Finite Group Databasebeta

← Group #11786742

Character table — Group #11786742

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order12222233444466666612121212223446666666121212121212121212126666666666121212121212121212124444121212121212121244888812121212242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-11-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111-1-11-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ71111111111111111111111-1-11-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-11-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1
χ911-1-1-11111-11-1-1-1-111-1-1-1111-111-11-1-1-1-111111-1-111-1-1-111-1-11-111-1-111-1-11-111-1-111-1-11111-1-1-1-1i−i1-1i−iii−i−i11-1-1ii−i−ii−iii−i−ii−i
χ1011-1-1-11111-11-1-1-1-111-1-1-1111-111-11-1-1-1-111111-1-111-1-1-111-1-11-111-1-111-1-11-111-1-111-1-11111-1-1-1-1−ii1-1−ii−i−iii11-1-1−i−iii−ii−i−iii−ii
χ1111-1-1-11111-11-1-1-1-111-1-1-1111-111-11-1-1-1-111111-1-111-1-1-111-1-11-111-1-111-1-11-111-1-1-1-111-1-1-1-11111i−i-11i−iii−i−i-1-111ii−i−i−ii−i−iii−ii
χ1211-1-1-11111-11-1-1-1-111-1-1-1111-111-11-1-1-1-111111-1-111-1-1-111-1-11-111-1-111-1-11-111-1-1-1-111-1-1-1-11111−ii-11−ii−i−iii-1-111−i−iiii−iii−i−ii−i
χ1311-1-1-11111-11-1-1-1-111-1-1-111-111-111-1-1-1-111111-1-111-1-1-1-1-1111-1-1-111-1-1111-1-1-11111-1-11111-1-1-1-1i−i-11−iiii−i−i-1-111−i−iii−iiii−i−i−ii
χ1411-1-1-11111-11-1-1-1-111-1-1-111-111-111-1-1-1-111111-1-111-1-1-1-1-1111-1-1-111-1-1111-1-1-11111-1-11111-1-1-1-1−ii-11i−i−i−iii-1-111ii−i−ii−i−i−iiii−i
χ1511-1-1-11111-11-1-1-1-111-1-1-111-111-111-1-1-1-111111-1-111-1-1-1-1-1111-1-1-111-1-1111-1-1-111-1-111-1-1-1-11111i−i1-1−iiii−i−i11-1-1−i−iiii−i−i−iiii−i
χ1611-1-1-11111-11-1-1-1-111-1-1-111-111-111-1-1-1-111111-1-111-1-1-1-1-1111-1-1-111-1-1111-1-1-111-1-111-1-1-1-11111−ii1-1i−i−i−iii11-1-1ii−i−i−iiii−i−i−ii
χ1722222222-2-2-2-2222222-2-2-2-2002002222222-2-2-2-2-2-2-2-2-2-200002200000000-2-20000000000000000000000000000000000002-22-200
χ1822222222-2-2-2-2222222-2-2-2-2002002222222-2-2-2-2-2-2-2-2-2-200002200000000-2-2000000000000000000000000000000000000-22-2200
χ192222222-1222222-12-1-1222222-122-12-1-1-1-122-1-12-1-1-1-1-1-12-12-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1000000000000220022-1-1-1-10000-1-1-1-100000000
χ202222222-1222222-12-1-1222222-122-12-1-1-1-122-1-12-1-1-1-1-1-12-12-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1000000000000-2-200-2-211110000111100000000
χ212222222-1222222-12-1-12222-2-2-1-2-2-12-1-1-1-122-1-12-1-1-1-1-1-1-21-21-1-11111-21-21-1-111110000000000002200-2-2-1-1-1-10000111100000000
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χ23222222-122222-1-12-122-1-1-1-122-1222-12-1-1-1-1-122-12-1-1-1-12-12-12-1-1-1-1-1-1-12-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022000000-1-1-1-1000000000000
χ24222222-122222-1-12-122-1-1-1-122-1222-12-1-1-1-1-122-12-1-1-1-12-12-12-1-1-1-1-1-1-12-12-1-1-1-1-1-1-2-2-2-21111111100-2-20000001111000000000000
χ25222222-122222-1-12-122-1-1-1-1-2-2-1-2-22-12-1-1-1-1-122-12-1-1-1-121-21-2-1-111111-21-2-1-111112222-1-1-1-1-1-1-1-100-2-20000001111000000000000
