12-2-1-1-1-122-2-2111111-1-1-1-1111100002-2-1-111000000000000
χ26222222-12-22-2-2-2-1-1-1-1-1-1-1222-2-2-2-2-1-1-11111-12-2-1-1-1-1-2-2221111111111-1-1-1-10000-2211-1-1000000000000
χ27222222-12-22-2-2-2-1-1-1-1-1-1-1-2-22-222-2-1-1-11111-1-22111122-2-211-1-1-1-1-1-1-1-111110000-2211-1-1000000000000
χ28222222-12-22-2-2-2-1-1-1-1-1-1-1-2-22-222-2-1-1-11111-1-221111-2-22211-1-1-1-11111-1-1-1-100002-2-1-111000000000000
χ292222-2-22222-22-2-2-2-2-222222-2-2-2-222-2-222-2-22-2222-2-200002-222-2-2000000000000000000000000000000
χ302222-2-22222-22-2-2-2-2-2222-2-2-2-22222-2-222-2-222-2-2-22200002-2-2-222000000000000000000000000000000
χ312222-2-222-222-22-2-2-2-222222-2222-22-2-2-2-2222-2-222-2-20000-22-2-222000000000000000000000000000000
χ322222-2-222-222-22-2-2-2-2222-2-2-22-2-2-22-2-2-2-222222-2-2220000-2222-2-2000000000000000000000000000000
χ332222-2-22-22-2-22-2-2-2-2-2222002200-2-22222-2-2-20000000000-220000000000000000000000002i−2i2i−2i000000
χ342222-2-22-22-2-22-2-2-2-2-2222002200-2-22222-2-2-20000000000-22000000000000000000000000−2i2i−2i2i000000
χ352222-2-22-2-2-22-22-2-2-2-2222002-2002-222-2-222-200000000002-20000000000000000000000002-2-22000000
χ362222-2-22-2-2-22-22-2-2-2-2222002-2002-222-2-222-200000000002-2000000000000000000000000-222-2000000
χ372222-2-2-1222-22-21111-1-1-122-2-2-2-22-111-1-111-1-22-1-1110000-11-1-111−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ382222-2-2-1222-22-21111-1-1-122-2-2-2-22-111-1-111-1-22-1-1110000-11-1-111i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ392222-2-2-1222-22-21111-1-1-1-2-2-2-2222-111-1-111-12-211-1-10000-1111-1-1−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ402222-2-2-1222-22-21111-1-1-1-2-2-2-2222-111-1-111-12-211-1-10000-1111-1-1i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ412222-2-2-12-222-221111-1-1-122-2222-2-11111-1-1-1-2-2-1-11100001-111-1-1−i3−i3i3i3i3i3−i3−i3000000−i3i3i3−i3000000000000
χ422222-2-2-12-222-221111-1-1-122-2222-2-11111-1-1-1-2-2-1-11100001-111-1-1i3i3−i3−i3−i3−i3i3i3000000i3−i3−i3i3000000000000
χ432222-2-2-12-222-221111-1-1-1-2-2-22-2-2-2-11111-1-1-12211-1-100001-1-1-111−i3−i3i3i3i3i3−i3−i3000000i3−i3−i3i3000000000000
χ442222-2-2-12-222-221111-1-1-1-2-2-22-2-2-2-11111-1-1-12211-1-100001-1-1-111i3i3−i3−i3−i3−i3i3i3000000−i3i3i3−i3000000000000
χ452-2-222-220202-2-222-2-2-2-2200000000002-22-200000002−22−20000002−22−22−22−22i−2i2i−2i000000000000−i2i2−i2i200
χ462-2-222-220202-2-222-2-2-2-2200000000002-22-200000002−22−20000002−22−22−22−2−2i2i−2i2i000000000000i2−i2i2−i200
χ472-2-222-220202-2-222-2-2-2-2200000000002-22-20000000−22−22000000−22−22−22−222i−2i2i−2i000000000000i2−i2i2−i200
χ482-2-222-220202-2-222-2-2-2-2200000000002-22-20000000−22−22000000−22−22−22−22−2i2i−2i2i000000000000−i2i2−i2i200
χ492-2-222-220-20-22222-2-2-2-220000000000-22-2200000002−2−220000002−22−2−22−222-2-22000000000000−222−200
χ502-2-222-220-20-22222-2-2-2-220000000000-22-2200000002−2−220000002−22−2−22−22-222-20000000000002−2−2200
χ512-2-222-220-20-22222-2-2-2-220000000000-22-220000000−222−2000000−22−222−22−22-2-220000000000002−2−2200
