Finite Group Databasebeta

← Group #10693849

Character table — Group #10693849

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11i−ii−i11-1-11-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1i−iii−i−iii−i−i11-1-1i−i
χ101-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11i−ii−i11-1-11-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-11111i−iii−i−i−i−iii-1-111−ii
χ111-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11i−ii−i-1-1111-1ii−i−iii−i−i-1-1-1-111111111-1-1-1-1−ii−i−iiiii−i−i-1-111−ii
χ121-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11i−ii−i-1-1111-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−ii−i−iii−i−iii11-1-1i−i
χ131-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11−ii−ii11-1-11-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−ii−i−iii−i−iii11-1-1−ii
χ141-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11−ii−ii11-1-11-1−i−iii−i−iii1111-1-1-1-1-1-1-1-11111−ii−i−iiiii−i−i-1-111i−i
χ151-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11−ii−ii-1-1111-1−i−iii−i−iii-1-1-1-111111111-1-1-1-1i−iii−i−i−i−iii-1-111i−i
χ161-1-1111-1-111-1-1-111-11-1-1111-1-11-1111-1-1-1-11−ii−ii-1-1111-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111i−iii−i−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-222222222-2-22-2-222-2-2222-2-20000-2-2-2-2-2-2222200000000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-22-2-222-2-22-2-2220000-2-22222-2-2-2-200000000000000000000000000000000
χ19222222222-2-2-22222-22222222-2-2-222-2-222-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ20222222222-2-2-22222-22222222-2-2-222-2-222-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000002i−2i2i−2i000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000−2i2i−2i2i000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2722222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-111-1-111-122-2-20000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-111-1-111-122-2-20000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-111-1-111-1-2-222000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-111-1-111-1-2-222000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2200022-2-20222-2-2-2-20002-2002-2000002−22−200000000002−22−22−22−2002-2002-200000000002−22−200
χ322222-2-2-2-2200022-2-20222-2-2-2-20002-2002-2000002−22−200000000002−22−22−22−200-2200-220000000000−22−2200
χ332222-2-2-2-2200022-2-20222-2-2-2-20002-2002-200000−22−220000000000−22−22−22−22002-2002-20000000000−22−2200
χ342222-2-2-2-2200022-2-20222-2-2-2-20002-2002-200000−22−220000000000−22−22−22−2200-2200-2200000000002−22−200
χ352-2-2222-2-222-2-22-2-222-2-2222-2-2-222-2-2-2-22222i−2i−2i2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ362-2-2222-2-222-2-22-2-222-2-2222-2-2-222-2-2-2-2222−2i2i2i−2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ372-2-2222-2-22-2222-2-22-2-2-2222-2-22-2-2-2-22222-2000000002-20000000000000000000000000000002-2-22000000
χ382-2-2222-2-22-2222-2-22-2-2-2222-2-22-2-2-2-22222-2000000002-2000000000000000000000000000000-222-2000000
χ392-2-2222-2-22-222-222-2-2-2-2222-2-2-22-22222-2-2-200000000-22000000000000000022-2-2-2-2220000000000000000
χ402-2-2222-2-22-222-222-2-2-2-2222-2-2-22-22222-2-2-200000000-220000000000000000-2-22222-2-20000000000000000
χ412-2-2222-2-2-12-2-22-2-22211-1-1-111-22-11111-1-1-12i−2i−2i2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ422-2-2222-2-2-12-2-22-2-22211-1-1-111-22-11111-1-1-12i−2i−2i2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ432-2-2222-2-2-12-2-22-2-22211-1-1-111-22-11111-1-1-1−2i2i2i−2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ442-2-2222-2-2-12-2-22-2-22211-1-1-111-22-11111-1-1-1−2i2i2i−2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ452-2-2222-2-2-12-2-2-222-2211-1-1-1112-2-1-1-11111-12i−2i2i−2i22-2-2-11−i−iii−i−iii-1-1-1-11111000000002i−2i−i−iii0000000000
