Finite Group Databasebeta

← Group #10782813

Character table — Group #10782813

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444444668888888888888888121212121216161616161616242424242424243232484848
order1222344446664888888121212122424242422448881212121212242424242424444884482424242424888881212248
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1111-1-111-1-1-1-1-1
χ3111111111111111111111111111-1-11111111111111111-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ5111111111111111-1-1-1-11111111111-1-1111-1-11-1-111-1-1-1-111111-1-111111-1-1111-1-1-1-1-1-11
χ6111111111111111-1-1-1-11111111111-1-1-1-11-1-11-1-111-1-1-1-11111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ7111111111111111-1-1-1-111111111-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-111-1
χ8111111111111111-1-1-1-111111111-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1111111-1-11
χ91111111111111-1-111111111-1-1-1-111-1-111-1-1-11-1-1-1-11111111-1-11-1-111-1-1-1-1-111111-1-11-1
χ101111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-11111111-1-1-111-1-111-1-1-1-1-111-111-11
χ111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11111-1-1-1111-1-111-1-1111-1-1-1-11-11-11
χ121111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-111-111-1-11111111-1-1-11-11-1
χ131111111111111-1-1-1-1-1-11111-1-1-1-1111111-111111-1-1-1-1-1-1111-1-1-11-111-1-111-111-1-1-111-1-1
χ141111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-1-1-1-1-1111-1-11-11-1-11111-1-1-1-1-11-1-111
χ151111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-1-111-11-111-1-1-1-11-1-111-11-111
χ161111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1111-11-1-111-1-1111111-11-1-1
χ17222222-2-22222-2220000-222-22222220000-200-200-2-20000-22-222000000000-2000000000
χ18222222-2-22222-2220000-222-22222-2-20000-200-200-2-200002-22-2-20000000002000000000
χ19222222-2-22222-2-2-20000-222-2-2-2-2-2220000200-200220000-22-2-2-20000000002000000000
χ20222222-2-22222-2-2-20000-222-2-2-2-2-2-2-20000200-2002200002-2222000000000-2000000000
χ2122222-222-2222-20000002-2-220000222-200022-2-2-20000002-2-2000000000-220000000000
χ2222222-222-2222-20000002-2-22000022-22000-2-2-2220000002-2-20000000002-20000000000
χ2322222-222-2222-20000002-2-220000-2-22-200022-2-2-2000000-2220000000002-20000000000
χ2422222-222-2222-20000002-2-220000-2-2-22000-2-2-222000000-222000000000-220000000000
χ2522222-2-2-2-22222002i2i−2i−2i-2-2-2-20000220000000200002i2i−2i−2i-2-22000000000000002i−2i00000
χ2622222-2-2-2-22222002i2i−2i−2i-2-2-2-20000-2-20000000200002i2i−2i−2i22-200000000000000−2i2i00000
χ2722222-2-2-2-2222200−2i−2i2i2i-2-2-2-2000022000000020000−2i−2i2i2i-2-2200000000000000−2i2i00000
χ2822222-2-2-2-2222200−2i−2i2i2i-2-2-2-20000-2-2000000020000−2i−2i2i2i22-2000000000000002i−2i00000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-10022222-1-1-1-1-1-1-1-1-1-1-100000222-1-1-1-10000000-1-1000
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10022-2-22-1-1-1-1-1-1-1-1-1-1-100000-2-2-21111000000011000
χ312222-12222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-100-2-222211-111-1-1111100000-2-22-1-1-1-1000000011000
χ322222-12222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-100-2-2-2-2211-111-1-111110000022-211110000000-1-1000
χ332222-12222-1-1-12-2-22222-1-1-1-1111100-2-222-211-11111-1-1-1-1000002-2-2-1-1110000000-11000
