Finite Group Databasebeta

← Group #10698539

Character table — Group #10698539

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12222222222236666666444466661212121244448888121212121212121212122424242424242424441212121244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-2000000000000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000-2-2220000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-200000000000000000000000000000000002-2
χ1622222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-20000000000000000000000000000000000-22
χ1722222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-200000000000000
χ1822222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000220000000000000000-22-2-22200000000000000
χ1922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−33333−3−3−3−32-2-1-11100000000000000
χ2022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−3−3−3−3−33333-2211-1-100000000000000
χ2122222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−333333333−3−3−3−3-2211-1-100000000000000
χ2222222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−33333−3−3−3−333332-2-1-11100000000000000
χ232222-2-2-2-222-2-22222-2-2-2-2000022-2-20000000022−2−2000000000022−2−222−2−2000000002-2000022−2−200
χ242222-2-2-2-222-2-22222-2-2-2-2000022-2-20000000022−2−2000000000022−2−222−2−200000000-220000−2−22200
χ252222-2-2-2-222-2-22222-2-2-2-2000022-2-200000000−2−2220000000000−2−222−2−222000000002-20000−2−22200
χ262222-2-2-2-222-2-22222-2-2-2-2000022-2-200000000−2−2220000000000−2−222−2−22200000000-22000022−2−200
χ2722-2-22-2-222-2-2222-2-222-2-200002-2-2200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i200
χ2822-2-22-2-222-2-2222-2-222-2-200002-2-2200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i200
χ2922-2-22-2-222-2-2222-2-222-2-200002-2-2200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i200
χ3022-2-22-2-222-2-2222-2-222-2-200002-2-2200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i200
χ3122-2-2-222-22-22-222-2-2-2-2222-2-222-22-222-2-200002i−2i−2i2i2-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ3222-2-2-222-22-22-222-2-2-2-2222-2-222-22-222-2-20000−2i2i2i−2i2-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ3322-2-2-222-22-22-222-2-2-2-222-222-22-22-2-2-22200000000-220000000000000000000000000000002i−2i−2i2i00
χ3422-2-2-222-22-22-222-2-2-2-222-222-22-22-2-2-22200000000-22000000000000000000000000000000−2i2i2i−2i00
χ3522-2-2-222-22-22-2-1-11111-1-12-2-22-11-11-1-11100002i−2i−2i2i-1133−3−333−3−3−iii−i−iii−i00−i3i3−i3i300000000000000
χ3622-2-2-222-22-22-2-1-11111-1-12-2-22-11-11-1-11100002i−2i−2i2i-11−3−333−3−333−iii−i−iii−i00i3−i3i3−i300000000000000
χ3722-2-2-222-22-22-2-1-11111-1-12-2-22-11-11-1-1110000−2i2i2i−2i-1133−3−333−3−3i−i−iii−i−ii00i3−i3i3−i300000000000000
χ3822-2-2-222-22-22-2-1-11111-1-12-2-22-11-11-1-1110000−2i2i2i−2i-11−3−333−3−333i−i−iii−i−ii00−i3i3−i3i300000000000000
χ3922-2-2-222-2-22-2222-2-2-2-22222-2-2-22-2222-2-200000000-22000000000000000000000000002i2i−2i−2i000000
χ4022-2-2-222-2-22-2222-2-2-2-22222-2-2-22-2222-2-200000000-2200000000000000000000000000−2i−2i2i2i000000
χ4122-2-2-222-2-22-2222-2-2-2-222-2-222-22-22-2-22222-2-200002-222-2-2-2-2220000000000000000000000000000
χ4222-2-2-222-2-22-2222-2-2-2-222-2-222-22-22-2-222-2-22200002-2-2-22222-2-20000000000000000000000000000
χ4322-2-2-222-2-22-22-1-11111-1-1-2-2221-11-111-1-122-2-20000-11-1-11111-1-1−i3i3i3−i3i3−i3−i3i300−i3i3i3−i300000000000000
χ4422-2-2-222-2-22-22-1-11111-1-1-2-2221-11-111-1-122-2-20000-11-1-11111-1-1i3−i3−i3i3−i3i3i3−i300i3−i3−i3i300000000000000
χ4522-2-2-222-2-22-22-1-11111-1-1-2-2221-11-111-1-1-2-2220000-1111-1-1-1-111−i3i3i3−i3i3−i3−i3i300i3−i3−i3i300000000000000
χ4622-2-2-222-2-22-22-1-11111-1-1-2-2221-11-111-1-1-2-2220000-1111-1-1-1-111i3−i3−i3i3−i3i3i3−i300−i3i3i3−i300000000000000
χ47444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-2-2-20000000022000000000000000000000000000000000000
χ494444-4-4-4-444-4-4-2-2-2-222220000-2-222000000002222−22−220000000000−2−222−2−22200000000000000000000
χ504444-4-4-4-444-4-4-2-2-2-222220000-2-22200000000−22−222222000000000022−2−222−2−200000000000000000000
χ514444-4-4-4-4-4-4444444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000000
χ524444-4-4-4-4-4-444-2-2-2-22222000022-2-2000000000000000000000066−6−6−6−66600000000000000000000
χ534444-4-4-4-4-4-444-2-2-2-22222000022-2-20000000000000000000000−6−66666−6−600000000000000000000
χ5444-4-44-4-444-4-44-2-222-2-2220000-222-200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000
χ5544-4-44-4-444-4-44-2-222-2-2220000-222-2000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000
χ5644-4-44-4-44-444-444-4-444-4-40000-444-400000000000000000000000000000000000000000000000000
χ5744-4-44-4-44-444-4-2-222-2-22200002-2-220000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000
χ5844-4-44-4-44-444-4-2-222-2-22200002-2-220000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000
χ5944-4-4-444-44-44-4-2-22222-2-2-444-4-22-2222-2-2000000002-2000000000000000000000000000000000000
χ6044-4-4-444-4-44-44-2-22222-2-244-4-42-22-2-2-222000000002-2000000000000000000000000000000000000
χ614-44-44-44-400004-44-44-4-440000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ624-44-44-44-400004-44-44-4-44000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ634-44-4-44-4400004-44-4-444-40000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ644-44-4-44-4400004-44-4-444-4000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ654-44-4-44-440000-22-222-2-220000000023−2323−232i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000
χ664-44-4-44-440000-22-222-2-220000000023−2323−23−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000
χ674-44-4-44-440000-22-222-2-2200000000−2323−23232i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000
χ684-44-4-44-440000-22-222-2-2200000000−2323−2323−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000
χ694-4-4444-4-400004-4-444-44-40000000000002i−2i−2i2i0000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ704-4-4444-4-400004-4-444-44-4000000000000−2i2i2i−2i000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ714-4-4444-4-40000-222-2-22-220000000023−23−23232i−2i−2i2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ220000000000000000000000000000
χ724-4-4444-4-40000-222-2-22-220000000023−23−2323−2i2i2i−2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ220000000000000000000000000000
χ734-4-4444-4-40000-222-2-22-2200000000−232323−232i−2i−2i2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ220000000000000000000000000000
χ744-4-4444-4-40000-222-2-22-2200000000−232323−23−2i2i2i−2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ220000000000000000000000000000
χ754-4-44-4-44400004-4-44-44-440000000000000000000000000000000000000000000000002-2-22000000
χ764-4-44-4-44400004-4-44-44-44000000000000000000000000000000000000000000000000-222-2000000
χ778-88-88-88-80000-44-44-444-40000000000000000000000000000000000000000000000000000000000
χ788-8-88-8-8880000-444-44-44-40000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.