Finite Group Databasebeta

← Group #10778181

Character table — Group #10778181

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444444466668888888888888888881212121216161616161624242424242424242432324848
order12223444466622444881212121224242424444466888888812121224242424242424884424242424448888888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ511111111111111111-1-11111-1-1-1-1111111-1-1-111-1-1111-1-1-1-1-1-111-1-11-111-1-111-1-1-1-1-1111-11-1
χ611111111111111111-1-11111-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-11-1-11111-111-1-1-1-1-11-11
χ711111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-1-1-1-1-1111-111-1-1-1-111111-1-11-1-11
χ811111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-111-11-1-111-1-11-1-11111-111-1
χ9111111111111-1-11-1-111111111111111-1-1-1-1111111-1-111-1-1-1-11111-1-11111-1-1111-1-111-1-1-1-1
χ10111111111111-1-11-1-111111111111111-1-1-1-11-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111
χ11111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111
χ12111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1
χ13111111111111-1-11-1-1-1-11111-1-1-1-11111-1-111-111-1-11-1-1-1-1111111-1-1-1111-1-1-1-1-1-1-11111-11-11
χ14111111111111-1-11-1-1-1-11111-1-1-1-11111-1-111-1-1-1111-1-1-1-1111111-1-11-1-1-111-1-1-11111-1-11-11-1
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-11-1-1-1-11111-1-111-1111-1-111111-1-1-1-1-111-1
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-1111-1-1-111111-1-1-1-1111-1-11
χ17222222-22-222200-20022-222-2222222220000-20000-200-2-20000-2-22200000000-20000000000
χ18222222-22-222200-20022-222-22222-2-2-2-20000-20000-200-2-2000022-2-20000000020000000000
χ19222222-22-222200-200-2-2-222-2-2-2-2-22222000020000-200220000-2-2-2-20000000020000000000
χ20222222-22-222200-200-2-2-222-2-2-2-2-2-2-2-2-2000020000-200220000222200000000-20000000000
χ2122222-22-2222222-2-2-2002-2-22000022-2-2220000000-2-2-2000000-22000000002-200000000000
χ2222222-22-2222222-2-2-2002-2-220000-2-222220000000-2-2-20000002-200000000-2200000000000
χ2322222-22-22222-2-2-222002-2-22000022-2-2-2-20000000-222000000-2200000000-2200000000000
χ2422222-22-22222-2-2-222002-2-220000-2-222-2-20000000-2220000002-2000000002-200000000000
χ2522222-2-2-2-22220020000-2-2-2-2000022-2-2002i−2i00000200002i2i−2i−2i2-200000000000002i−2i000000
χ2622222-2-2-2-22220020000-2-2-2-2000022-2-200−2i2i0000020000−2i−2i2i2i2-20000000000000−2i2i000000
χ2722222-2-2-2-22220020000-2-2-2-20000-2-222002i−2i00000200002i2i−2i−2i-220000000000000−2i2i000000
χ2822222-2-2-2-22220020000-2-2-2-20000-2-22200−2i2i0000020000−2i−2i2i2i-2200000000000002i−2i000000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-10000-1-12222222-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000-1-100
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10000-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-10000-2-211110000000001100
χ312222-12222-1-1-122222-2-2-1-1-1-111110000-1-1-2-2-222-2-2-1-1-111111100002-2-1-111000000000-1100
χ322222-12222-1-1-122222-2-2-1-1-1-111110000-1-1-2-2-2-2-222-1-1-11111110000-2211-1-10000000001-100
χ332222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-1000011-2-222222-111-1-111110000-2-2-1-1-1-10000000001100
χ342222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-1000011-2-22-2-2-2-2-111-1-111110000221111000000000-1-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1111100001122-222-2-2-11111-1-1-1-10000-22-1-1110000000001-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-1111100001122-2-2-222-11111-1-1-1-100002-211-1-1000000000-1100
