Finite Group Databasebeta

← Group #11780117

Character table — Group #11780117

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212122424242424242424242424243636484848727272
order12223344446666661212121234446661212121212121212121212122666666661212121212121212121212121288882424242424242424888824242424242424242241212444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ5111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-11-1-1
χ6111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111
χ7111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ92222222-22-2222222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2222222-2-2222200000000000000000000000000000000
χ102222222-22-2222222-2-2-2-22-2-2-2222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000
χ11222222-22-222222222222200-2222-2-2-2222222-2-2-2000000000-20000-2-2-2-2000000000000000000000000000022000-200
χ12222222-22-222222222222200-2222-2-2-2222222-2-2-2000000000-20000-2-2-2-20000000000000000000000000000-2-2000200
χ13222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-200000000020000-2-22200000000000000000000000000000000002-2
χ14222222-2-2-2-2222222-2-2-2-22002222-2-2-2-2-2-2-2-2-222-200000000020000-2-2220000000000000000000000000000000000-22
χ1522222-1222222-1-12-12222-1222-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1002-1-1000
χ1622222-1222222-1-12-12222-1222-1-1-122-1-1-1-1-1-1-122-1222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000-2-20000111100-211000
χ1722222-1222222-1-12-12222-1-2-22-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000220000-1-1-1-100-211000
χ1822222-1222222-1-12-12222-1-2-22-1-1-122-1-1-1-1-1-1-122-1-2-2-2111111-1-2-211-1-1-1-1111100000000000000-2-200001111002-1-1000
χ1922222-12-22-222-1-12-1-2-2-2-2-122-2-1-1-122-1111111-2-2-1-2-2-2111111122-1-1-1-111-1-1-1-100000000000000000000−i3−i3i3i3000−i3i3000
χ2022222-12-22-222-1-12-1-2-2-2-2-122-2-1-1-122-1111111-2-2-1-2-2-2111111122-1-1-1-111-1-1-1-100000000000000000000i3i3−i3−i3000i3−i3000
χ2122222-12-22-222-1-12-1-2-2-2-2-1-2-2-2-1-1-122-1111111-2-2-1222-1-1-1-1-1-11-2-211-1-111111100000000000000000000−i3−i3i3i3000i3−i3000
χ2222222-12-22-222-1-12-1-2-2-2-2-1-2-2-2-1-1-122-1111111-2-2-1222-1-1-1-1-1-11-2-211-1-111111100000000000000000000i3i3−i3−i3000−i3i3000
χ232222-122222-1-122-12-1-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200-1-1-1-1000000000000
χ242222-122222-1-122-12-1-1-1-1-1222-1-1-1-1-1222-1-1-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2001111000000000000
χ252222-122222-1-122-12-1-1-1-1-1-2-22-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2001111000000000000
χ262222-122222-1-122-12-1-1-1-1-1-2-22-1-1-1-1-1222-1-1-1-1-1-12-211-2-21111211-2-2-1-1-1-11111-2-2-2-2111111112200-1-1-1-1000000000000
χ272222-122-22-2-1-122-121111-122-2-1-1-1-1-12-2-21111112-211-2-21111-2-1-122-1-111-1-1-1-100003333−3−3−3−3000033−3−3000000000000
χ282222-122-22-2-1-122-121111-122-2-1-1-1-1-12-2-21111112-211-2-21111-2-1-122-1-111-1-1-1-10000−3−3−3−333330000−3−333000000000000
χ292222-122-22-2-1-122-121111-1-2-2-2-1-1-1-1-12-2-211111122-1-122-1-1-1-1-211-2-2-1-111111100003333−3−3−3−30000−3−333000000000000
χ302222-122-22-2-1-122-121111-1-2-2-2-1-1-1-1-12-2-211111122-1-122-1-1-1-1-211-2-2-1-11111110000−3−3−3−33333000033−3−3000000000000
χ312-22-222-20202-22-2-2-2000022i−2i02-2-22-2-200000000200000000002i−2i2i−2i2-2002i2i−2i−2i22−2−222−2−222−2−2−i2i200−i2i2−i2i2000000000000
χ322-22-222-20202-22-2-2-2000022i−2i02-2-22-2-200000000200000000002i−2i2i−2i2-2002i2i−2i−2i−2−222−2−222−2−222i2−i200i2−i2i2−i2000000000000
χ332-22-222-20202-22-2-2-200002−2i2i02-2-22-2-20000000020000000000−2i2i−2i2i2-200−2i−2i2i2i22−2−222−2−222−2−2i2−i200i2−i2i2−i2000000000000
χ342-22-222-20202-22-2-2-200002−2i2i02-2-22-2-20000000020000000000−2i2i−2i2i2-200−2i−2i2i2i−2−222−2−222−2−222−i2i200−i2i2−i2i2000000000000