χ462-2-2222-2-2-12-2-2-222-2211-1-1-1112-2-1-1-11111-12i−2i2i−2i-2-222-11−i−iii−i−iii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ472-2-2222-2-2-12-2-2-222-2211-1-1-1112-2-1-1-11111-1−2i2i−2i2i22-2-2-11ii−i−iii−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ482-2-2222-2-2-12-2-2-222-2211-1-1-1112-2-1-1-11111-1−2i2i−2i2i-2-222-11ii−i−iii−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ492-2-22-2-2222000-22-220-2-22-2-2220002-200-22000002−2−2200000000002−22−2−22−22002-200-2200000000002−2−2200
χ502-2-22-2-2222000-22-220-2-22-2-2220002-200-22000002−2−2200000000002−22−2−22−2200-22002-20000000000−222−200
χ512-2-22-2-2222000-22-220-2-22-2-2220002-200-2200000−222−20000000000−22−222−22−2002-200-220000000000−222−200
χ522-2-22-2-2222000-22-220-2-22-2-2220002-200-2200000−222−20000000000−22−222−22−200-22002-200000000002−2−2200
χ5344444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-42-2-222-2-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-44000-4-4440444-4-4-4-4000-4400-44000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-200044-4-40-2-2-22222000-2200-220000022−2222−220000000000−22−22−22−22000000000000000000000000
χ574444-4-4-4-4-200044-4-40-2-2-22222000-2200-2200000−2222−222200000000002−22−22−22−2000000000000000000000000
χ584444-4-4-4-4-2000-4-4440-2-2-222220002-2002-20000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ594444-4-4-4-4-2000-4-4440-2-2-222220002-2002-20000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ6044-4-44-44-44000000004-4-44-4-44000000000000000000000000000000000000−2i22i200−2i22i2000000000000000000
χ6144-4-44-44-44000000004-4-44-4-440000000000000000000000000000000000002i2−2i2002i2−2i2000000000000000000
χ6244-4-4-44-44444-40000-44-4-4-444-4004004-400-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4-44000044-4-4-444-400-400-4400400000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-244-40000-4-2222-2-2200-200-220020000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ6544-4-4-44-44-244-40000-4-2222-2-2200-200-2200200000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ6644-4-4-44-44-2-4-4400004-2222-2-22002002-200-20000000000000023−2323−2300000000000000000000000000000000
χ6744-4-4-44-44-2-4-4400004-2222-2-22002002-200-200000000000000−2323−232300000000000000000000000000000000
χ684-44-44-4-44400000000-44-44-44-4000000000000000000000000000000000000−2i22i2002i2−2i2000000000000000000
χ694-44-44-4-44400000000-44-44-44-40000000000000000000000000000000000002i2−2i200−2i22i2000000000000000000
χ704-44-4-444-444-440000-4-44-4-44-4400400-4400-400000000000000000000000000000000000000000000000000
χ714-44-4-444-44-44-400004-44-4-44-4400-4004-400400000000000000000000000000000000000000000000000000
χ724-44-4-444-4-24-440000-42-222-22-200-2002-2002000000000023−23−2323000000000000000000000000000000000000
χ734-44-4-444-4-24-440000-42-222-22-200-2002-20020000000000−232323−23000000000000000000000000000000000000
χ744-44-4-444-4-2-44-4000042-222-22-200200-2200-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ754-44-4-444-4-2-44-4000042-222-22-200200-2200-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ764-4-4444-4-4-2-4444-4-44-422-2-2-2224-4222-2-2-2-2200000000-220000000000000000000000000000000000000000
χ774-4-4444-4-4-2-444-444-4-422-2-2-222-442-2-2-2-2222000000002-20000000000000000000000000000000000000000
χ784-4-44-4-44440004-44-40-4-44-4-444000-44004-4000000000000000000000000000000000000000000000000000
χ794-4-44-4-444-20004-44-4022-222-2-20002-200-220000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-44-4-444-20004-44-4022-222-2-20002-200-220000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-44-4-444-2000-44-44022-222-2-2000-22002-20000022−22−22220000000000−22−222−22−2000000000000000000000000
χ824-4-44-4-444-2000-44-44022-222-2-2000-22002-200000−222222−2200000000002−22−2−22−22000000000000000000000000
χ8388-8-88-88-8-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-88-88-8-88-4000000004-44-44-44000000000000000000000000000000000000000000000000000000000000

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