Finite Group Databasebeta

← Group #11778938

Character table — Group #11778938

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242444224881212121224242424448888266664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1111
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
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ92222222-22-22222222-22222-2-2-22222222-200-2-2-2-2-2-200000000000000002200-20022-2-20000000000000000
χ102222222-22-22222222-22222-2-2-22222222-200-2-2-2-2-2-20000000000000000-2-200200-2-2220000000000000000
χ11222222-22-222222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ12222222-22-222222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000002-2000000000000000000002-20
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-222000000000000000000-2200000000000000000000-220
χ1522222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12200200-1-1-1-100000000002-1-1000
χ1622222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-20011110000000000-211000
χ1722222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-21111111111112200200-1-1-1-10000000000-211000
χ1822222-12222222-1-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-22-1-1-1-1-1-2-2-2-2111111111111-2-200-200111100000000002-1-1000
χ1922222-12-22-2222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i32200-200-1-11100000000000−i3i3000
χ2022222-12-22-2222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-20020011-1-100000000000i3−i3000
χ2122222-12-22-2222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i32200-200-1-11100000000000i3−i3000
χ2222222-12-22-2222-1-1-1-1-2-1-1-12-211-1-1-12-1-1-1-200-2111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-20020011-1-100000000000−i3i3000
χ232222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100220220000-1-1-1-1000000000-1-10
χ242222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-122-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100-2-20-2-200001111000000000110
χ252222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100220-2-200001111000000000-1-10
χ262222-122222-1-1-1222-12-1-1-1-1-1222-1-1-12-1-1-1-2-2-12-1-1-1-11111-2-21111-2-2111100-2-20220000-1-1-1-1000000000110
χ272222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−3002-2000000033−3−3000000000-110
χ282222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-133−3−30033−3−30033−3−300-220000000−3−3330000000001-10
χ292222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−333002-20000000−3−333000000000-110
χ302222-12-2-2-2-2-1-1-1222-12-1-1-111-2-2-2111-211100-1211-1-1−3−33300−3−33300−3−33300-22000000033−3−30000000001-10
χ3122-2-22220-202-2-2-22-2202-2-22000222-2-2-2-200000000000000000000000002i−2i000−i2i22i−2i00−i2i2−i2i20022−2−2000000
χ3222-2-22220-202-2-2-22-2202-2-22000222-2-2-2-200000000000000000000000002i−2i000i2−i22i−2i00i2−i2i2−i200−2−222000000
χ3322-2-22220-202-2-2-22-2202-2-22000222-2-2-2-20000000000000000000000000−2i2i000−i2i2−2i2i00−i2i2−i2i200−2−222000000
χ3422-2-22220-202-2-2-22-2202-2-22000222-2-2-2-20000000000000000000000000−2i2i000i2−i2−2i2i00i2−i2i2−i20022−2−2000000
χ352-22-222020-2-22-22-2-220-22-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000002i−2i2−22−2000000
χ362-22-222020-2-22-22-2-220-22-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000−2i2i−22−22000000
χ372-22-222020-2-22-22-2-220-22-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000002i−2i−22−22000000
χ382-22-222020-2-22-22-2-220-22-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000−2i2i2−22−2000000
χ3944444-2-44-44444-2-2-2-2-4-2-2-2-44-2-2222-4222400-42-2-2220000000000000000000000000000000000000000000
χ4044444-2-4-4-4-4444-2-2-2-24-2-2-2-4-422222-4222-4004-222-2-20000000000000000000000000000000000000000000
χ414444-244-44-4-2-2-2444-2-4-2-2-2-22-4-44-2-2-24-2-22002-422220000000000000000000000000000000000000000000
χ424444-24-44-44-2-2-2444-2-4-2-2-22-244-4222-422-2002-4-2-2220000000000000000000000000000000000000000000
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
χ454444-2-24-44-4-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000
χ464444-2-24-44-4-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000