χ342222-12222-1-1-12-2-22222-1-1-1-1111100-2-2-2-2-211-11111-1-1-1-100000-22211-1-100000001-1000
χ352222-12222-1-1-12-2-2-2-2-2-2-1-1-1-11111002222-2-1-1-1-1-111111100000-22-2-1-11100000001-1000
χ362222-12222-1-1-12-2-2-2-2-2-2-1-1-1-111110022-2-2-2-1-1-1-1-1111111000002-2211-1-10000000-11000
χ374444-24-4-44-2-2-2-44400002-2-22-2-2-2-2000000-400200220000000000000000000000000000
χ384444-24-4-44-2-2-2-4-4-400002-2-222222000000400200-2-20000000000000000000000000000
χ394444-2-444-4-2-2-2-4000000-222-20000004-4000-2-2222000000000000000000000000000000
χ404444-2-444-4-2-2-2-4000000-222-2000000-44000222-2-2000000000000000000000000000000
χ414444-2-4-4-4-4-2-2-24004i4i−4i−4i22220000000000000-20000−2i−2i2i2i000000000000000000000000
χ424444-2-4-4-4-4-2-2-2400−4i−4i4i4i22220000000000000-200002i2i−2i−2i000000000000000000000000
χ4344-4-4404-40-44-400022−2222−22400-400000000000000000022−2222−22000000000000000000000000
χ4444-4-4404-40-44-4000−2222−2222400-4000000000000000000−2222−2222000000000000000000000000
χ4544-4-440-440-44-4000−2i22i22i2−2i2-4004000000000000000000−2i22i22i2−2i2000000000000000000000000
χ4644-4-440-440-44-40002i2−2i2−2i22i2-40040000000000000000002i2−2i2−2i22i2000000000000000000000000
χ4744-4-4-204-402-2200022−2222−22-2002i6i6−i6−i60000000−2i32i3000i6−i6−22−22000000000000000000000000
χ4844-4-4-204-402-2200022−2222−22-2002−i6−i6i6i600000002i3−2i3000−i6i6−22−22000000000000000000000000
χ4944-4-4-204-402-22000−2222−2222-2002i6i6−i6−i600000002i3−2i3000i6−i62−22−2000000000000000000000000
χ5044-4-4-204-402-22000−2222−2222-2002−i6−i6i6i60000000−2i32i3000−i6i62−22−2000000000000000000000000
χ5144-4-4-20-4402-22000−2i22i22i2−2i2200-2i6i6−i6−i6000000000023−23−i6i6i2−i2−i2i2000000000000000000000000
χ5244-4-4-20-4402-22000−2i22i22i2−2i2200-2−i6−i6i6i60000000000−2323i6−i6i2−i2−i2i2000000000000000000000000
χ5344-4-4-20-4402-220002i2−2i2−2i22i2200-2i6i6−i6−i60000000000−2323−i6i6−i2i2i2−i2000000000000000000000000
χ5444-4-4-20-4402-220002i2−2i2−2i22i2200-2−i6−i6i6i6000000000023−23i6−i6−i2i2i2−i2000000000000000000000000
χ554-44-44400-44-4-4000000004-400000000022−220000000000000000000022−2200000000000000
χ564-44-44400-44-4-4000000004-4000000000−222200000000000000000000−222200000000000000
χ574-44-44-40044-4-400000000-4400000000000000000000000000000000000000−2i22i20000000
χ584-44-44-40044-4-400000000-44000000000000000000000000000000000000002i2−2i20000000
χ594-44-4-2400-4-22200000000-220−2i32i3−2i32i3000022−2200000000000000000000−22i6−i6000000000000
χ604-44-4-2400-4-22200000000-220−2i32i3−2i32i30000−2222000000000000000000002−2−i6i6000000000000
χ614-44-4-2400-4-22200000000-2202i3−2i32i3−2i3000022−2200000000000000000000−22−i6i6000000000000
χ624-44-4-2400-4-22200000000-2202i3−2i32i3−2i30000−2222000000000000000000002−2i6−i6000000000000
χ634-4-4440000-4-44022−220000000022−22−22224-4000000000000000000022−220000000000000000000
χ644-4-4440000-4-44022−220000000022−22−2222-440000000000000000000−22220000000000000000000
χ654-4-4440000-4-440−222200000000−222222−224-40000000000000000000−22220000000000000000000
χ664-4-4440000-4-440−222200000000−222222−22-44000000000000000000022−220000000000000000000
χ678-88-8-4-8008-444000000004-400000000000000000000000000000000000000000000000
χ688-8-88-4000044-4042−4200000000−222222−22000000000000000000000000000000000000000000
χ698-8-88-4000044-40−42420000000022−22−2222000000000000000000000000000000000000000000

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