Finite Group Databasebeta

← Group #11779740

Character table — Group #11779740

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242422224668812122424242422888846612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-1-1-111-1-11111-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-111-1-11
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-11111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1111
χ92222222-22-22222222-222222-2-2-2222222-200-2-2-2-2-2-200000000000000002200-22200-2-20000000000000000
χ102222222-22-22222222-222222-2-2-2222222-200-2-2-2-2-2-20000000000000000-2-2002-2-200220000000000000000
χ11222222-22-222222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ12222222-22-222222222-2222-2-2222-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000002-20000000000000000002-2000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000-22000000000000000000-22000
χ1522222-1222222-1-1-12-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220002200-1-1-1-10000000-1-1000
χ1622222-1222222-1-1-12-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2000-2-2001111000000011000
χ1722222-1222222-1-1-12-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-1-1-2-2-2-21111111111110022000-2-20011110000000-1-1000
χ1822222-1222222-1-1-12-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-1-1-2-2-2-211111111111100-2-20002200-1-1-1-1000000011000
χ1922222-1-2-2-2-222-1-1-12-12-1-1-1-211-2-211-21111002-111-1-10000333333−3−3−3−3−3−3002-2000000033−3−30000000-11000
χ2022222-1-2-2-2-222-1-1-12-12-1-1-1-211-2-211-21111002-111-1-10000333333−3−3−3−3−3−300-220000000−3−33300000001-1000
χ2122222-1-2-2-2-222-1-1-12-12-1-1-1-211-2-211-21111002-111-1-10000−3−3−3−3−3−3333333002-20000000−3−3330000000-11000
χ2222222-1-2-2-2-222-1-1-12-12-1-1-1-211-2-211-21111002-111-1-10000−3−3−3−3−3−333333300-22000000033−3−300000001-1000
χ232222-122222-1-1222-1-12-1-1-1-122-1-1-1-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122002-1-100-1-10000000000200-1-10
χ242222-122222-1-1222-1-12-1-1-1-122-1-1-1-1-12-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200-21100110000000000-200110
χ252222-122222-1-1222-1-12-1-1-1-122-1-1-1-1-12-1-12-2-2-12-1-1-1-11111-2-21111-2-2111122002-1-100-1-10000000000-200110
χ262222-122222-1-1222-1-12-1-1-1-122-1-1-1-1-12-1-12-2-2-12-1-1-1-11111-2-21111-2-21111-2-200-21100110000000000200-1-10
χ272222-122-22-2-1-1222-1-1-2-1-1-1-12-211-1-1-12-1-1-2001-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i32200-2-1-100110000000000000−i3i30
χ282222-122-22-2-1-1222-1-1-2-1-1-1-12-211-1-1-12-1-1-2001-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-20021100-1-10000000000000i3−i30
χ292222-122-22-2-1-1222-1-1-2-1-1-1-12-211-1-1-12-1-1-2001-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i32200-2-1-100110000000000000i3−i30
χ302222-122-22-2-1-1222-1-1-2-1-1-1-12-211-1-1-12-1-1-2001-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-20021100-1-10000000000000−i3i30
χ312-22-2220-202-2-22-2-22202-2-200-22-200000022−2002-2002−22−22−22−22−22−22−22−20000000000000002-222−2−2000000
χ322-22-2220-202-2-22-2-22202-2-200-22-200000022−2002-2002−22−22−22−22−22−22−22−2000000000000000-22−2−222000000
χ332-22-2220-202-2-22-2-22202-2-200-22-20000002−22002-200−22−22−22−22−22−22−22−220000000000000002-2−2−222000000
χ342-22-2220-202-2-22-2-22202-2-200-22-20000002−22002-200−22−22−22−22−22−22−22−22000000000000000-2222−2−2000000
χ352-2-222220-202-2-22-2-220-22-22200022-2-2-2-200000000000000000000000002-20002-2−i2i200−i2i2−i2i200−i2i2−i2i2000000
χ362-2-222220-202-2-22-2-220-22-22200022-2-2-2-200000000000000000000000002-20002-2i2−i200i2−i2i2−i200i2−i2i2−i2000000
χ372-2-222220-202-2-22-2-220-22-22200022-2-2-2-20000000000000000000000000-22000-22−i2i200−i2i2−i2i200i2−i2i2−i2000000
χ382-2-222220-202-2-22-2-220-22-22200022-2-2-2-20000000000000000000000000-22000-22i2−i200i2−i2i2−i200−i2i2−i2i2000000
χ3944444-24-44-444-2-2-24-2-4-2-2-24-22-4-4-2-24-2-2-2200-4222220000000000000000000000000000000000000000000
χ4044444-2-44-4444-2-2-24-2-4-2-2-2-42-24422-4222-200-42-2-2220000000000000000000000000000000000000000000
χ414444-24-44-44-2-2444-2-2-4-2-2-22-44-2-2222-4224002-4-2-2220000000000000000000000000000000000000000000
χ424444-24-4-4-4-4-2-2444-2-24-2-2-22-4-422222-422-400-2422-2-20000000000000000000000000000000000000000000
χ434444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000
