Finite Group Databasebeta

← Group #11780207

Character table — Group #11780207

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444488888888888888888888888121212121212121212121212121212122424242424242424242448484872727272
order12223344446666661212121234666121212121212121212121212881212121212242424242424242424242424242424242244888824242424242424244466121212121212412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1
χ61111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111-1-111
χ71111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-11111-1-1-1-1-111
χ81111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1
χ92222222-2-22222222-2-2-2-22-22222222-2-2-2-2-2-2-2-200-222-2-2000000000000000022000000000000000-222-2-200000000000
χ102222222-2-22222222-2-2-2-22-22222222-2-2-2-2-2-2-2-200-222-2-20000000000000000-2-20000000000000002-2-22200000000000
χ11222222-222-222222222222-2222-2-2-2-2222222-2-200-2-2-2-2-200000000000000000022000000000000-200000-2-2220000000
χ12222222-222-222222222222-2222-2-2-2-2222222-2-200-2-2-2-2-2000000000000000000-2-200000000000020000022-2-20000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-222002-2-2220000000000000000000000000000000000000000000002-200
χ14222222-2-2-2-2222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-222002-2-222000000000000000000000000000000000000000000000-2200
χ1522222-122222-1-12-12-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-102-1-1-1-100000000000
χ1622222-122222-1-12-12-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2-2-2111111110-2111100000000000
χ1722222-122222-1-12-12-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-22-1-1-1-11111-2-2-2-2111111112200-2-2-2-21111111102-1-1-1-100000000000
χ1822222-122222-1-12-12-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-22-1-1-1-11111-2-2-2-211111111-2-2002222-1-1-1-1-1-1-1-10-2111100000000000
χ1922222-12-2-222-1-12-121111-1-2-1-1-122-1-1-211-2111100-2-1-11133−3−300003333−3−3−3−3220000003333−3−3−3−30-2-1-11100000000000
χ2022222-12-2-222-1-12-121111-1-2-1-1-122-1-1-211-2111100-2-1-11133−3−300003333−3−3−3−3-2-2000000−3−3−3−333330211-1-100000000000
χ2122222-12-2-222-1-12-121111-1-2-1-1-122-1-1-211-2111100-2-1-111−3−3330000−3−3−3−3333322000000−3−3−3−333330-2-1-11100000000000
χ2222222-12-2-222-1-12-121111-1-2-1-1-122-1-1-211-2111100-2-1-111−3−3330000−3−3−3−33333-2-20000003333−3−3−3−30211-1-100000000000
χ232222-122222-122-12-12222-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022000000000000200000-1-1-1-12-1-10000
χ242222-122222-122-12-12222-12-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2000000000000-2000001111-2110000
χ252222-122222-122-12-12222-12-1-1-1-1-122-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-21111111111110022000000000000200000-1-1-1-1-2110000
χ262222-122222-122-12-12222-12-1-1-1-1-122-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100-2-2000000000000-20000011112-1-10000
χ272222-12-222-2-122-12-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30022000000000000-20000011-1-10−i3i30000
χ282222-12-222-2-122-12-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300-2-2000000000000200000-1-1110i3−i30000
χ292222-12-222-2-122-12-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30022000000000000-20000011-1-10i3−i30000
χ302222-12-222-2-122-12-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-200111110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300-2-2000000000000200000-1-1110−i3i30000
χ3122-2-222200-222-2-2-2-20000202-2-22-22-2000000002−202-2002−22−22−22−22−22−22−22−22-20022−2−222−2−222−2−2002-20000000000000
χ3222-2-222200-222-2-2-2-20000202-2-22-22-2000000002−202-2002−22−22−22−22−22−22−22−2-2200−2−222−2−222−2−22200-220000000000000
χ3322-2-222200-222-2-2-2-20000202-2-22-22-200000000−2202-200−22−22−22−22−22−22−22−222-200−2−222−2−222−2−222002-20000000000000
χ3422-2-222200-222-2-2-2-20000202-2-22-22-200000000−2202-200−22−22−22−22−22−22−22−22-220022−2−222−2−222−2−200-220000000000000
χ3522-2-22-1200-22-11-21-23−33−3-10-1112-2-1103−303−33−32−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232-20022−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300-113−300000000000
χ3622-2-22-1200-22-11-21-23−33−3-10-1112-2-1103−303−33−32−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-2200−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23001-1−3300000000000
χ3722-2-22-1200-22-11-21-23−33−3-10-1112-2-1103−303−33−3−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232-200−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300-113−300000000000
χ3822-2-22-1200-22-11-21-23−33−3-10-1112-2-1103−303−33−3−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-220022−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23001-1−3300000000000
χ3922-2-22-1200-22-11-21-2−33−33-10-1112-2-110−330−33−332−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72-20022−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700-11−3300000000000
χ4022-2-22-1200-22-11-21-2−33−33-10-1112-2-110−330−33−332−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-2200−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7001-13−300000000000
χ4122-2-22-1200-22-11-21-2−33−33-10-1112-2-110−330−33−33−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72-200−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700-11−3300000000000
χ4222-2-22-1200-22-11-21-2−33−33-10-1112-2-110−330−33−33−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-220022−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7001-13−300000000000
χ432-2-22220-220-2-2-2-222-2-22220-22-20000-2-2-22220000000000000000000000000002-22−22−22−22−22−22−2000000002-2000002−2
χ442-2-22220-220-2-2-2-222-2-22220-22-20000-2-2-22220000000000000000000000000002-2−22−22−22−22−22−22000000002-200000−22
