Finite Group Databasebeta

← Group #11780119

Character table — Group #11780119

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444488888888888888888888888121212121212121212121212121212122424242424242424242448484872727272
order122233444466666612121212346661212121212121212121212128812121212122424242424242424242424242424242422448888242424242424242424666612121212412124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1111-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111111-1-1-1-1
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
χ61111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111-1-111
χ71111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-111-1-111-1-1-1-1-111
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
χ92222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-200000000000000000022000000000000-2000-2-200220000000
χ102222222-22-222222222222-22222-2-2-2-222222-2-200-2-2-2-2-2000000000000000000-2-200000000000020002200-2-20000000
χ11222222-22-22222222-2-2-2-22-2222-22222-2-2-2-2-2-2-200-222-2-2000000000000000022000000000000000-22200-2-2000000000
χ12222222-22-22222222-2-2-2-22-2222-22222-2-2-2-2-2-2-200-222-2-20000000000000000-2-20000000000000002-2-20022000000000
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
χ1522222-1222222-1-12-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220000000000002000-1-100-1-12-1-10000
χ1622222-1222222-1-12-12222-12-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2000000000000-2000110011-2110000
χ1722222-1222222-1-12-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100220000000000002000-1-100-1-1-2110000
χ1822222-1222222-1-12-12222-12-1-1-1-122-1-1-1-1-1-1-122-2-2-1-1-1-1-1-2-2-2-211111111111100-2-2000000000000-20001100112-1-10000
χ1922222-12-22-222-1-12-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i30022000000000000-20001100-1-10−i3i30000
χ2022222-12-22-222-1-12-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i300-2-20000000000002000-1-100110i3−i30000
χ2122222-12-22-222-1-12-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i30022000000000000-20001100-1-10i3−i30000
χ2222222-12-22-222-1-12-12222-1-2-1-1-1-1-2-211-1-1-1-1-1-2-200111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i300-2-20000000000002000-1-100110−i3i30000
χ232222-122222-1-122-12-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122002222-1-1-1-1-1-1-1-102-1-100-1-1000000000
χ242222-122222-1-122-12-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-200-2-2-2-2111111110-2110011000000000
χ252222-122222-1-122-12-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-211112200-2-2-2-21111111102-1-100-1-1000000000
χ262222-122222-1-122-12-1-1-1-1-12-1-1-12-1-122-1-12-1-1-1-1-2-22-1-1-1-11111-2-21111-2-21111-2-2002222-1-1-1-1-1-1-1-10-2110011000000000
χ272222-12-22-22-1-122-121111-1-2-1-1-1-2-1-12211-2111100-2-1-11133−3−30033−3−30033−3−3220000003333−3−3−3−30-2-1-10011000000000
χ282222-12-22-22-1-122-121111-1-2-1-1-1-2-1-12211-2111100-2-1-11133−3−30033−3−30033−3−3-2-2000000−3−3−3−33333021100-1-1000000000
χ292222-12-22-22-1-122-121111-1-2-1-1-1-2-1-12211-2111100-2-1-111−3−33300−3−33300−3−33322000000−3−3−3−333330-2-1-10011000000000
χ302222-12-22-22-1-122-121111-1-2-1-1-1-2-1-12211-2111100-2-1-111−3−33300−3−33300−3−333-2-20000003333−3−3−3−3021100-1-1000000000
χ312-22-222-2020-2-22-22-2-2-222202-2-2-20000-2-22220000000000000000000000000002i−2i22−2−222−2−222−2−2000000002i−2i00000−i2i2
χ322-22-222-2020-2-22-22-2-2-222202-2-2-20000-2-22220000000000000000000000000002i−2i−2−222−2−222−2−222000000002i−2i00000i2−i2
χ332-22-222-2020-2-22-22-2-2-222202-2-2-20000-2-2222000000000000000000000000000−2i2i22−2−222−2−222−2−200000000−2i2i00000i2−i2
χ342-22-222-2020-2-22-22-2-2-222202-2-2-20000-2-2222000000000000000000000000000−2i2i−2−222−2−222−2−22200000000−2i2i00000−i2i2