χ444444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000
χ454444-2-24-44-4-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000000
χ464444-2-24-44-4-2-2-2-2-2-21-4111-2-222211-2-21120022-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000000
χ474444-2-2-44-44-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ484444-2-2-44-44-2-2-2-2-2-21-411122-2-2-2-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ494444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000000
χ504444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000000
χ5144-4-4440000-44-4-44-440-4-44000000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ5244-4-4440000-44-4-44-440-4-4400000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ534-44-444040-4-4-44-4-44404-4-4004-44000000-40000-44000000000000000000000000000000000000000000000
χ544-44-44-2040-4-4-4-2224-20-22200-2-44000000200002-20000006−66−66−6−66−66−66000000000000000000000000000
χ554-44-44-2040-4-4-4-2224-20-22200-2-44000000200002-2000000−66−66−666−66−66−6000000000000000000000000000
χ564-44-44-20-404-4-4-2224-20-2220024-4000000-222−2200-220022−2222−22−22−22−22−22−22−22000000000000000000000000000
χ574-44-44-20-404-4-4-2224-20-2220024-4000000-2−222200-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000
χ584-44-4-24040-4224-4-4-2-20-2220042-2000000-400002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000000
χ594-44-4-24040-4224-4-4-2-20-2220042-2000000-400002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000000
χ604-44-4-240-404224-4-4-2-20-22200-4-22000000422−2200-2200−22−2222−22−22−2222−22−22−22000000000000000000000000000
χ614-44-4-240-404224-4-4-2-20-22200-4-220000004−222200-22002−22−2−22222−22−2−22222−22−2000000000000000000000000000
χ624-44-4-2-2040-422-222-2101-1-100-22-23i−3i003i−3i20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ634-44-4-2-2040-422-222-2101-1-100-22-23i−3i003i−3i20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ644-44-4-2-2040-422-222-2101-1-100-22-2−3i3i00−3i3i20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ654-44-4-2-2040-422-222-2101-1-100-22-2−3i3i00−3i3i20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ664-44-4-2-20-40422-222-2101-1-1002-223i−3i003i−3i-222−22001-1−3i3i−22−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23000000000000000000000000000
χ674-44-4-2-20-40422-222-2101-1-1002-223i−3i003i−3i-2−2222001-1−3i3i2−22−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ232−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23000000000000000000000000000
χ684-44-4-2-20-40422-222-2101-1-1002-22−3i3i00−3i3i-222−22001-13i−3i−22−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23000000000000000000000000000
χ694-44-4-2-20-40422-222-2101-1-1002-22−3i3i00−3i3i-2−2222001-13i−3i2−22−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23000000000000000000000000000
χ704-4-4444-40404-4-44-4-440-44-4-4-4000-4-444440000000000000000000000000000000000000000000000000000
χ714-4-444-240-404-42-22-4-202-224-2000-2-2-422200000000000000000000000000000000−2i22i200i2−i2i2−i2000000000000
χ724-4-444-240-404-42-22-4-202-224-2000-2-2-4222000000000000000000000000000000002i2−2i200−i2i2−i2i2000000000000
χ734-4-444-2-40404-42-22-4-202-22-42000224-2-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ744-4-444-2-40404-42-22-4-202-22-42000224-2-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ754-4-44-2440-40-22-44-42-202-22-24000-2-22-42200000000000000000000000004-4000-2200000000000000000000
χ764-4-44-2440-40-22-44-42-202-22-24000-2-22-4220000000000000000000000000-440002-200000000000000000000
χ774-4-44-24-4040-22-44-42-202-222-400022-24-2-2000000000000000000000000000000000023−230000000000000000
χ784-4-44-24-4040-22-44-42-202-222-400022-24-2-20000000000000000000000000000000000−23230000000000000000
χ7988-8-88-40000-8844-4-8-4044-4000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-4800004-4-8-884-4044-4000000000000000000000000000000000000000000000000000000000000000
χ8188-8-8-4-400004-444-4420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ8288-8-8-4-400004-444-4420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000
χ838-8-88-4-480-80-444-44420-22-2-4-40002244-2-20000000000000000000000000000000000000000000000000000
χ848-8-88-4-4-8080-444-44420-22-244000-2-2-4-4220000000000000000000000000000000000000000000000000000

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