Finite Group Databasebeta

← Group #10778357

Character table — Group #10778357

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444466668888888888888888881212121212121616161616161616161624242424242424244848
order12222234444444466644661212121212121212888888888888121224242424242424248888884412121212242424242244888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ91111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111111111-1-111-1-1-111111-1-1-1-111-1-1-1-11-111-1-111-1-11-11-111-1-11-1
χ101111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111111111-1-1-1-111-111111-1-1-1-111-1-1-1-1-11-1-111-1-111-11-1111-1-1-11
χ111111-1-11-1-1-1-11111111-11-1-11-1-1-1-11111111-1-11111-1-1-11-1-1-1-1111111-1-1-1-1-11-1-11111-1-11-11-1-1-111-11
χ121111-1-11-1-1-1-11111111-11-1-11-1-1-1-11111111-1-111-1-111-11-1-1-1-1111111-1-1-1-11-111-1-1-1-111-11-11-1-1111-1
χ131111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111-1-1-1-111-1-111-1-1-111111-1-1-1-1-1-111111-111-1-111-1-1-11-11-1-111-11
χ141111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111-1-1-1-111-1-1-1-111-111111-1-1-1-1-1-11111-11-1-111-1-1111-11-1-1-1111-1
χ151111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111-1-1-1-1-1-11111-1-1-11-1-1-1-11111-1-11111-11-1-11111-1-1-11-1111-1-11-1
χ161111-1-11-1-1-1-11111111-11-1-11-1-1-1-1111-1-1-1-1-1-111-1-111-11-1-1-1-11111-1-111111-111-1-1-1-1111-11-111-1-1-11
χ17222222222-2-2-2-2-2-2222-2222-2-2-222-2-2-2000000002i−2i2i−2i-22000000000000000000002i−2i2i−2i0000000000
χ18222222222-2-2-2-2-2-2222-2222-2-2-222-2-2-200000000−2i2i−2i2i-2200000000000000000000−2i2i−2i2i0000000000
χ192222222-2-2222-2-22222-2-222222-2-2-2-22222200000000-2-200000000-2-2-2-22200000000000000000000
χ202222222-2-2222-2-22222-2-222222-2-2-2-22-2-2-2-200000000-2-2000000002222-2-200000000000000000000
χ212222222-2-2-2-2-222-22222-222-2-2-2-2-222-20000000000002-20000000000000000000000002-2-22000000
χ222222222-2-2-2-2-222-22222-222-2-2-2-2-222-20000000000002-2000000000000000000000000-222-2000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-100002222-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-22222-1-111111111000000-2-21111-1-1-1-10000000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-1-11111111100000022-1-1-1-111110000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-22-1-1111-1-1111000000002i−2i2i−2i1-133−3−333−3−300000000−i3i3−i3i3−ii−ii0000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-22-1-1111-1-1111000000002i−2i2i−2i1-1−3−333−3−33300000000i3−i3i3−i3−ii−ii0000000000
χ29222222-122-2-2-2-2-2-2-1-1-1-22-1-1111-1-111100000000−2i2i−2i2i1-133−3−333−3−300000000i3−i3i3−i3i−ii−i0000000000
χ30222222-122-2-2-2-2-2-2-1-1-1-22-1-1111-1-111100000000−2i2i−2i2i1-1−3−333−3−33300000000−i3i3−i3i3i−ii−i0000000000
χ312222-2-222222-222-2222-2-2-2-2-2222222-2000000000000-2-200000000000000000000000022-2-2000000
χ322222-2-222222-222-2222-2-2-2-2-2222222-2000000000000-2-2000000000000000000000000-2-222000000
χ332222-2-2222-2-22-2-222222-2-2-22-2-222-2-222222000000002-200000000-2-222-2-200000000000000000000
χ342222-2-2222-2-22-2-222222-2-2-22-2-222-2-22-2-2-2-2000000002-20000000022-2-22200000000000000000000
χ352222-2-22-2-222-2-2-2-222222-2-2-222-2-2-2-2-2000000002i−2i−2i2i22000000000000000000002i−2i−2i2i0000000000
χ362222-2-22-2-222-2-2-2-222222-2-2-222-2-2-2-2-200000000−2i2i2i−2i2200000000000000000000−2i2i2i−2i0000000000
χ372222-2-2-1-2-222-2-2-2-2-1-1-122111-1-111111000000002i−2i−2i2i-1-133−3−3−3−33300000000−i3i3i3−i3−iii−i0000000000
χ382222-2-2-1-2-222-2-2-2-2-1-1-122111-1-111111000000002i−2i−2i2i-1-1−3−33333−3−300000000i3−i3−i3i3−iii−i0000000000
χ392222-2-2-1-2-222-2-2-2-2-1-1-122111-1-11111100000000−2i2i2i−2i-1-133−3−3−3−33300000000i3−i3−i3i3i−i−ii0000000000
χ402222-2-2-1-2-222-2-2-2-2-1-1-122111-1-11111100000000−2i2i2i−2i-1-1−3−33333−3−300000000−i3i3i3−i3i−i−ii0000000000