χ352-2-22220-2022-2-2-2-22000020-22-202-22-200000002−202-2002−22−22−22−22−22−22−22−22-2002−22−22−22−22−22−2002-20000000000000
χ362-2-22220-2022-2-2-2-22000020-22-202-22-200000002−202-2002−22−22−22−22−22−22−22−2-2200−22−22−22−22−22−2200-220000000000000
χ372-2-22220-2022-2-2-2-22000020-22-202-22-20000000−2202-200−22−22−22−22−22−22−22−222-200−22−22−22−22−22−22002-20000000000000
χ382-2-22220-2022-2-2-2-22000020-22-202-22-20000000−2202-200−22−22−22−22−22−22−22−22-22002−22−22−22−22−22−200-220000000000000
χ392-2-22-120-202-11-2-2123−33−3-101-110-112-23−303−33−32−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232-2002−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300-11003−3000000000
χ402-2-22-120-202-11-2-2123−33−3-101-110-112-23−303−33−32−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23-2200−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23001-100−33000000000
χ412-2-22-120-202-11-2-2123−33−3-101-110-112-23−303−33−3−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ232-200−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300-11003−3000000000
χ422-2-22-120-202-11-2-2123−33−3-101-110-112-23−303−33−3−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23-22002−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23001-100−33000000000
χ432-2-22-120-202-11-2-212−33−33-101-110-112-2−330−33−332−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72-2002−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700-1100−33000000000
χ442-2-22-120-202-11-2-212−33−33-101-110-112-2−330−33−332−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7-2200−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7001-1003−3000000000
χ452-2-22-120-202-11-2-212−33−33-101-110-112-2−330−33−33−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ72-200−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700-1100−33000000000
χ462-2-22-120-202-11-2-212−33−33-101-110-112-2−330−33−33−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7-22002−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7001-1003−3000000000
χ4744444-2-44-4444-2-24-2-4-4-4-4-2-4-2-2-2244-2-222222-4-4002-2-2220000000000000000000000000000000000000000000000000
χ4844444-2-4-4-4-444-2-24-2-4-4-4-4-24-2-2-22-4-422222224400-222-2-20000000000000000000000000000000000000000000000000
χ494444-244-44-4-2-244-24-2-2-2-2-2-4-2-2-2422-4-4-2-24-2-22200-422220000000000000000000000000000000000000000000000000
χ504444-24-4-4-4-4-2-244-242222-24-2-2-2-422-4-422-422-2-200422-2-20000000000000000000000000000000000000000000000000
χ514444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-244-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2-4-4-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-10000−2i3−2i3i3i3i3i32i32i3−i3−i3−i3−i3000000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-2-2-2-2-21-4111-2222211-21122002-1-1-1-100002i32i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3000000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-222221-41112-2-2-2-2-1-12-1-12200211-1-12323−23−2300−3−33300−3−333000000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-222221-41112-2-2-2-2-1-12-1-12200211-1-1−23−2323230033−3−30033−3−3000000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-1110000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-222221411122222-1-12-1-1-2-200-2-1-111000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000000000
χ5944-4-4440000-44-44-4-4000040-4-440000000000000000000000000000000000000002-2-222-2-222-2-2200000000000000000
χ6044-4-4440000-44-44-4-4000040-4-44000000000000000000000000000000000000000-222-2-222-2-222-200000000000000000
χ6144-4-4-2400002-2-442-423−23−2323-2022-20000023−230−2323000000000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000
χ6244-4-4-2400002-2-442-423−23−2323-2022-20000023−230−232300000000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000