χ372-22-22-2020-2-22000002i−2i02-202i2i−2i−2i2i−2i2i−2i00000−i2i22−2000000000002-200−i2i22−2000−i2i2002−20000
χ382-22-22-2020-2-22000002i−2i02-202i2i−2i−2i2i−2i2i−2i00000i2−i2−22000000000002-200i2−i2−22000i2−i200−220000
χ392-22-22-2020-2-22000002i−2i02-202i2i−2i−2i−2i2i−2i2i00000−i2i22−200000000000-2200−i2i22−2000i2−i200−220000
χ402-22-22-2020-2-22000002i−2i02-202i2i−2i−2i−2i2i−2i2i00000i2−i2−2200000000000-2200i2−i2−22000−i2i2002−20000
χ412-22-22-2020-2-2200000−2i2i02-20−2i−2i2i2i2i−2i2i−2i00000−i2i2−2200000000000-2200−i2i2−22000i2−i2002−20000
χ422-22-22-2020-2-2200000−2i2i02-20−2i−2i2i2i2i−2i2i−2i00000i2−i22−200000000000-2200i2−i22−2000−i2i200−220000
χ432-22-22-2020-2-2200000−2i2i02-20−2i−2i2i2i−2i2i−2i2i00000−i2i2−22000000000002-200−i2i2−22000−i2i200−220000
χ442-22-22-2020-2-2200000−2i2i02-20−2i−2i2i2i−2i2i−2i2i00000i2−i22−2000000000002-200i2−i22−2000i2−i2002−20000
χ454444-24-44-4-2-2-200-400442-2-22-2-2-2-200000000-4000020022000000000000000000000000000
χ464444-24-44-4-2-2-200-400-4-42-2-2222220000000040000200-2-2000000000000000000000000000
χ474444-2-44-44-2-2-244-4-4-400-222-200000000-2-2000000022200000000000000000000000000000
χ484444-2-44-44-2-2-2-4-4-44400-222-2000000002200000002-2-200000000000000000000000000000
χ494444-2-4-4-4-4-2-2-20040000222200000000004i−4i00000-20000−2i−2i2i2i00000000000000000000000
χ504444-2-4-4-4-4-2-2-2004000022220000000000−4i4i00000-200002i2i−2i−2i00000000000000000000000
χ514-44-4440-40-4-4400000000-44000004i−4i−4i4i00000000000000000000000000000000000000000
χ524-44-4440-40-4-4400000000-4400000−4i4i4i−4i00000000000000000000000000000000000000000
χ534-44-4-2-404022-2000004i−4i0-220−2i−2i2i2i000000000−2i22i222−22000000000000000i2−i2−220000000000000
χ544-44-4-2-404022-2000004i−4i0-220−2i−2i2i2i0000000002i2−2i2−2222000000000000000−i2i22−20000000000000
χ554-44-4-2-404022-200000−4i4i0-2202i2i−2i−2i000000000−2i22i2−2222000000000000000i2−i22−20000000000000
χ564-44-4-2-404022-200000−4i4i0-2202i2i−2i−2i0000000002i2−2i222−22000000000000000−i2i2−220000000000000
χ574-4-444040-44-4-44-400000400-4000000004-4000000000000000000000000000000000000000
χ584-4-444040-44-4-4-4400000400-400000000-44000000000000000000000000000000000000000
χ594-4-4440-4044-4-40004i−4i00-40040000000000000000004i−4i00000000000000000000000000000
χ604-4-4440-4044-4-4000−4i4i00-4004000000000000000000−4i4i00000000000000000000000000000
χ614-4-44-2040-4-2224-400000-2002i6−i6i6−i60000-220000000000i6−i6i6−i6i6−i600000000000000000000000
χ624-4-44-2040-4-2224-400000-2002−i6i6−i6i60000-220000000000−i6i6−i6i6−i6i600000000000000000000000
χ634-4-44-2040-4-222-4400000-2002i6−i6i6−i600002-20000000000i6−i6−i6i6−i6i600000000000000000000000
χ644-4-44-2040-4-222-4400000-2002−i6i6−i6i600002-20000000000−i6i6i6−i6i6−i600000000000000000000000
χ654-4-44-20-404-2220004i−4i00200-2i6−i6i6−i600000000000000−2i2i−i6i66−6−6600000000000000000000000
χ664-4-44-20-404-2220004i−4i00200-2−i6i6−i6i600000000000000−2i2ii6−i6−666−600000000000000000000000
χ674-4-44-20-404-222000−4i4i00200-2i6−i6i6−i6000000000000002i−2i−i6i6−666−600000000000000000000000
χ684-4-44-20-404-222000−4i4i00200-2−i6i6−i6i6000000000000002i−2ii6−i66−6−6600000000000000000000000
χ6988-8-880000-88-8000000000000000000000000000000000000000000000000000000000000
χ7088-8-8-400004-440000000000026−26−2626000000000000000000000000000000000000000000000
χ7188-8-8-400004-4400000000000−262626−26000000000000000000000000000000000000000000000
χ728-88-8-480-8044-4000000004-400000000000000000000000000000000000000000000000000

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