Finite Group Databasebeta

← Group #10697095

Character table — Group #10697095

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884488121212122424242488882244
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ922222222-2-2-2-2222222-2-222-2-2222-2-220000-2-2000000000000000000000000000022-2-20000
χ1022222222-2-2-2-2222222-2-222-2-2222-2-220000-2-20000000000000000000000000000-2-2220000
χ112222222-222-2-2-2-2-22222-22222-2-2-2-2-2-200002-20000000000000000002i−2i00002i2i−2i−2i00000000
χ122222222-222-2-2-2-2-22222-22222-2-2-2-2-2-200002-2000000000000000000−2i2i0000−2i−2i2i2i00000000
χ132222222-2-2-222-2-2-2222-2222-2-2-2-2-222-20000-22000000000000000000000000000000002-200
χ142222222-2-2-222-2-2-2222-2222-2-2-2-2-222-20000-2200000000000000000000000000000000-2200
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-113333−3−3−3−300000000002i−2i−i3−i3i3i3−i−iii00000000
χ20222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-113333−3−3−3−30000000000−2i2ii3i3−i3−i3ii−i−i00000000
χ21222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-11−3−3−3−3333300000000002i−2ii3i3−i3−i3−i−iii00000000
χ22222222-1-222-2-2-2-2-2-1-1-12-2-1-1-1-11111110000-11−3−3−3−333330000000000−2i2i−i3−i3i3i3ii−i−i00000000
χ232222-2-22222-2-22-2-2222-22-2-2222-2-2-2-220000-22000000002222-2-2-2-200000000000000000000
χ242222-2-22222-2-22-2-2222-22-2-2222-2-2-2-220000-2200000000-2-2-2-2222200000000000000000000
χ252222-2-222-2-2222-2-22222-2-2-2-2-22-2-222222-2-22-222-2-222-2-20000000000000000000000000000
χ262222-2-222-2-2222-2-22222-2-2-2-2-22-2-2222-2-2222-2-2-222-2-2220000000000000000000000000000
χ272222-2-22-22222-222222-2-2-2-222-22222-20000-2-200000000000000000000000000000000002-2
χ282222-2-22-22222-222222-2-2-2-222-22222-20000-2-20000000000000000000000000000000000-22
χ292222-2-22-2-2-2-2-2-22222222-2-2-2-2-222-2-2-200002200000000000000002-2002-22-2000000000000
χ302222-2-22-2-2-2-2-2-22222222-2-2-2-2-222-2-2-20000220000000000000000-2200-22-22000000000000
χ312222-2-2-12-2-2222-2-2-1-1-12-21111-111-1-1-122-2-2-11-1-111-1-111000000000000−i3i3i3−i3−i3i3−i3i300000000
χ322222-2-2-12-2-2222-2-2-1-1-12-21111-111-1-1-122-2-2-11-1-111-1-111000000000000i3−i3−i3i3i3−i3i3−i300000000
χ332222-2-2-12-2-2222-2-2-1-1-12-21111-111-1-1-1-2-222-1111-1-111-1-1000000000000−i3i3i3−i3i3−i3i3−i300000000
χ342222-2-2-12-2-2222-2-2-1-1-12-21111-111-1-1-1-2-222-1111-1-111-1-1000000000000i3−i3−i3i3−i3i3−i3i300000000
χ352222-2-2-1-2-2-2-2-2-222-1-1-12211111-1-11110000-1-133−3−3−3−333000000002-200-11-113−3−3300000000
χ362222-2-2-1-2-2-2-2-2-222-1-1-12211111-1-11110000-1-133−3−3−3−33300000000-22001-11-1−333−300000000
χ372222-2-2-1-2-2-2-2-2-222-1-1-12211111-1-11110000-1-1−3−33333−3−3000000002-200-11-11−333−300000000
χ382222-2-2-1-2-2-2-2-2-222-1-1-12211111-1-11110000-1-1−3−33333−3−300000000-22001-11-13−3−3300000000
χ3922-2-22-2220000-22-2-2-22002-20022-200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i222−2−222−2−2000000000000002i−2i0000
χ4022-2-22-2220000-22-2-2-22002-20022-200-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2−222−2−22200000000000000−2i2i0000
χ4122-2-22-2220000-22-2-2-22002-20022-200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i222−2−222−2−200000000000000−2i2i0000
χ4222-2-22-2220000-22-2-2-22002-20022-200-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2−222−2−222000000000000002i−2i0000
χ4322-2-2-22220000-2-22-2-2200-22002-2200-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i222−2−2−2−2220000000000002i−2i000000
χ4422-2-2-22220000-2-22-2-2200-22002-2200-2−i2i2i2−i200−i2i2i2−i2−i2i2i2−i2−2−22222−2−2000000000000−2i2i000000
χ4522-2-2-22220000-2-22-2-2200-22002-2200-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i222−2−2−2−222000000000000−2i2i000000
χ4622-2-2-22220000-2-22-2-2200-22002-2200-2i2−i2−i2i200i2−i2−i2i2i2−i2−i2i2−2−22222−2−20000000000002i−2i000000
χ47444444-24-4-4-4-4444-2-2-2-4-4-2-222-2-2-222-2000022000000000000000000000000000000000000
χ48444444-2-4-4-444-4-4-4-2-2-2-44-2-222222-2-2200002-2000000000000000000000000000000000000
χ494444-4-4-2444-4-44-4-4-2-2-2-4422-2-2-22222-200002-2000000000000000000000000000000000000
χ504444-4-4-2-44444-444-2-2-2-4-422-2-22-2-2-2-22000022000000000000000000000000000000000000
χ5144-4-44-44-400004-44-4-44004-400-4-44004000000000000000000000000000000000000000000
χ5244-4-44-4-240000-44-422-200-2200-2-22002−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ5344-4-44-4-240000-44-422-200-2200-2-220022i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ5444-4-44-4-2-400004-4422-200-220022-200-2000000i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ5544-4-44-4-2-400004-4422-200-220022-200-2000000−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ5644-4-4-444-4000044-4-4-4400-4400-44-4004000000000000000000000000000000000000000000
χ5744-4-4-44-240000-4-4422-2002-200-22-2002−2i22i22i2−2i200i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ5844-4-4-44-240000-4-4422-2002-200-22-20022i2−2i2−2i22i200−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ5944-4-4-44-2-4000044-422-2002-2002-2200-2000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ6044-4-4-44-2-4000044-422-2002-2002-2200-2000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ614-44-40040004-40004-4-40000000004-40000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ624-44-40040004-40004-4-40000000004-4000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ634-44-4004000-440004-4-4000000000-440000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-4004000-440004-4-4000000000-44000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-4400404-400000-44-400004-4000000000000000000000000−2i22i22i2−2i200000000000000000000
χ664-4-4400404-400000-44-400004-40000000000000000000000002i2−2i2−2i22i200000000000000000000
χ674-4-440040-4400000-44-40000-4400000000000000000000−2i22i22i2−2i2000000000000000000000000
χ684-4-440040-4400000-44-40000-44000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ698-88-800-40008-8000-444000000000-440000000000000000000000000000000000000000000
χ708-88-800-4000-88000-4440000000004-40000000000000000000000000000000000000000000
χ718-8-8800-408-8000004-440000-44000000000000000000000000000000000000000000000000
χ728-8-8800-40-88000004-4400004-4000000000000000000000000000000000000000000000000

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