χ412222-2-2-1-2-2-2-22222-1-1-1-2211-11111-1-1-1000022-2-222-2-21-1-1-1-1-111110000002-2-1-111-1-1110000000000
χ422222-2-2-1-2-2-2-22222-1-1-1-2211-11111-1-1-1000022-2-2-2-2221-1-1-1-1-11111000000-2211-1-111-1-10000000000
χ432222-2-2-1-2-2-2-22222-1-1-1-2211-11111-1-1-10000-2-22222-2-21-11111-1-1-1-1000000-2211-1-1-1-1110000000000
χ442222-2-2-1-2-2-2-22222-1-1-1-2211-11111-1-1-10000-2-222-2-2221-11111-1-1-1-10000002-2-1-11111-1-10000000000
χ452-2-222-22002-2200-22-2-2002-222-20000-22i2i−2i−2i2−22−20000002−22−22−22−200002i−2i00000000000000−i2i2−i2i200
χ462-2-222-22002-2200-22-2-2002-222-20000-22i2i−2i−2i−22−22000000−22−22−22−2200002i−2i00000000000000i2−i2i2−i200
χ472-2-222-22002-2200-22-2-2002-222-20000-2−2i−2i2i2i2−22−20000002−22−22−22−20000−2i2i00000000000000i2−i2i2−i200
χ482-2-222-22002-2200-22-2-2002-222-20000-2−2i−2i2i2i−22−22000000−22−22−22−220000−2i2i00000000000000−i2i2−i2i200
χ492-2-22-22200-22200-22-2-200-222-220000-22i2i−2i−2i2−2−220000002−22−2−22−220000−2i2i00000000000000−i2i2i2−i200
χ502-2-22-22200-22200-22-2-200-222-220000-22i2i−2i−2i−222−2000000−22−222−22−20000−2i2i00000000000000i2−i2−i2i200
χ512-2-22-22200-22200-22-2-200-222-220000-2−2i−2i2i2i2−2−220000002−22−2−22−2200002i−2i00000000000000i2−i2−i2i200
χ522-2-22-22200-22200-22-2-200-222-220000-2−2i−2i2i2i−222−2000000−22−222−22−200002i−2i00000000000000−i2i2i2−i200
χ53444444-2-4-4444-4-44-2-2-2-4-4-2-2-2-2-22222-2000000000000220000000000000000000000000000000000
χ54444444-2-4-4-4-4-444-4-2-2-24-4-2-222222-2-22000000000000-220000000000000000000000000000000000
χ554444-4-4-24444-444-4-2-2-2-4-4222-2-2-2-2-2-22000000000000220000000000000000000000000000000000
χ564444-4-4-244-4-44-4-44-2-2-24-422-222-2-222-2000000000000-220000000000000000000000000000000000
χ5744-4-4004000004-40-44-40000000004-4022−2222−2200000000000000000022−22000000000000000000000000
χ5844-4-4004000004-40-44-40000000004-40−2222−2222000000000000000000−2222000000000000000000000000
χ5944-4-400400000-440-44-4000000000-44022−2222−22000000000000000000−2222000000000000000000000000
χ6044-4-400400000-440-44-4000000000-440−2222−222200000000000000000022−22000000000000000000000000
χ614-44-40044-4000000-4-4400000004-4000−2i22i22i2−2i200000000000000000000−2i22i20000000000000000000000
χ624-44-40044-4000000-4-4400000004-40002i2−2i2−2i22i2000000000000000000002i2−2i20000000000000000000000
χ634-44-4004-44000000-4-440000000-44000−2i22i22i2−2i2000000000000000000002i2−2i20000000000000000000000
χ644-44-4004-44000000-4-440000000-440002i2−2i2−2i22i200000000000000000000−2i22i20000000000000000000000
χ654-4-444-4400-44-40044-4-4004-4-4-4400004000000000000000000000000000000000000000000000000
χ664-4-444-4-2004-4400-4-22200-22-2-2200002000022−2222−22000000−22−22−22−2200000000000000000000000000
χ674-4-444-4-2004-4400-4-22200-22-2-22000020000−2222−22220000002−22−22−22−200000000000000000000000000
χ684-4-444-4-200-44-4004-22200-2222-20000-2000000000000006−6−666−6−6600000000000000000000000000
χ694-4-444-4-200-44-4004-22200-2222-20000-200000000000000−666−6−666−600000000000000000000000000
χ704-4-44-444004-4-40044-4-400-44-44-400004000000000000000000000000000000000000000000000000
χ714-4-44-44-2004-4-4004-222002-22-220000-2000000000000006−6−66−666−600000000000000000000000000
χ724-4-44-44-2004-4-4004-222002-22-220000-200000000000000−666−66−6−6600000000000000000000000000
χ734-4-44-44-200-44400-4-222002-2-22-200002000022−22−2222000000−22−222−22−200000000000000000000000000
χ744-4-44-44-200-44400-4-222002-2-22-2000020000−222222−220000002−22−2−22−2200000000000000000000000000
χ7588-8-800-4000008-804-44000000000-440000000000000000000000000000000000000000000000000
χ7688-8-800-400000-8804-440000000004-40000000000000000000000000000000000000000000000000
χ778-88-800-48-800000044-40000000-44000000000000000000000000000000000000000000000000000
χ788-88-800-4-8800000044-400000004-4000000000000000000000000000000000000000000000000000

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