Finite Group Databasebeta

← Group #10697830

Character table — Group #10697830

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order1222223444444446664466121212121212121288881212242424242424242444444444226666882424242488882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111
χ92222222222-2-22-2-2222-2-222222-2-2-2-220000-2-2000000002222-2-2-2-200000000000000000000
χ102222222222-2-22-2-2222-2-222222-2-2-2-220000-2-200000000-2-2-2-2222200000000000000000000
χ112222222-2-2-222-2-2-22222-222-2-2-2-2-222-200002-200000000000000000000000000000000002-2
χ122222222-2-2-222-2-2-22222-222-2-2-2-2-222-200002-20000000000000000000000000000000000-22
χ132222222-2-2-2-2-2-222222-2222-2-2-222-2-2-20000-2200000000000000002-222-2-200000000000000
χ142222222-2-2-2-2-2-222222-2222-2-2-222-2-2-20000-220000000000000000-22-2-22200000000000000
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-1-1-2-2111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2111122-1-1-1-100000000
χ19222222-1-2-2-2-2-2-222-1-1-1-22-1-1111-1-111100001-13333−3−3−3−3000000002-2-1-1110033−3−300000000
χ20222222-1-2-2-2-2-2-222-1-1-1-22-1-1111-1-111100001-13333−3−3−3−300000000-2211-1-100−3−33300000000
χ21222222-1-2-2-2-2-2-222-1-1-1-22-1-1111-1-111100001-1−3−3−3−33333000000002-2-1-11100−3−33300000000
χ22222222-1-2-2-2-2-2-222-1-1-1-22-1-1111-1-111100001-1−3−3−3−3333300000000-2211-1-10033−3−300000000
χ232222-2-2222-222-222222-2-2-2-222-22222-20000-2-2000000000000000000000000000000002-200
χ242222-2-2222-222-222222-2-2-2-222-22222-20000-2-200000000000000000000000000000000-2200
χ252222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-200002200000000000000000000002i−2i2i−2i2i−2i00000000
χ262222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-20000220000000000000000000000−2i2i−2i2i−2i2i00000000
χ272222-2-22-2-22222-2-2222-22-2-2-2-22-2-222222-2-2-2222-2-222-2-20000000000000000000000000000
χ282222-2-22-2-22222-2-2222-22-2-2-2-22-2-2222-2-222-22-2-222-2-2220000000000000000000000000000
χ292222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-2000000000000000000000000000022-2-20000
χ302222-2-22-2-22-2-22222222-2-2-2-2-2222-2-2200002-20000000000000000000000000000-2-2220000
χ312222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-133−3−3−3−3330000000000−i3i3−i3i32i−2i−ii−ii00000000
χ322222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-133−3−3−3−3330000000000i3−i3i3−i3−2i2ii−ii−i00000000
χ332222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-1−3−33333−3−30000000000−i3i3−i3i3−2i2ii−ii−i00000000
χ342222-2-2-122-2-2-2-2-2-2-1-1-12211-1-11111110000-1-1−3−33333−3−30000000000i3−i3i3−i32i−2i−ii−ii00000000
χ352222-2-2-1-2-22222-2-2-1-1-1-221111-111-1-1-122-2-21-1-1-111-1-1110000000000−i3i3i3−i300−i3i3i3−i300000000
χ362222-2-2-1-2-22222-2-2-1-1-1-221111-111-1-1-122-2-21-1-1-111-1-1110000000000i3−i3−i3i300i3−i3−i3i300000000
χ372222-2-2-1-2-22222-2-2-1-1-1-221111-111-1-1-1-2-2221-111-1-111-1-10000000000−i3i3i3−i300i3−i3−i3i300000000
χ382222-2-2-1-2-22222-2-2-1-1-1-221111-111-1-1-1-2-2221-111-1-111-1-10000000000i3−i3−i3i300−i3i3i3−i300000000
χ392-22-22-222-2200-2002-2-2002-22-220000-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i200002i2i−2i−2i0000000000002−22−20000
χ402-22-22-222-2200-2002-2-2002-22-220000-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000−2i−2i2i2i000000000000−22−220000
χ412-22-22-222-2200-2002-2-2002-22-220000-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i200002i2i−2i−2i000000000000−22−220000
χ422-22-22-222-2200-2002-2-2002-22-220000-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000−2i−2i2i2i0000000000002−22−20000
χ432-22-2-222-22200-2002-2-200-22-2220000-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i22i2i−2i−2i00000000000000002−2−220000
χ442-22-2-222-22200-2002-2-200-22-2220000-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2−2i−2i2i2i0000000000000000−222−20000
χ452-22-2-222-22200-2002-2-200-22-2220000-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i22i2i−2i−2i0000000000000000−222−20000
χ462-22-2-222-22200-2002-2-200-22-2220000-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2−2i−2i2i2i00000000000000002−2−220000
χ47444444-2444-4-44-4-4-2-2-2-4-4-2-2-2-2-22222-2000022000000000000000000000000000000000000
χ48444444-2-4-4-444-4-4-4-2-2-24-4-2-222222-2-220000-22000000000000000000000000000000000000
χ494444-4-4-244-444-444-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-222-20000-22000000000000000000000000000000000000
χ5144-4-40040004-4000-44-40000000004-40000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ5244-4-40040004-4000-44-40000000004-4000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ5344-4-4004000-44000-44-4000000000-440000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5444-4-4004000-44000-44-4000000000-44000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ554-44-44-44-44-4004004-4-4004-4-44-400004000000000000000000000000000000000000000000
χ564-44-44-4-24-4400-400-22200-22-22-200002−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ574-44-44-4-24-4400-400-22200-22-22-2000022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ584-44-44-4-2-44-400400-22200-222-220000-2000000i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ594-44-44-4-2-44-400400-22200-222-220000-2000000−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ604-44-4-4444-4-4004004-4-400-444-4-400004000000000000000000000000000000000000000000
χ614-44-4-44-24-4-400400-222002-2-2220000-2000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ624-44-4-44-24-4-400400-222002-2-2220000-2000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ634-44-4-44-2-44400-400-222002-22-2-200002−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ644-44-4-44-2-44400-400-222002-22-2-2000022i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ654-4-440040000004-4-4-4400000004-4000000000000000002-2-222-2-2200000000000000000000
χ664-4-440040000004-4-4-4400000004-400000000000000000-222-2-222-200000000000000000000
χ674-4-44004000000-44-4-440000000-44000000000000000002-2-22-222-200000000000000000000
χ684-4-44004000000-44-4-440000000-4400000000000000000-222-22-2-2200000000000000000000
χ6988-8-800-40008-80004-44000000000-440000000000000000000000000000000000000000000
χ7088-8-800-4000-880004-440000000004-40000000000000000000000000000000000000000000
χ718-8-8800-40000008-844-40000000-44000000000000000000000000000000000000000000000
χ728-8-8800-4000000-8844-400000004-4000000000000000000000000000000000000000000000

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