χ6344-4-4-2400002-2-442-4−232323−23-2022-200000−2323023−23000000000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000
χ6444-4-4-2400002-2-442-4−232323−23-2022-200000−2323023−2300000000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000
χ654-44-44440-40-4-44-44-444-4-4404-4-44000044-4-4-40000000000000000000000000000000000000000000000000000000000
χ664-44-44-240-40-4-4-224244-4-4-20-222-20000-2-2222000000000000000000000000000000000000000000000−2i32i300000000000
χ674-44-44-240-40-4-4-224244-4-4-20-222-20000-2-22220000000000000000000000000000000000000000000002i3−2i300000000000
χ684-44-44-2-4040-4-4-2242-4-444-20-2222000022-2-2-20000000000000000000000000004i−4i00000000000000000000−2i2i0000000
χ694-44-44-2-4040-4-4-2242-4-444-20-2222000022-2-2-2000000000000000000000000000−4i4i000000000000000000002i−2i0000000
χ704-44-4-2440-40224-4-2-4-2-222-20-22240000-2-2-42200000000000000000000000000000000066−6−6−6−66600000000000000000
χ714-44-4-2440-40224-4-2-4-2-222-20-22240000-2-2-422000000000000000000000000000000000−6−66666−6−600000000000000000
χ724-44-4-24-4040224-4-2-422-2-2-20-222-40000224-2-2000000000000000000000000000002222−22−22−2−222−2−22200000000000000000
χ734-44-4-24-4040224-4-2-422-2-2-20-222-40000224-2-200000000000000000000000000000−22−22222222−2−222−2−200000000000000000
χ744-4-4444040-44-4-4-4-44000040-44-40-44-440000000000-44000000000000000000000000000000000000000000000000000
χ754-4-444-2040-44-422-4-20000-202-220-442-200000000002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000000000
χ764-4-444-2040-44-422-4-20000-202-220-442-200000000002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000000000
χ774-4-444-20-4044-422-4-20000-202-2204-4-22000000022−220-220022−2222−22−22−22−22−22−22−22000000000000000000000000000000000
χ784-4-444-20-4044-422-4-20000-202-2204-4-220000000−22220-2200−2222−22222−22−22−22−22−22−2000000000000000000000000000000000
χ794-4-44-24040-4-22-4-42423−2323−23-202-2202-2-4423−23023−23−23230002-2−23230000000000000000000000000000000000000000000000000
χ804-4-44-24040-4-22-4-424−2323−2323-202-2202-2-44−23230−232323−230002-223−230000000000000000000000000000000000000000000000000
χ814-4-44-2-2040-4-22222-223−2323−2310-11-102-22-2−330−33−2323000-113−30000i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23000000000000000000000000000000000
χ824-4-44-2-2040-4-22222-223−2323−2310-11-102-22-2−330−33−2323000-113−30000−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23000000000000000000000000000000000
χ834-4-44-2-2040-4-22222-2−2323−232310-11-102-22-23−303−323−23000-11−330000i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23000000000000000000000000000000000
χ844-4-44-2-2040-4-22222-2−2323−232310-11-102-22-23−303−323−23000-11−330000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23000000000000000000000000000000000
χ854-4-44-2-20-404-22222-223−2323−2310-11-10-22-22−330−3323−2322−2201-1−332ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000000000000000000000000
χ864-4-44-2-20-404-22222-223−2323−2310-11-10-22-22−330−3323−23−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000000000000000000000000
χ874-4-44-2-20-404-22222-2−2323−232310-11-10-22-223−303−3−232322−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000000000000000000000000
χ884-4-44-2-20-404-22222-2−2323−232310-11-10-22-223−303−3−2323−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000000000000000000000000
χ8988-8-88-40000-884-4-840000-4044-400000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-400004-44-44443−43−434320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-400004-44-444−434343−4320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000
χ928-88-8-4-480-8044-44-44-4-444202-2-2-40000224-2-20000000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-808044-44-4444-4-4202-2-240000-2-2-4220000000000000000000000000000000000000000000000000000000000

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