χ26222222-122222-1-12-122-1-1-1-1-2-2-1-2-22-12-1-1-1-1-122-12-1-1-1-121-21-2-1-111111-21-2-1-11111-2-2-2-2111111110022000000-1-1-1-1000000000000
χ272222-2-2222-2-22222222-2-2-2-2222-2-2-2-2-2222-222-22-2-2-2-2-222222-2-22222-2-2-2-222-2-2-2-200000000000000000000000000000000000000
χ282222-2-2222-2-22222222-2-2-2-2-2-2222-2-2-2222-222-22-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2222222222200000000000000000000000000000000000000
χ292222-2-222-222-2222222222200200-2-2-2222-2-2-22-222222-20000-2-200000000-2-20000000000000000000000000000000000220000-2-2
χ302222-2-222-222-2222222222200200-2-2-2222-2-2-22-222222-20000-2-200000000-2-20000000000000000000000000000000000-2-2000022
χ312222-2-22-12-2-2222-12-1-1-2-2-2-222-1-2-21-21-1-1-1-22-11211111-12-12-111-1-1-1-1-21-21-1-11111000000000000000000−i3i3−i3i30000−i3i3−i3i300000000
χ322222-2-22-12-2-2222-12-1-1-2-2-2-222-1-2-21-21-1-1-1-22-11211111-12-12-111-1-1-1-1-21-21-1-11111000000000000000000i3−i3i3−i30000i3−i3i3−i300000000
χ332222-2-22-12-2-2222-12-1-1-2-2-2-2-2-2-1221-21-1-1-1-22-11211111-1-21-211111112-12-1-1-1-1-1-1-1000000000000000000−i3i3−i3i30000i3−i3i3−i300000000
χ342222-2-22-12-2-2222-12-1-1-2-2-2-2-2-2-1221-21-1-1-1-22-11211111-1-21-211111112-12-1-1-1-1-1-1-1000000000000000000i3−i3i3−i30000−i3i3−i3i300000000
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χ362222-2-2-122-2-22-1-12-122111122-1-2-2-21-2-1-1-11-12-2-1-211112-12-1211-1-1-1-11-21-2-1-111110000−3−333−3−3330000000000−33−33000000000000
χ372222-2-2-122-2-22-1-12-1221111-2-2-122-21-2-1-1-11-12-2-1-2111121-21-2111111-12-12-1-1-1-1-1-1000033−3−333−3−30000000000−33−33000000000000
χ382222-2-2-122-2-22-1-12-1221111-2-2-122-21-2-1-1-11-12-2-1-2111121-21-2111111-12-12-1-1-1-1-1-10000−3−333−3−33300000000003−33−3000000000000
χ3922-2-22-22222-2-2-2-2-222-222-2-22-22-22-222-2-22-222-2-22-2-222-222-2-2-2222-2-2-2-2222-2-2-22200000000000000000000000000000000000000
χ4022-2-22-22222-2-2-2-2-222-222-2-2-2222-2-222-2-22-222-2-22-2-222-2-2-222-22-2-22222-2-22-222-2-200000000000000000000000000000000000000
χ4122-2-22-222-2-222-2-2-222-2-2-22200200-222-2-22-2-2-222-222-2-220000-2200000000-2200000000000000000000000000000000002i−2i0000−2i2i
χ4222-2-22-222-2-222-2-2-222-2-2-22200200-222-2-22-2-2-222-222-2-220000-2200000000-220000000000000000000000000000000000−2i2i00002i−2i
χ4322-2-22-22-122-2-2-2-212-1122-2-22-2-1-2212-111-1-22-11-2-111-1-112-1-211-1-1-111-212-1-1111-1-10000000000000000003−3−3300003−3−3300000000
χ4422-2-22-22-122-2-2-2-212-1122-2-22-2-1-2212-111-1-22-11-2-111-1-112-1-211-1-1-111-212-1-1111-1-1000000000000000000−333−30000−333−300000000
χ4522-2-22-22-122-2-2-2-212-1122-2-2-22-12-212-111-1-22-11-2-111-1-11-212-11-111-1-12-1-21-11-1-1110000000000000000003−3−330000−333−300000000
χ4622-2-22-22-122-2-2-2-212-1122-2-2-22-12-212-111-1-22-11-2-111-1-11-212-11-111-1-12-1-21-11-1-111000000000000000000−333−300003−3−3300000000
χ4722-2-22-2-1222-2-211-2-12-2-1-1112-2-1-22-2-1211-11-12-21211-1-1-2-121-21-1-1-1111-2-12-1111-1-1000033−3−3−3−33300000000003−3−33000000000000
χ4822-2-22-2-1222-2-211-2-12-2-1-1112-2-1-22-2-1211-11-12-21211-1-1-2-121-21-1-1-1111-2-12-1111-1-10000−3−33333−3−30000000000−333−3000000000000