χ352-22-2-12-2020-112-21-23−33−3-12i−2i0-111-11-20033−3−33−320−i3i300−i3−i3i3i30−ii2i−2i-113−3−i−iii22−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ362-22-2-12-2020-112-21-23−33−3-12i−2i0-111-11-20033−3−33−320−i3i300−i3−i3i3i30−ii2i−2i-113−3−i−iii−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ372-22-2-12-2020-112-21-23−33−3-1−2i2i0-111-11-20033−3−33−320i3−i300i3i3−i3−i30i−i−2i2i-113−3ii−i−i22−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23i2−i200−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ382-22-2-12-2020-112-21-23−33−3-1−2i2i0-111-11-20033−3−33−320i3−i300i3i3−i3−i30i−i−2i2i-113−3ii−i−i−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−i2i200ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ392-22-2-12-2020-112-21-2−33−33-12i−2i0-111-11-200−3−333−3320i3−i300i3i3−i3−i30−ii2i−2i-11−33−i−iii22−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ402-22-2-12-2020-112-21-2−33−33-12i−2i0-111-11-200−3−333−3320i3−i300i3i3−i3−i30−ii2i−2i-11−33−i−iii−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ412-22-2-12-2020-112-21-2−33−33-1−2i2i0-111-11-200−3−333−3320−i3i300−i3−i3i3i30i−i−2i2i-11−33ii−i−i22−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7i2−i200−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ422-22-2-12-2020-112-21-2−33−33-1−2i2i0-111-11-200−3−333−3320−i3i300−i3−i3i3i30i−i−2i2i-11−33ii−i−i−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−i2i200ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ432-2-22220-202-2-2-2-222-2-2222000-2-220002-22-22-200000000000000000000000002−22−22−22−22−22−2002−200002−22−22-2000000
χ442-2-22220-202-2-2-2-222-2-2222000-2-220002-22-22-200000000000000000000000002−22−22−22−22−22−200−220000−22−22-22000000
χ452-2-22220-202-2-2-2-222-2-2222000-2-220002-22-22-20000000000000000000000000−22−22−22−22−22−22002−200002−22−2-22000000
χ462-2-22220-202-2-2-2-222-2-2222000-2-220002-22-22-20000000000000000000000000−22−22−22−22−22−2200−220000−22−222-2000000
χ4744444-2-44-4444-2-24-24444-200-4-2-2-2-4-42-2-2-2-2-2-2-4-42000000000200002222000000000000000000000000000000000000
χ4844444-2-4-4-4-444-2-24-2-4-4-4-4-2004-2-2-2-4-42222222442000000000-2000022-2-2000000000000000000000000000000000000
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χ514444-2-24444-2-2-2-2-2-2-2-2-2-21444111-2-2-2-2-21111-2-2-24-2-2-2-21111-2-2-2-2-21111111100000000000000000000000000000000
χ524444-2-24444-2-2-2-2-2-2-2-2-2-21-4-44111-2-2-2-2-21111-2-2-2-42222-1-1-1-1-222221111-1-1-1-100000000000000000000000000000000
χ534444-2-24-44-4-2-2-2-2-2-22222144-4111-2-2-222-1-1-1-122-2-42222-1-1-1-12-2-2-2-211-1-1111100000000000000000000000000000000
χ544444-2-24-44-4-2-2-2-2-2-222221-4-4-4111-2-2-222-1-1-1-122-24-2-2-2-211112222211-1-1-1-1-1-100000000000000000000000000000000
χ554444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111222-2-21111222000003-33-320000-1-1-1-13-33-300000000000000000000000000000000
χ564444-2-2-44-44-2-2-2-2-2-2-2-2-2-2100-4111222-2-2111122200000-33-3320000-1-1-1-1-33-3300000000000000000000000000000000
χ574444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222-1-1-1-1-2-22000003-33-3-20000-1-111-33-3300000000000000000000000000000000
χ584444-2-2-4-4-4-4-2-2-2-2-2-22222100411122222-1-1-1-1-2-2200000-33-33-20000-1-1113-33-300000000000000000000000000000000
χ5944-4-4440000-44-44-4-400004000-44-400000000000000000000000000000000002-2-222-2-222-2-2200000000000000000000
χ6044-4-4440000-44-44-4-400004000-44-40000000000000000000000000000000000-222-2-222-2-222-200000000000000000000
χ6144-4-4-2400002-2-442-423−23−2323-20002-2200000−232323−2300000000000000000000000002-2-22−1−31+31+3−1−3−1+31−31−3−1+300000000000000000000
