Finite Group Databasebeta

← Group #10772500

Character table — Group #10772500

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222234444444466644661212121212121212244488881212242424242424242444448888888824666121212121244444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-111-1-111-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-11111-1-111-1-1
χ91111-1-111-1-1-1-1111111-11-1-1111-1-1-1-111-1-1111-1-1-111111-1-1-1-111-1-11111-1-1-1-11-11111-1-1-1-111-11-1-11-1
χ101111-1-111-1-1-1-1111111-11-1-1111-1-1-1-111-1-1111-1-1-111111-1-1-1-1-1-111-1-1-1-111111-11111-1-1-1-1-1-11-111-11
χ111111-1-111-1-1-1-1111111-11-1-1111-1-1-1-111-1-11-1-111-11-1-1-1-1111111-1-1-1-1-1-11111-111-1-11-1-11111-11-1-1-11
χ121111-1-111-1-1-1-1111111-11-1-1111-1-1-1-111-1-11-1-111-11-1-1-1-11111-1-1111111-1-1-1-1-111-1-11-1-111-1-11-1111-1
χ131111-1-111-1-1-1-1111111-11-1-1111-1-1-1-11-111-111-1-1-111111-1-1-1-111-1-11111-1-1-1-1-11-1-1-1-11111-1-1-1111-11
χ141111-1-111-1-1-1-1111111-11-1-1111-1-1-1-11-111-111-1-1-111111-1-1-1-1-1-111-1-1-1-11111-11-1-1-1-11111111-1-1-11-1
χ151111-1-111-1-1-1-1111111-11-1-1111-1-1-1-11-111-1-1-111-11-1-1-1-1111111-1-1-1-1-1-111111-1-111-111-1-1-1-1-11111-1
χ161111-1-111-1-1-1-1111111-11-1-1111-1-1-1-11-111-1-1-111-11-1-1-1-11111-1-1111111-1-1-1-11-1-111-111-1-1111-1-1-1-11
χ172222222222-2-22-2-2222-2-2222-2-222-2-222-22-20000-2-20000000000000000000000200-2-220000000000
χ182222222222-2-22-2-2222-2-2222-2-222-2-22-22-220000-2-20000000000000000000000-20022-20000000000
χ192222222-2-2-222-2-2-2222-2222-2-2-2-2-222-200000000-220000000000000000000000000000002-2002-200
χ202222222-2-2-222-2-2-2222-2222-2-2-2-2-222-200000000-22000000000000000000000000000000-2200-2200
χ212222222-2-2-2-2-2-2222222-222-222-2-2-2-2-2000000002-20000000022-2-2000000000000000000002-20000
χ222222222-2-2-2-2-2-2222222-222-222-2-2-2-2-2000000002-200000000-2-22200000000000000000000-220000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-111-1-1-11100000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000221-1-1111-1-100000000
χ27222222-1222-2-22-2-2-1-1-1-2-2-1-1-111-1-111-12-22-2000011−i3−i3i3i3−i3−i3i3i300000000000000-1−i3i311-1−i3i300000000
χ28222222-1222-2-22-2-2-1-1-1-2-2-1-1-111-1-111-12-22-2000011i3i3−i3−i3i3i3−i3−i300000000000000-1i3−i311-1i3−i300000000
χ29222222-1222-2-22-2-2-1-1-1-2-2-1-1-111-1-111-1-22-22000011−i3−i3i3i3−i3−i3i3i3000000000000001i3−i3-1-11i3−i300000000
χ30222222-1222-2-22-2-2-1-1-1-2-2-1-1-111-1-111-1-22-22000011i3i3−i3−i3i3i3−i3−i3000000000000001−i3i3-1-11−i3i300000000
χ312222-2-222-2-2222-2-22222-2-2-22-2-2-2-222222-2-200002-20000000000000000000000200-22-20000000000
χ322222-2-222-2-2222-2-22222-2-2-22-2-2-2-2222-2-22200002-20000000000000000000000-2002-220000000000
χ332222-2-22-22222-222222-2-2-2-2-2222222-200000000-2-200000000222200000000000000000000-2-20000
χ342222-2-22-22222-222222-2-2-2-2-2222222-200000000-2-200000000-2-2-2-200000000000000000000220000
χ352222-2-22-222-2-2-2-2-222222-2-2-2-2-222-2-2-200000000220000000000000000000000000000002-200-2200
χ362222-2-22-222-2-2-2-2-222222-2-2-2-2-222-2-2-20000000022000000000000000000000000000000-22002-200
χ372222-2-2-12-2-2222-2-2-1-1-12-211-11111-1-1-122-2-20000-11−i3−i3i3i3i3i3−i3−i300000000000000-1−i3i31-11i3−i300000000
χ382222-2-2-12-2-2222-2-2-1-1-12-211-11111-1-1-122-2-20000-11i3i3−i3−i3−i3−i3i3i300000000000000-1i3−i31-11−i3i300000000
χ392222-2-2-12-2-2222-2-2-1-1-12-211-11111-1-1-1-2-2220000-11−i3−i3i3i3i3i3−i3−i3000000000000001i3−i3-11-1−i3i300000000
χ402222-2-2-12-2-2222-2-2-1-1-12-211-11111-1-1-1-2-2220000-11i3i3−i3−i3−i3−i3i3i3000000000000001−i3i3-11-1i3−i300000000
χ412222-2-2-12-2-2-2-2222-1-1-1-2211-1-1-11111-12-2-2222-2-21-1-1-1-1-111110000000000002-2-1-1-1-1111100000000
χ422222-2-2-12-2-2-2-2222-1-1-1-2211-1-1-11111-12-2-22-2-2221-11111-1-1-1-1000000000000-22-111-111-1-100000000