χ474444-2-2-44-44-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ484444-2-2-44-44-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ494444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1112323−23−2300−3−33300−3−333000000000000000000000000000
χ504444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-111−23−2323230033−3−30033−3−3000000000000000000000000000
χ5144-4-444-40404-4-4-44-4404-4-4-4000-4-4-444440000000000000000000000000000000000000000000000000000
χ5244-4-44-240-404-4-42-22-20-2224000-2-2-2-422200000000000000000000000004i−4i00000−2i2i000000000000000000
χ5344-4-44-240-404-4-42-22-20-2224000-2-2-2-42220000000000000000000000000−4i4i000002i−2i000000000000000000
χ5444-4-44-2-40404-4-42-22-20-222-40002224-2-2-20000000000000000000000000000000000−2i32i30000000000000000
χ5544-4-44-2-40404-4-42-22-20-222-40002224-2-2-200000000000000000000000000000000002i3−2i30000000000000000
χ5644-4-4-2440-40-222-44-4-20-222-20004-2-22-422000000000000000000000000000000−2i22i20000i2−i2i2−i2000000000000
χ5744-4-4-2440-40-222-44-4-20-222-20004-2-22-4220000000000000000000000000000002i2−2i20000−i2i2−i2i2000000000000
χ5844-4-4-24-4040-222-44-4-20-2222000-422-24-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ5944-4-4-24-4040-222-44-4-20-2222000-422-24-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ604-44-4440-404-44-44-4-440-44-40-4-44000000040000-44000000000000000000000000000000000000000000000
χ614-44-44-2040-4-44-4-222-202-2204-220000000-4−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000
χ624-44-44-2040-4-44-4-222-202-2204-220000000-42i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000
χ634-44-44-20-404-44-4-222-202-220-42-20000000400002-20000006−66−66−6−66−66−66000000000000000000000000000
χ644-44-44-20-404-44-4-222-202-220-42-20000000400002-2000000−66−66−666−66−66−6000000000000000000000000000
χ654-44-4-24040-42-224-4-4-202-220-24-400000002−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000
χ664-44-4-24040-42-224-4-4-202-220-24-4000000022i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000
χ674-44-4-240-4042-224-4-4-202-2202-440000000-200002-200i6−i6−i6i600i6−i6−i6i600i6−i6−i6i6000000000000000000000000000
χ684-44-4-240-4042-224-4-4-202-2202-440000000-200002-200−i6i6i6−i600−i6i6i6−i600−i6i6i6−i6000000000000000000000000000
χ694-44-4-2-2040-42-22-22210-11-10-2-2203i−3i003i−3i2−2i22i2001-13i−3ii2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000
χ704-44-4-2-2040-42-22-22210-11-10-2-2203i−3i003i−3i22i2−2i2001-13i−3i−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000
χ714-44-4-2-2040-42-22-22210-11-10-2-220−3i3i00−3i3i2−2i22i2001-1−3i3ii2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000
χ724-44-4-2-2040-42-22-22210-11-10-2-220−3i3i00−3i3i22i2−2i2001-1−3i3i−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000
χ734-44-4-2-20-4042-22-22210-11-1022-203i−3i003i−3i-20000-11−3i3ii6−i6−i6i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ136−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ744-44-4-2-20-4042-22-22210-11-1022-203i−3i003i−3i-20000-11−3i3i−i6i6i6−i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ754-44-4-2-20-4042-22-22210-11-1022-20−3i3i00−3i3i-20000-113i−3ii6−i6−i6i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ764-44-4-2-20-4042-22-22210-11-1022-20−3i3i00−3i3i-20000-113i−3i−i6i6i6−i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ236−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ774-4-44440000-4-44-4-4440-4-44000000000000000000000000000000000000000000000000000002-2-22000000
χ784-4-44440000-4-44-4-4440-4-4400000000000000000000000000000000000000000000000000000-222-2000000
χ7988-8-8-4-480-80-4444-44202-2-2-4000-42244-2-20000000000000000000000000000000000000000000000000000
χ8088-8-8-4-4-8080-4444-44202-2-240004-2-2-4-4220000000000000000000000000000000000000000000000000000
χ818-8-888-40000-8-8844-4-4044-4000000000000000000000000000000000000000000000000000000000000000
χ828-8-88-48000044-4-8-88-4044-4000000000000000000000000000000000000000000000000000000000000000
χ838-8-88-4-4000044-444-420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ848-8-88-4-4000044-444-420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000

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