Finite Group Databasebeta

← Group #10830952

Character table — Group #10830952

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222222234444666666644666612121212444488881212121212121212121224242424242424248888888844121212122444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-11-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
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
χ911111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-1-111-1-111-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-111-1-111-1-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-11111-1-1-1-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-1111-1-1-1-11111-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-1111-1-1-1-1111-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-11111-1-1-11-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1-111-1-111-11-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-11-1-111-1-11-11
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-200000000000000000000000000000022-20000-200
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-200000000-2-2000000000000000000000000000000-2-220000200
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000002-220000-200
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000-22-20000200
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-222-2-211-1-1-1-11111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-2-22211-1-1-1-111111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-222-2-222111111-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-2-2-22-22000022-2-222-2-2-22-220000002-22-2002-2000000000022-2-200000000000022-2-20000000002-200000
χ3022-2-2-22-22000022-2-222-2-2-22-220000002-22-2002-2000000000022-2-2000000000000-2-222000000000-2200000
χ3122-2-2-22-22000022-2-222-2-2-22-220000002-22-200-220000000000-2-22200000000000022-2-2000000000-2200000
χ3222-2-2-22-22000022-2-222-2-2-22-220000002-22-200-220000000000-2-222000000000000-2-2220000000002-200000
χ332-22-2-2-22200002-22-22-22-2-2-222000000-222-22-20000000022-2-200000000000000002-22-2000000000002-2000
χ342-22-2-2-22200002-22-22-22-2-2-222000000-222-22-20000000022-2-20000000000000000-22-2200000000000-22000
χ352-22-2-2-22200002-22-22-22-2-2-222000000-222-2-2200000000-2-22200000000000000002-22-200000000000-22000
χ362-22-2-2-22200002-22-22-22-2-2-222000000-222-2-2200000000-2-2220000000000000000-22-22000000000002-2000
χ372-2-222-2-2222-2-2222-2-2-2-222-2-222-222-2-222-2-200002i−2i2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-222-2-2222-2-2222-2-2-2-222-2-222-222-2-222-2-20000−2i2i−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-222-2-2222-2-22-2-222-2-222-2-22-2222-2-2-2-22200000000-22000000000000000022-2-22-2-220000000000000000
χ402-2-222-2-2222-2-22-2-222-2-222-2-22-2222-2-2-2-22200000000-220000000000000000-2-222-222-20000000000000000
χ412-2-222-2-2222-2-2-122-2-211-1-111-12-2-1-111-1-11100002i−2i2i−2i-11−i3i3−i3i3−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ422-2-222-2-2222-2-2-122-2-211-1-111-12-2-1-111-1-11100002i−2i2i−2i-11i3−i3i3−i3i3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ432-2-222-2-2222-2-2-122-2-211-1-111-12-2-1-111-1-1110000−2i2i−2i2i-11−i3i3−i3i3−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ442-2-222-2-2222-2-2-122-2-211-1-111-12-2-1-111-1-1110000−2i2i−2i2i-11i3−i3i3−i3i3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ452-2-222-2-22-2-222222-2-2-2-222-2-22-22-2-22222-2-200002i−2i−2i2i-22000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ462-2-222-2-22-2-222222-2-2-2-222-2-22-22-2-22222-2-20000−2i2i2i−2i-2200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ472-2-222-2-22-2-2222-2-222-2-222-2-222-2-2-222-2-222000000002-2000000000000000022-2-2-222-20000000000000000
χ482-2-222-2-22-2-2222-2-222-2-222-2-222-2-2-222-2-222000000002-20000000000000000-2-2222-2-220000000000000000