χ4922-2-22-2-1222-2-211-2-12-2-1-111-22-12-2-2-1211-11-12-21211-1-1-21-2-121-111-1-1-121-2-11-1-111000033−3−3−3−3330000000000−333−3000000000000
χ5022-2-22-2-1222-2-211-2-12-2-1-111-22-12-2-2-1211-11-12-21211-1-1-21-2-121-111-1-1-121-2-11-1-1110000−3−33333−3−300000000003−3−33000000000000
χ5122-2-2-2222-22-22-2-2-222-222-2-2002002-2-2-2-222-2-2-222-2-222200002-200000000-220000000000000000000000000000000000002i−2i−2i2i00
χ5222-2-2-2222-22-22-2-2-222-222-2-2002002-2-2-2-222-2-2-222-2-222200002-200000000-22000000000000000000000000000000000000−2i2i2i−2i00
χ5322-2-2-222-12-22-2-2-212-11-2-2222-2-12-2-1-2111-122-1-1-21-1-11112-1-21-11-1-1112-1-21-11-1-1110000000000002i−2i002i−2i−i−iii0000−i−iii00000000
χ5422-2-2-222-12-22-2-2-212-11-2-2222-2-12-2-1-2111-122-1-1-21-1-11112-1-21-11-1-1112-1-21-11-1-111000000000000−2i2i00−2i2iii−i−i0000ii−i−i00000000
χ5522-2-2-222-12-22-2-2-212-11-2-222-22-1-22-1-2111-122-1-1-21-1-1111-212-1-1111-1-1-212-1-1111-1-10000000000002i−2i00−2i2i−i−iii0000ii−i−i00000000
χ5622-2-2-222-12-22-2-2-212-11-2-222-22-1-22-1-2111-122-1-1-21-1-1111-212-1-1111-1-1-212-1-1111-1-1000000000000−2i2i002i−2iii−i−i0000−i−iii00000000
χ5722-2-2-22-122-22-211-2-12-211-1-12-2-12-221-211-1-1-1221-2-1-111-2-121-2-11-1-111-121-2-11-1-11122-2-2-1-1-1-11111002-2000000-1-111000000000000
χ5822-2-2-22-122-22-211-2-12-211-1-12-2-12-221-211-1-1-1221-2-1-111-2-121-2-11-1-111-121-2-11-1-111-2-2221111-1-1-1-100-2200000011-1-1000000000000
χ5922-2-2-22-122-22-211-2-12-211-1-1-22-1-2221-211-1-1-1221-2-1-111-21-2-12-1111-1-11-2-12-1111-1-122-2-2-1-1-1-1111100-2200000011-1-1000000000000
χ6022-2-2-22-122-22-211-2-12-211-1-1-22-1-2221-211-1-1-1221-2-1-111-21-2-12-1111-1-11-2-12-1111-1-1-2-2221111-1-1-1-1002-2000000-1-111000000000000
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χ924-4-4400440000-444-4-4-4000000400000-44-40000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ934-4-4400-2400002-242-4-423−23−232300-2000002-22000000−232323−230000000000000000000002i−2i−2i2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ944-4-4400-2400002-242-4-423−23−232300-2000002-22000000−232323−23000000000000000000000−2i2i2i−2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ954-4-4400-2400002-242-4-4−232323−2300-2000002-2200000023−23−23230000000000000000000002i−2i−2i2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ964-4-4400-2400002-242-4-4−232323−2300-2000002-2200000023−23−2323000000000000000000000−2i2i2i−2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ978-88-8008-400008-84-84-4000000-400000-444000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-800-4-40000-44444-443−4343−43002000002-2-2000000−2323−232300000000000000000000000000000000000000000000000000000000000
χ998-88-800-4-40000-44444-4−4343−4343002000002-2-200000023−2323−2300000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-40000-88-4-844000000-4000004-44000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-400004-4-444443−43−434300200000-22-200000023−23−232300000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-400004-4-4444−434343−4300200000-22-2000000−232323−2300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.