Finite Group Databasebeta

← Group #10697921

Character table — Group #10697921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424444444444444121212121212121288884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-2000000002222-2-2-2-200000000000000000000
χ102222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000
χ112222222-2-2-222-2-2-22222-222-2-2-2-2-2-2220000-2200000000000000002-2000022-2-20000000000
χ122222222-2-2-222-2-2-22222-222-2-2-2-2-2-2220000-220000000000000000-220000-2-2220000000000
χ132222222-2-2-2-2-222-2222-2222-2-2-2-222-2-200002-2000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-2222-2-2-2-222-2-200002-200000000000000000000000000000000-2200
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
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-211-1-1-1-11100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-222-1-11111-1-100000000
χ19222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-100001-1−i3−i3−i3−i3i3i3i3i3000000002-200−i3i3-1-111−i3i300000000
χ20222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-100001-1−i3−i3−i3−i3i3i3i3i300000000-2200i3−i311-1-1i3−i300000000
χ21222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-100001-1i3i3i3i3−i3−i3−i3−i3000000002-200i3−i3-1-111i3−i300000000
χ22222222-1-2-2-222-2-2-2-1-1-12-2-1-1111111-1-100001-1i3i3i3i3−i3−i3−i3−i300000000-2200−i3i311-1-1−i3i300000000
χ232222-2-2222-22222-2222-2-2-2-222-2-222220000-2-20000000000000000002-2-2-200002200000000
χ242222-2-2222-22222-2222-2-2-2-222-2-222220000-2-2000000000000000000-22220000-2-200000000
χ252222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-200002200000000000000000000000000000000002i−2i
χ262222-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2-2-20000220000000000000000000000000000000000−2i2i
χ272222-2-22-2-2222-2-22222-22-2-2-2-222-2-22222-2-22-222-2-222-2-20000000000000000000000000000
χ282222-2-22-2-2222-2-22222-22-2-2-2-222-2-222-2-2222-2-2-222-2-2220000000000000000000000000000
χ292222-2-22-2-22-2-22222222-2-2-2-2-22222-2-20000-22000000000000000000000000000022-2-20000
χ302222-2-22-2-22-2-22222222-2-2-2-2-22222-2-20000-220000000000000000000000000000-2-2220000
χ312222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i300000000002-211−i3i3−i3i3-1-100000000
χ322222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011−i3−i3i3i3i3i3−i3−i30000000000-22-1-1i3−i3i3−i31100000000
χ332222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i300000000002-211i3−i3i3−i3-1-100000000
χ342222-2-2-122-22222-2-1-1-1-2-211-1-111-1-1-1-1000011i3i3−i3−i3−i3−i3i3i30000000000-22-1-1−i3i3−i3i31100000000
χ352222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-122-2-2-11-1-111-1-111000000000000−i3i3i3−i3−i3i3i3−i300000000
χ362222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-122-2-2-11-1-111-1-111000000000000i3−i3−i3i3i3−i3−i3i300000000
χ372222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-1-2-222-1111-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i300000000
χ382222-2-2-1-2-2222-2-22-1-1-1-221111-1-111-1-1-2-222-1111-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i300000000
χ3922-2-22-222-220000-22-2-2002-22-22-200002−22−2002−22−22−22−2000022-2-20000000000002−22−20000
χ4022-2-22-222-220000-22-2-2002-22-22-200002−22−2002−22−22−22−20000-2-222000000000000−22−220000
χ4122-2-22-222-220000-22-2-2002-22-22-20000−22−2200−22−22−22−22000022-2-2000000000000−22−220000
χ4222-2-22-222-220000-22-2-2002-22-22-20000−22−2200−22−22−22−220000-2-2220000000000002−22−20000
χ4322-2-2-222-2220000-22-2-200-22-222-200002−2−22002−2−222−2−2222-2-200000000000000002−2−220000
χ4422-2-2-222-2220000-22-2-200-22-222-200002−2−22002−2−222−2−22-2-2220000000000000000−222−20000
χ4522-2-2-222-2220000-22-2-200-22-222-20000−222−200−222−2−222−222-2-20000000000000000−222−20000
χ4622-2-2-222-2220000-22-2-200-22-222-20000−222−200−222−2−222−2-2-22200000000000000002−2−220000
χ47444444-2444-4-4-4-44-2-2-2-4-4-2-2-2-2-2-22222000022000000000000000000000000000000000000
χ48444444-2-4-4-4-4-444-4-2-2-2-44-2-22222-2-2220000-22000000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-4-4-2-2-24422-2-22222220000-2-2000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-2-22200002-2000000000000000000000000000000000000
χ5144-4-44-44-44-4000044-4-4004-4-44-440000000000000000000000000000000000000000000000
χ5244-4-44-4-24-440000-4-22200-22-22-22000022−2222−2200−22−22−22−220000000000000000000000000000
χ5344-4-44-4-24-440000-4-22200-22-22-220000−2222−2222002−22−22−22−20000000000000000000000000000
χ5444-4-44-4-2-44-400004-22200-222-22-20000000000i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ5544-4-44-4-2-44-400004-22200-222-22-20000000000−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ5644-4-4-4444-4-4000044-4-400-444-4-440000000000000000000000000000000000000000000000
χ5744-4-4-44-24-4-400004-222002-2-222-20000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ5844-4-4-44-24-4-400004-222002-2-222-20000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ5944-4-4-44-2-4440000-4-222002-22-2-22000022−22−222200−222−2−222−20000000000000000000000000000
χ6044-4-4-44-2-4440000-4-222002-22-2-220000−222222−22002−2−222−2−220000000000000000000000000000
χ614-44-40040004-4000-4-4400000000004-4000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ624-44-40040004-4000-4-4400000000004-400000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ634-44-4004000-44000-4-440000000000-44000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ644-44-4004000-44000-4-440000000000-4400000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ654-4-44004000004-40-44-4000000004-400000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ664-4-44004000004-40-44-4000000004-40000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ674-4-4400400000-440-44-400000000-4400000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ684-4-4400400000-440-44-400000000-440000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ698-88-800-40008-800044-40000000000-44000000000000000000000000000000000000000000
χ708-88-800-4000-8800044-400000000004-4000000000000000000000000000000000000000000
χ718-8-8800-4000008-804-4400000000-4400000000000000000000000000000000000000000000
χ728-8-8800-400000-8804-44000000004-400000000000000000000000000000000000000000000

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