χ492-2-222-2-22-2-222-122-2-211-1-111-1-2211-1-1-1-11100002i−2i−2i2i1-1−i3i3−i3i3i3−i3i3−i3−i−iiiii−i−i00000000003−3−330000000000
χ502-2-222-2-22-2-222-122-2-211-1-111-1-2211-1-1-1-11100002i−2i−2i2i1-1i3−i3i3−i3−i3i3−i3i3−i−iiiii−i−i0000000000−333−30000000000
χ512-2-222-2-22-2-222-122-2-211-1-111-1-2211-1-1-1-1110000−2i2i2i−2i1-1−i3i3−i3i3i3−i3i3−i3ii−i−i−i−iii0000000000−333−30000000000
χ522-2-222-2-22-2-222-122-2-211-1-111-1-2211-1-1-1-1110000−2i2i2i−2i1-1i3−i3i3−i3−i3i3−i3i3ii−i−i−i−iii00000000003−3−330000000000
χ53444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000220000000000000000000000000000000000000000
χ5444444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-44-44-440000-4-44-444-4004-44-4000000000000000000000000000000000000000000000000000000
χ564444-4-4-4-44-44-4-2000022-22-2-2200-22-2200000000000000000000006−66−66−66−6000000000000000000000000
χ574444-4-4-4-44-44-4-2000022-22-2-2200-22-220000000000000000000000−66−66−66−66000000000000000000000000
χ584444-4-4-4-4-44-4440000-4-44-444-400-44-44000000000000000000000000000000000000000000000000000000
χ594444-4-4-4-4-44-44-2000022-22-2-22002-22-200000000000000000000006−66−6−66−66000000000000000000000000
χ604444-4-4-4-4-44-44-2000022-22-2-22002-22-20000000000000000000000−66−666−66−6000000000000000000000000
χ6144-4-44-44-4000040000-44-444-4-400000000000000000000000000000000000022−2222−2200000000000000000000
χ6244-4-44-44-4000040000-44-444-4-4000000000000000000000000000000000000−2222−222200000000000000000000
χ6344-4-4-44-4400004-444-44-4-4-44-44000000-44-4400000000000000000000000000000000000000000000000000
χ6444-4-4-44-440000-24-4-44-2222-22-2000000-22-22004-40000000000-2-22200000000000000000000000000000000
χ6544-4-4-44-440000-24-4-44-2222-22-2000000-22-2200-44000000000022-2-200000000000000000000000000000000
χ6644-4-4-44-440000-2-444-4-2222-22-20000002-22-20000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ6744-4-4-44-440000-2-444-4-2222-22-20000002-22-200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ684-44-444-4-40000400004-4-44-44-400000000000000000000000000000000000022−22−222200000000000000000000
χ694-44-444-4-40000400004-4-44-44-4000000000000000000000000000000000000−222222−2200000000000000000000
χ704-44-4-4-444000044-44-4-44-4-4-4440000004-4-4400000000000000000000000000000000000000000000000000
χ714-44-4-4-4440000-24-44-42-2222-2-2000000-222-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ724-44-4-4-4440000-24-44-42-2222-2-2000000-222-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ734-44-4-4-4440000-2-44-442-2222-2-20000002-2-224-400000000-2-222000000000000000000000000000000000000
χ744-44-4-4-4440000-2-44-442-2222-2-20000002-2-22-440000000022-2-2000000000000000000000000000000000000
χ754-4-444-4-4444-4-4-2-4-44422-2-222-2-44-2-22222-2-2000000002-20000000000000000000000000000000000000000
χ764-4-444-4-44-4-444-2-4-44422-2-222-24-422-2-222-2-200000000-220000000000000000000000000000000000000000
χ774-4-44-444-44-4-4440000444-4-4-4-4004-4-44000000000000000000000000000000000000000000000000000000
χ784-4-44-444-44-4-44-20000-2-2-2222200-222-20000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ794-4-44-444-44-4-44-20000-2-2-2222200-222-20000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ804-4-44-444-4-444-440000444-4-4-4-400-444-4000000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-444-4-20000-2-2-22222002-2-220000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ824-4-44-444-4-444-4-20000-2-2-22222002-2-220000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ8388-8-88-88-80000-400004-44-4-444000000000000000000000000000000000000000000000000000000000000
χ848-88-888-8-80000-40000-444-44-44000000000000000000000000000000000000000000000000000000000000

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