Finite Group Databasebeta

← Group #10698977

Character table — Group #10698977

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121222446666888812121212121224242424242424248888888844121212128888888822
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
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
χ9222222222222-2-2-2-222222222-2-2222-2-2-2-2222-2-222220000-2-2-2-2-2-200000000000000000000000000000000
χ10222222222222-2-2-2-222222222-2-2222-2-2-2-22-2-222-2-2-2-20000-2-2222200000000000000000000000000000000
χ11222222222-2-2-22222-22222222-2-2-2-2-22222-2000000000000-2-20000000000002222-2-2-2-20000000000000000
χ12222222222-2-2-22222-22222222-2-2-2-2-22222-2000000000000-2-2000000000000-2-2-2-222220000000000000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000022000000000000000000000000002i2i−2i−2i000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000002200000000000000000000000000−2i−2i2i2i000000
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-11111111111110000000022-1-1-1-10000000000
χ1922222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2-1-1-1-10000111111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2221111000011-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ23222-2-2-22-2200022-2-2022-2-2-22-20000022-2-2000000000−i2−i2i2i2000000−i2−i2i2i2−i2−i2i2i200002i2i−2i−2i000000000022−2−200
χ24222-2-2-22-2200022-2-2022-2-2-22-20000022-2-2000000000−i2−i2i2i2000000−i2−i2i2i2−i2−i2i2i20000−2i−2i2i2i0000000000−2−22200
χ25222-2-2-22-2200022-2-2022-2-2-22-20000022-2-2000000000i2i2−i2−i2000000i2i2−i2−i2i2i2−i2−i200002i2i−2i−2i0000000000−2−22200
χ26222-2-2-22-2200022-2-2022-2-2-22-20000022-2-2000000000i2i2−i2−i2000000i2i2−i2−i2i2i2−i2−i20000−2i−2i2i2i000000000022−2−200
χ2722-2-22-2-22222-20000-22-2-22-2-220022-20000-2002i−2i00000000002i2i−2i−2i0000000022−2−22−22−2000000−i2i2−i2i2000000
χ2822-2-22-2-22222-20000-22-2-22-2-220022-20000-2002i−2i00000000002i2i−2i−2i00000000−2−222−22−22000000i2−i2i2−i2000000
χ2922-2-22-2-22222-20000-22-2-22-2-220022-20000-200−2i2i0000000000−2i−2i2i2i0000000022−2−22−22−2000000i2−i2i2−i2000000
χ3022-2-22-2-22222-20000-22-2-22-2-220022-20000-200−2i2i0000000000−2i−2i2i2i00000000−2−222−22−22000000−i2i2−i2i2000000
χ3122-2-22-2-222-2-22000022-2-22-2-2200-2-22000022-20022-2-200000000000000000022−2−2−22−220000002−2−22000000
χ3222-2-22-2-222-2-22000022-2-22-2-2200-2-22000022-20022-2-2000000000000000000−2−2222−22−2000000−222−2000000
χ3322-2-22-2-222-2-22000022-2-22-2-2200-2-2200002-2200-2-22200000000000000000022−2−2−22−22000000−222−2000000
χ3422-2-22-2-222-2-22000022-2-22-2-2200-2-2200002-2200-2-222000000000000000000−2−2222−22−20000002−2−22000000
χ352-2-22-2-2222000-22-220-2-22-2-222000002-22-20000000002−22−20000002−22−22−22−22-22-2000000000000002−22−200
χ362-2-22-2-2222000-22-220-2-22-2-222000002-22-20000000002−22−20000002−22−22−22−2-22-2200000000000000−22−2200
χ372-2-22-2-2222000-22-220-2-22-2-222000002-22-2000000000−22−22000000−22−22−22−222-22-200000000000000−22−2200
χ382-2-22-2-2222000-22-220-2-22-2-222000002-22-2000000000−22−22000000−22−22−22−22-22-22000000000000002−22−200
χ392-2-2-2222-222-222-2-22-2-2-2-2222-22-22-22-222-2-20000000000002-2000000000000000000002i−2i2i−2i2i−2i0000000000
χ402-2-2-2222-222-222-2-22-2-2-2-2222-22-22-22-222-2-20000000000002-200000000000000000000−2i2i−2i2i−2i2i0000000000
χ412-2-2-2222-222-22-222-2-2-2-2-2222-2-222-222-2-22-2000000002i−2i−2i2i-2200002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ422-2-2-2222-222-22-222-2-2-2-2-2222-2-222-222-2-22-200000000−2i2i2i−2i-220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ432-2-2-2222-22-22-22-2-222-2-2-2222-2-22-22-2-222-22000000000000-2200000000000000000000000000000000002-2
χ442-2-2-2222-22-22-22-2-222-2-2-2222-2-22-22-2-222-22000000000000-220000000000000000000000000000000000-22
χ452-2-2-2222-22-22-2-222-22-2-2-2222-22-2-22-22-2-2220000000000002-20000000000000000000000000000002-2-2200
χ462-2-2-2222-22-22-2-222-22-2-2-2222-22-2-22-22-2-2220000000000002-2000000000000000000000000000000-222-200