χ522-2-222-220-20-22222-2-2-2-220000000000-22-220000000−222−2000000−22−222−22−2-222-2000000000000−222−200
χ53444444-2-44-4444-2-2-2-2-2-2-200-4-400-4222-2-2-2-220000000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-2-2-2-200-44004222222220000000000-2-20000000000000000000000000000000000
χ554444-4-4-2-44-4-44-42222-2-2-2004400-42-2-2-2-222200000000002-20000000000000000000000000000000000
χ564444-4-4-2-4-4-44-442222-2-2-2004-40042-2-222-2-220000000000-220000000000000000000000000000000000
χ5744-4-400440-400000004-4-44-4000004000000-4004-4000000000000000000000000000000000000000000
χ5844-4-400440-400000004-4-4-44000004000000-400-44000000000000000000000000000000000000000000
χ5944-4-4004-40400000004-4-400004i−4i0-40000004000000000000004i−4i000000000000000000000000000000
χ6044-4-4004-40400000004-4-40000−4i4i0-4000000400000000000000−4i4i000000000000000000000000000000
χ6144-4-400-240-4000−2i32i3−2i32i3-2224-400000-2−2i32i30000200-22−2i32i30000000000000000000000000000000000000000
χ6244-4-400-240-4000−2i32i3−2i32i3-222-4400000-2−2i32i300002002-22i3−2i30000000000000000000000000000000000000000
χ6344-4-400-240-40002i3−2i32i3−2i3-2224-400000-22i3−2i30000200-222i3−2i30000000000000000000000000000000000000000
χ6444-4-400-240-40002i3−2i32i3−2i3-222-4400000-22i3−2i300002002-2−2i32i30000000000000000000000000000000000000000
χ6544-4-400-2-404000−2i32i3−2i32i3-22200004i−4i022i3−2i30000-200000000000023−23−2i2i000000000000000000000000000000
χ6644-4-400-2-404000−2i32i3−2i32i3-2220000−4i4i022i3−2i30000-2000000000000−23232i−2i000000000000000000000000000000
χ6744-4-400-2-4040002i3−2i32i3−2i3-22200004i−4i02−2i32i30000-2000000000000−2323−2i2i000000000000000000000000000000
χ6844-4-400-2-4040002i3−2i32i3−2i3-2220000−4i4i02−2i32i30000-200000000000023−232i−2i000000000000000000000000000000
χ694-4-444-4-20404-4-4-2-22222-20000000000-22-22000000022−2222−22000000−22−22−22−220000000000000000000000
χ704-4-444-4-20404-4-4-2-22222-20000000000-22-220000000−2222−22220000002−22−22−22−20000000000000000000000
χ714-4-444-4-20-40-444-2-22222-200000000002-22-2000000022−22−2222000000−22−222−22−20000000000000000000000
χ724-4-444-4-20-40-444-2-22222-200000000002-22-20000000−222222−220000002−22−2−22−220000000000000000000000
χ734-4-44-444040-4-44-4-444-4-4400000000004-4-4400000000000000000000000000000000000000000000000
χ744-4-44-4440-4044-4-4-444-4-440000000000-444-400000000000000000000000000000000000000000000000
χ754-4-44-44-2040-4-4422-2-222-20000000000-222-200000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ764-4-44-44-2040-4-4422-2-222-20000000000-222-200000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ774-4-44-44-20-4044-422-2-222-200000000002-2-2200000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ784-4-44-44-20-4044-422-2-222-200000000002-2-2200000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ798-88-80080000000000-88-80000000000000000000000000000000000000000000000000000000000000
χ808-88-800-4000000−4i34i34i3−4i34-440000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004i3−4i3−4i34i34-440000000000000000000000000000000000000000000000000000000000000

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