Finite Group Databasebeta

← Group #11781595

Character table — Group #11781595

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222224444444444444444466668888888888888888888888812121212121212121212121212122424242424242424242436363636484848144
order1222334444666666121212123466612121212121212121212121288888812121212122424242424242424242424242424242444448824242424242424248812121212242424248888412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111-1
χ92222222-22-222222222222-2222-2-2-2-2222222-2-2000000-2-2-2-2-2000000000000000022-2-200000000000022-2-2000000000000
χ102222222-22-222222222222-2222-2-2-2-2222222-2-2000000-2-2-2-2-20000000000000000-2-222000000000000-2-222000000000000
χ11222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-222222200-222-2-200000000000000000000-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-222222-2-2-2-2-2-2-2-222-2-2-2-200-222-2-20000000000000000000022-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-22200000000000000000000000000000000000000002i2i−2i−2i0000
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-2220000000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000-1-1-1-1000000002-1-10
χ1622222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000111100000000-2110
χ1722222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-21111111111112222000000000000-1-1-1-100000000-2110
χ1822222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-2111111111111-2-2-2-20000000000001111000000002-1-10
χ1922222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-2-2000000000000-1-111000000000−i3i30
χ2022222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-22200000000000011-1-1000000000i3−i30
χ2122222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-2-2000000000000-1-111000000000i3−i30
χ2222222-12-22-2222-1-1-12222-1-2-1-1-111-2-2-1-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-22200000000000011-1-1000000000−i3i30
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022-1-1-1-1-1-1-1-1220000-1-1-1-100000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-12222-2-22-1-1-1-11111-2-21111-2-21111000022-1-1-1-1-1-1-1-1-2-20000111100000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-211111111-2-20000111100000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-12-1-12-1-1-1-1-2-2-2-2-2-22-1-1-1-11111-2-21111-2-211110000-2-211111111220000-1-1-1-100000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1222200-2-1-11133−3−30033−3−30033−3−30000-2-2-1-1-1-1111100000033−3−300000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1222200-2-1-111−3−33300−3−33300−3−3330000-2-2-1-1-1-11111000000−3−33300000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1-2-2-2-200-2-1-11133−3−30033−3−30033−3−30000221111-1-1-1-1000000−3−33300000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-12211-211-211-1-1-2-2-2-200-2-1-111−3−33300−3−33300−3−3330000221111-1-1-1-100000033−3−300000000
χ3122-2-22220-202-2-2-22-222-2-2202-2-20000222-2-2-20022−2−2000000000000000000000002-2002−222−2−222−2−2002-20000002−22−20000
χ3222-2-22220-202-2-2-22-222-2-2202-2-20000222-2-2-20022−2−200000000000000000000000-22002−222−2−222−2−200-22000000−22−220000
χ3322-2-22220-202-2-2-22-222-2-2202-2-20000222-2-2-200−2−222000000000000000000000002-200−22−2−222−2−222002-2000000−22−220000
χ3422-2-22220-202-2-2-22-222-2-2202-2-20000222-2-2-200−2−22200000000000000000000000-2200−22−2−222−2−22200-220000002−22−20000
χ3522-2-222-20202-2-2-22-2-2-222202-2-20000-2-2-22220022−2−200000000000000000000000002i−2i−2222−2−2−2−22200002i−2i0000−i2i2i2−i20000
χ3622-2-222-20202-2-2-22-2-2-222202-2-20000-2-2-22220022−2−20000000000000000000000000−2i2i−2222−2−2−2−2220000−2i2i0000i2−i2−i2i20000
χ3722-2-222-20202-2-2-22-2-2-222202-2-20000-2-2-222200−2−22200000000000000000000000002i−2i2−2−2−22222−2−200002i−2i0000i2−i2−i2i20000
χ3822-2-222-20202-2-2-22-2-2-222202-2-20000-2-2-222200−2−2220000000000000000000000000−2i2i2−2−2−22222−2−20000−2i2i0000−i2i2i2−i20000
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χ422-2-22220-202-22-22-2-2000020-22-22-2000000002-2−2i2i−2i2i−2202-200−22−22−22−22−22−22−22−22000000−2i2i−2i2i0000−i2i20000−i2i2−i2i200000000
χ432-2-22-120-2021-112-2-23−33−3-101-112-23−303−303−3-112i−2i2i−2i2−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000−ii−ii−i3i3−i3i3−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ442-2-22-120-2021-112-2-23−33−3-101-112-23−303−303−3-112i−2i2i−2i−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000−ii−ii−i3i3−i3i3i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ452-2-22-120-2021-112-2-23−33−3-101-112-23−303−303−3-11−2i2i−2i2i2−20-113−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000i−ii−ii3−i3i3−i3i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ462-2-22-120-2021-112-2-23−33−3-101-112-23−303−303−3-11−2i2i−2i2i−220-113−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000i−ii−ii3−i3i3−i3−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ472-2-22-120-2021-112-2-2−33−33-101-112-2−330−330−33-112i−2i2i−2i2−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000−ii−iii3−i3i3−i3−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ482-2-22-120-2021-112-2-2−33−33-101-112-2−330−330−33-112i−2i2i−2i−220-11−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000−ii−iii3−i3i3−i3i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ492-2-22-120-2021-112-2-2−33−33-101-112-2−330−330−33-11−2i2i−2i2i2−20-11−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000i−ii−i−i3i3−i3i3i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
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χ554444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-2000044-21111-2-2-2-2-2-21111-2-2111100000000000000000000000000000000
χ564444-2-24444-2-2-2-2-2-2-2-2-2-214111-2-2-2-2-211-211-2-20000-4-4-21111222222-1-1-1-122-1-1-1-100000000000000000000000000000000
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χ604444-2-2-44-44-2-2-2-2-2-222221-4111-2-2222-1-12-1-1-2-2000000211-1-1−23−2323230033−3−30033−3−300000000000000000000000000000000
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χ894-4-44-2-20-4042-22-22223−2323−2310-11-1-2223−230−330−33-220000−222201-1−33−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000000000000000
χ904-4-44-2-20-4042-22-222−2323−232310-11-1-22−232303−303−3-22000022−2201-13−32ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000000000000000
χ914-4-44-2-20-4042-22-222−2323−232310-11-1-22−232303−303−3-220000−222201-13−3−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000000000000000
χ9288-8-8-4-480-80-4444-44-4-444202-2-20000-4224-2-20000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-8080-4444-4444-4-4202-2-200004-2-2-4220000000000000000000000000000000000000000000000000000000000000
χ948-88-88-40000-8-8844-40000-4044-400000000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4000044-444-443−43−434320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4000044-444-4−434343−4320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000000

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