χ452-2-22220-220-2-2-2-222-2-22220-22-20000-2-2-2222000000000000000000000000000-222−22−22−22−22−22−200000000-2200000−22
χ462-2-22220-220-2-2-2-222-2-22220-22-20000-2-2-2222000000000000000000000000000-22−22−22−22−22−22−2200000000-22000002−2
χ4744444-2-444-44-2-24-24-2-2-2-2-2-4-2-2-2-4-4224-2-24-2-22200-422220000000000000000000000000000000000000000000000000
χ4844444-2-4-4-4-44-2-24-242222-24-2-2-2-4-422-422-422-2-200422-2-20000000000000000000000000000000000000000000000000
χ494444-244-4-44-244-24-2-4-4-4-4-2-4-2-2-2-2-244222222-4-4002-2-2220000000000000000000000000000000000000000000000000
χ504444-24-4-4-4-4-244-24-2-4-4-4-4-24-2-2-222-4-42222224400-222-2-20000000000000000000000000000000000000000000000000
χ514444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-244-21111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2-4-4-2111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ534444-2-24-4-44-2-2-2-2-2-222221-4111-2-2-2-22-1-12-1-12200211-1-12323−23−230000−3−3−3−33333000000000000000000000000000000000
χ544444-2-24-4-44-2-2-2-2-2-222221-4111-2-2-2-22-1-12-1-12200211-1-1−23−23232300003333−3−3−3−3000000000000000000000000000000000
χ554444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-41112222-211-21122002-1-1-1-10000−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000
χ564444-2-2-444-4-2-2-2-2-2-2-2-2-2-21-41112222-211-21122002-1-1-1-100002i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-111000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-11100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000000000
χ5944-4-444-400444-4-4-4-40000404-4-4-44-4400000000000-44000000000000000000000000000000000000000000000000000
χ6044-4-44-2-40044-22-42-423−2323−23-20-222-442-2023−23023−23−23230002-2−23230000000000000000000000000000000000000000000000000
χ6144-4-44-2-40044-22-42-4−2323−2323-20-222-442-20−23230−232323−230002-223−230000000000000000000000000000000000000000000000000
χ6244-4-4-24400-4-24-42-420000-20-222-224-40000000022−220-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000000
χ6344-4-4-24400-4-24-42-420000-20-222-224-400000000−22220-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000000
χ6444-4-4-24-4004-24-42-420000-20-2222-2-44000000000002-2000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000
χ6544-4-4-24-4004-24-42-420000-20-2222-2-44000000000002-2000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000
χ6644-4-4-2-2400-4-2-2222223−2323−23101-1-1-22-220−330−3323−2322−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000000000000000000000000
χ6744-4-4-2-2400-4-2-2222223−2323−23101-1-1-22-220−330−3323−23−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000000000000000000000000
χ6844-4-4-2-2400-4-2-22222−2323−2323101-1-1-22-2203−303−3−232322−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000000000000000000000000
χ6944-4-4-2-2400-4-2-22222−2323−2323101-1-1-22-2203−303−3−2323−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000000000000000000000000
χ7044-4-4-2-2-4004-2-2222223−2323−23101-1-12-22-20−330−33−2323000-113−30000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000000
χ7144-4-4-2-2-4004-2-2222223−2323−23101-1-12-22-20−330−33−2323000-113−30000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000000
χ7244-4-4-2-2-4004-2-22222−2323−2323101-1-12-22-203−303−323−23000-11−330000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000000
χ7344-4-4-2-2-4004-2-22222−2323−2323101-1-12-22-203−303−323−23000-11−330000−i6i6i6−i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000000
χ744-44-4440000-4-444-4-4000040-4-440000000000000000000000000000000000000002-2-222-2-222-2-2200000000000000000
χ754-44-4440000-4-444-4-4000040-4-44000000000000000000000000000000000000000-222-2-222-2-222-200000000000000000
χ764-44-44-20000-42-242-423−23−2323-2022-20000023−230−2323000000000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000
χ774-44-44-20000-42-242-423−23−2323-2022-20000023−230−232300000000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000
χ784-44-44-20000-42-242-4−232323−23-2022-200000−2323023−23000000000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000
χ794-44-44-20000-42-242-4−232323−23-2022-200000−2323023−2300000000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000
χ804-4-444404-40-4-4-4-44444-4-440-44-40000444-4-4-40000000000000000000000000000000000000000000000000000000000
χ814-4-444-204-40-422-4-24-2-222-202-2200004-2-2-4220000000000000000000000000000000006−66−6−66−6600000000000000000
χ824-4-444-204-40-422-4-24-2-222-202-2200004-2-2-422000000000000000000000000000000000−66−666−66−600000000000000000
χ834-4-444-20-440-422-4-2422-2-2-202-220000-4224-2-20000000000000000000000000000022−2222−22−22−22−22−2200000000000000000
χ844-4-444-20-440-422-4-2422-2-2-202-220000-4224-2-200000000000000000000000000000−2222−22222−22−22−22−200000000000000000
χ854-4-44-2404-402-4-424-244-4-4-202-220000-2-2-22220000000000000000000000000000000000000000000000023−23000000000
χ864-4-44-2404-402-4-424-244-4-4-202-220000-2-2-222200000000000000000000000000000000000000000000000−2323000000000
χ874-4-44-240-4402-4-424-2-4-444-202-220000222-2-2-20000000000000000000000000004-400000000000000000000-220000000
χ884-4-44-240-4402-4-424-2-4-444-202-220000222-2-2-2000000000000000000000000000-44000000000000000000002-20000000
χ898-88-8-4800004-88-4-840000-4044-400000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-4-4000044-4-44443−43−434320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000
χ918-88-8-4-4000044-4-444−434343−4320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-408-804444-4-4-4-44420-22-20000-4224-2-20000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-40-8804444-4-444-4-420-22-200004-2-2-4220000000000000000000000000000000000000000000000000000000000

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