χ432222-2-2-12-2-2-2-2222-1-1-1-2211-1-1-11111-1-222-222-2-21-1-1-1-1-11111000000000000-221111-1-1-1-100000000
χ442222-2-2-12-2-2-2-2222-1-1-1-2211-1-1-11111-1-222-2-2-2221-11111-1-1-1-10000000000002-21-1-11-1-11100000000
χ452-2-2200202i−2i2i−2i02-22-2-2000002-22i−2i2i−2i000002−2−i2i2002−22−2−i2i2−i2i22i−2i2-2−i2−i2i2i222−2−2000000000000000000
χ462-2-2200202i−2i2i−2i02-22-2-2000002-22i−2i2i−2i000002−2−i2i2002−22−2−i2i2−i2i2−2i2i-22i2i2−i2−i2−2−222000000000000000000
χ472-2-2200202i−2i2i−2i02-22-2-2000002-22i−2i2i−2i00000−22i2−i200−22−22i2−i2i2−i22i−2i2-2i2i2−i2−i2−2−222000000000000000000
χ482-2-2200202i−2i2i−2i02-22-2-2000002-22i−2i2i−2i00000−22i2−i200−22−22i2−i2i2−i2−2i2i-22−i2−i2i2i222−2−2000000000000000000
χ492-2-220020−2i2i−2i2i02-22-2-2000002-2−2i2i−2i2i000002−2i2−i2002−22−2i2−i2i2−i22i−2i-22−i2−i2i2i2−2−222000000000000000000
χ502-2-220020−2i2i−2i2i02-22-2-2000002-2−2i2i−2i2i000002−2i2−i2002−22−2i2−i2i2−i2−2i2i2-2i2i2−i2−i222−2−2000000000000000000
χ512-2-220020−2i2i−2i2i02-22-2-2000002-2−2i2i−2i2i00000−22−i2i200−22−22−i2i2−i2i22i−2i-22i2i2−i2−i222−2−2000000000000000000
χ522-2-220020−2i2i−2i2i02-22-2-2000002-2−2i2i−2i2i00000−22−i2i200−22−22−i2i2−i2i2−2i2i2-2−i2−i2i2i2−2−222000000000000000000
χ53444444-2-4-4-444-4-4-4-2-2-2-44-2-222222-2-22000000002-200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-444-2-2-24-4-2-22-2-22222200000000-2200000000000000000000000000000000000000
χ554444-4-4-2-44444-444-2-2-2-4-4222-2-2-2-2-2-22000000002200000000000000000000000000000000000000
χ564444-4-4-2-444-4-4-4-4-4-2-2-24422222-2-222200000000-2-200000000000000000000000000000000000000
χ5744-4-400440000-400-44-400004000000-4000000000000000000000022−2222−220000000000000000000000
χ5844-4-400440000-400-44-400004000000-40000000000000000000000−2222−22220000000000000000000000
χ5944-4-4004-40000400-44-40000-4000000400000000000000000000000000−2i22i2−2i22i2000000000000000000
χ6044-4-4004-40000400-44-40000-40000004000000000000000000000000002i2−2i22i2−2i2000000000000000000
χ614-44-44-4400000000-4-44004-40000000000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ624-44-44-4400000000-4-44004-4000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ634-44-4-44400000000-4-4400-440000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ644-44-4-44400000000-4-4400-44000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ654-4-4400404i−4i−4i4i0-444-4-400000-444i−4i−4i4i0000000000000000000000000000000000000000000000000
χ664-4-440040−4i4i4i−4i0-444-4-400000-44−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ674-4-4400-204i−4i4i−4i04-4-22200000-22−2i2i−2i2i0000022−22−2i22i200−22−22i2−i2i2−i2000000000000000000000000000000
χ684-4-4400-204i−4i4i−4i04-4-22200000-22−2i2i−2i2i00000−22222i2−2i2002−22−2−i2i2−i2i2000000000000000000000000000000
χ694-4-4400-204i−4i−4i4i0-44-222000002-2−2i2i2i−2i00000000000i6−i6−i6i66−6−66000000000000000000000000000000
χ704-4-4400-204i−4i−4i4i0-44-222000002-2−2i2i2i−2i00000000000−i6i6i6−i6−666−6000000000000000000000000000000
χ714-4-4400-20−4i4i4i−4i0-44-222000002-22i−2i−2i2i00000000000i6−i6−i6i6−666−6000000000000000000000000000000
χ724-4-4400-20−4i4i4i−4i0-44-222000002-22i−2i−2i2i00000000000−i6i6i6−i66−6−66000000000000000000000000000000
χ734-4-4400-20−4i4i−4i4i04-4-22200000-222i−2i2i−2i0000022−222i2−2i200−22−22−i2i2−i2i2000000000000000000000000000000
χ744-4-4400-20−4i4i−4i4i04-4-22200000-222i−2i2i−2i00000−2222−2i22i2002−22−2i2−i2i2−i2000000000000000000000000000000
χ7588-8-800-480000-8004-440000-40000004000000000000000000000000000000000000000000000000
χ7688-8-800-4-800008004-4400004000000-4000000000000000000000000000000000000000000000000
χ778-88-88-8-40000000044-400-4400000000000000000000000000000000000000000000000000000000
χ788-88-8-88-40000000044-4004-400000000000000000000000000000000000000000000000000000000

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