χ472-2-2-2222-2-12-222-2-22-2111-1-1-112-2-11-11-1-1110000−i3i3−i3i30000-11−i3i3−i3i33−3−33−333−3000000002i−2i−ii−ii0000000000
χ482-2-2-2222-2-12-222-2-22-2111-1-1-112-2-11-11-1-1110000−i3i3−i3i30000-11−i3i3−i3i3−333−33−3−3300000000−2i2ii−ii−i0000000000
χ492-2-2-2222-2-12-222-2-22-2111-1-1-112-2-11-11-1-1110000i3−i3i3−i30000-11i3−i3i3−i33−3−33−333−300000000−2i2ii−ii−i0000000000
χ502-2-2-2222-2-12-222-2-22-2111-1-1-112-2-11-11-1-1110000i3−i3i3−i30000-11i3−i3i3−i3−333−33−3−33000000002i−2i−ii−ii0000000000
χ512-2-2-2222-2-12-22-222-2-2111-1-1-11-22-11-1-111-110000−i3i3−i3i32i−2i−2i2i1-1i3−i3i3−i3−iii−i−iii−i00000000003−3−330000000000
χ522-2-2-2222-2-12-22-222-2-2111-1-1-11-22-11-1-111-110000−i3i3−i3i3−2i2i2i−2i1-1i3−i3i3−i3i−i−iii−i−ii0000000000−333−30000000000
χ532-2-2-2222-2-12-22-222-2-2111-1-1-11-22-11-1-111-110000i3−i3i3−i32i−2i−2i2i1-1−i3i3−i3i3−iii−i−iii−i0000000000−333−30000000000
χ542-2-2-2222-2-12-22-222-2-2111-1-1-11-22-11-1-111-110000i3−i3i3−i3−2i2i2i−2i1-1−i3i3−i3i3i−i−iii−i−ii00000000003−3−330000000000
χ5544444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000022000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000
χ57444-4-4-44-44000-4-444044-4-4-44-400000-4-444000000000000000000000000000000000000000000000000000
χ58444-4-4-44-4-200044-4-40-2-2222-2200000-2-222000000000−2i2−2i22i22i2000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ59444-4-4-44-4-200044-4-40-2-2222-2200000-2-2220000000002i22i2−2i2−2i2000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ60444-4-4-44-4-2000-4-4440-2-2222-220000022-2-2000000000000000000066−6−6−6−666000000000000000000000000
χ61444-4-4-44-4-2000-4-4440-2-2222-220000022-2-20000000000000000000−6−66666−6−6000000000000000000000000
χ6244-44-44-4-44000000004-44-44-4-40000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ6344-44-44-4-44000000004-44-44-4-400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ6444-4-44-4-44-244-40000-4-222-222-200-2-2200002004i−4i0000000000−2i−2i2i2i00000000000000000000000000000000
χ6544-4-44-4-44-244-40000-4-222-222-200-2-220000200−4i4i00000000002i2i−2i−2i00000000000000000000000000000000
χ6644-4-44-4-44-2-4-4400004-222-222-20022-20000-24-400-2-222000000000000000000000000000000000000000000
χ6744-4-44-4-44-2-4-4400004-222-222-20022-20000-2-440022-2-2000000000000000000000000000000000000000000
χ684-4444-4-4-444-4-400004-4444-4-4-4004-4-40000400000000000000000000000000000000000000000000000000
χ694-4444-4-4-44-4440000-4-4444-4-4-400-4440000-400000000000000000000000000000000000000000000000000
χ704-4444-4-4-4-24-4-4000042-2-2-222200-2220000-20000000000000023−23−232300000000000000000000000000000000
χ714-4444-4-4-4-24-4-4000042-2-2-222200-2220000-200000000000000−232323−2300000000000000000000000000000000
χ724-4444-4-4-4-2-4440000-42-2-2-2222002-2-2000020000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ734-4444-4-4-4-2-4440000-42-2-2-2222002-2-20000200002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ744-44-4-44-44400000000-44-4-44-4400000000000000000000000000000000000022−22−222200000000000000000000
χ754-44-4-44-44400000000-44-4-44-44000000000000000000000000000000000000−222222−2200000000000000000000
χ764-4-44-4-44440004-44-40-4-44-4-44400000-44-44000000000000000000000000000000000000000000000000000
χ774-4-44-4-444-20004-44-4022-222-2-2000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ784-4-44-4-444-20004-44-4022-222-2-2000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ794-4-44-4-444-2000-44-44022-222-2-200000-22-2200000000022−2222−22000000−22−22−22−22000000000000000000000000
χ804-4-44-4-444-2000-44-44022-222-2-200000-22-22000000000−2222−22220000002−22−22−22−2000000000000000000000000
χ814-4-4-4444-4-2-44-44-4-444222-2-2-22-442-222-2-22-20000000000002-2000000000000000000000000000000000000
χ824-4-4-4444-4-2-44-4-444-44222-2-2-224-42-22-222-2-2000000000000-22000000000000000000000000000000000000
χ8388-88-88-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-88-8-88-88-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000

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