χ6244-4-4-2400002-2-442-423−23−2323-20002-2200000−232323−230000000000000000000000000-222-21+3−1−3−1−31+31−3−1+3−1+31−300000000000000000000
χ6344-4-4-2400002-2-442-4−232323−23-20002-220000023−23−232300000000000000000000000002-2-22−1+31−31−3−1+3−1−31+31+3−1−300000000000000000000
χ6444-4-4-2400002-2-442-4−232323−23-20002-220000023−23−23230000000000000000000000000-222-21−3−1+3−1+31−31+3−1−3−1−31+300000000000000000000
χ654-44-44440-404-44-4-4-4000040004-4-4-44400000000-400000000000000-4400000000000000000000000000000000000000
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χ684-44-44-2-40404-4-22-420000-24i−4i0-2224-4200000000-200000000004i−4i−2i2i-2200−2i−2i2i2i00000000000000000000000000000000
χ694-44-44-2-40404-4-22-420000-2−4i4i0-2224-4200000000-20000000000−4i4i2i−2i-22002i2i−2i−2i00000000000000000000000000000000
χ704-44-4-2440-40-224-42-423−2323−23-2000-2222-24002323−23−23−2323-4000000000000002-2−2323000000000000000000000000000000000000
χ714-44-4-2440-40-224-42-4−2323−2323-2000-2222-2400−23−23232323−23-4000000000000002-223−23000000000000000000000000000000000000
χ724-44-4-2-240-40-22-222223−2323−2310001-1-12-2-200−3−333−23232000−2i32i3i3−i3−i3i300000-113−3−3i3i3i−3i00000000000000000000000000000000
χ734-44-4-2-240-40-22-222223−2323−2310001-1-12-2-200−3−333−232320002i3−2i3−i3i3i3−i300000-113−33i−3i−3i3i00000000000000000000000000000000
χ744-44-4-2-240-40-22-2222−2323−232310001-1-12-2-20033−3−323−232000−2i32i3i3−i3−i3i300000-11−333i−3i−3i3i00000000000000000000000000000000
χ754-44-4-2-240-40-22-2222−2323−232310001-1-12-2-20033−3−323−2320002i3−2i3−i3i3i3−i300000-11−33−3i3i3i−3i00000000000000000000000000000000
χ764-44-4-2-2-4040-22-222223−2323−2314i−4i01-1-1-22200−3−33323−23-20−2i32i300i3i3−i3−i30−2i2i−2i2i1-1−33ii−i−i00000000000000000000000000000000
χ774-44-4-2-2-4040-22-222223−2323−231−4i4i01-1-1-22200−3−33323−23-202i3−2i300−i3−i3i3i302i−2i2i−2i1-1−33−i−iii00000000000000000000000000000000
χ784-44-4-2-2-4040-22-2222−2323−232314i−4i01-1-1-2220033−3−3−2323-202i3−2i300−i3−i3i3i30−2i2i−2i2i1-13−3ii−i−i00000000000000000000000000000000
χ794-44-4-2-2-4040-22-2222−2323−23231−4i4i01-1-1-2220033−3−3−2323-20−2i32i300i3i3−i3−i302i−2i2i−2i1-13−3−i−iii00000000000000000000000000000000
χ804-4-4444040-4-4-4-4-44444-4-44000-4-44000-44-44-44000000000000000000000000000000000000000000000000000000000
χ814-4-444-2040-4-4-4224-244-4-4-200022-20002-22-22-2000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ824-4-444-2040-4-4-4224-244-4-4-200022-20002-22-22-2000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ834-4-444-20-404-4-4224-2-4-444-200022-2000-22-22-2200000000000000000000000000000000000000022−220000−22−2200000000
χ844-4-444-20-404-4-4224-2-4-444-200022-2000-22-22-22000000000000000000000000000000000000000−222200002−22−200000000
χ854-4-44-24040-422-4-4-24-2-222-200022-2000-442-22-2000000000000000000000000000006−66−6−66−6600000000000000000000
χ864-4-44-24040-422-4-4-24-2-222-200022-2000-442-22-200000000000000000000000000000−66−666−66−600000000000000000000
χ874-4-44-240-40422-4-4-2422-2-2-200022-20004-4-22-22000000000000000000000000022−2222−22−22−22−22−2200000000000000000000
χ884-4-44-240-40422-4-4-2422-2-2-200022-20004-4-22-220000000000000000000000000−2222−22222−22−22−22−200000000000000000000
χ8988-8-88-40000-884-4-840000-40004-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-400004-44-44443−43−43432000-22-20000023−23−2323000000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-400004-44-444−434343−432000-22-200000−232323−23000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-4080-84444-4-4-4-4442000-2-220004-4-22-22000000000000000000000000000000000000000000000000000000000
χ938-8-88-4-40-8084444-4-444-4-42000-2-22000-442-22-2000000000000000000000000000000000000000000000000000000000

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