Finite Group Databasebeta

← Group #11781588

Character table — Group #11781588

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222222222222224444444444444444466668888888888888888888888812121212121212121212121212122424242424242424242436363636484848144
order1222334444666666121212123466612121212121212121212121288888812121212122424242424242424242424242424242488888824242424242424248824242424242424244444412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1
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
χ71111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-1
χ92222222-22-222222222222-22222-2-2-222222-2-2-2000000-2-2-2-2-2000000000000000000000000000000000000000022-2-20000
χ102222222-22-222222222222-22222-2-2-222222-2-2-2000000-2-2-2-2-20000000000000000000000000000000000000000-2-2220000
χ11222222-22-22222222-2-2-2-22-2222-22-2-2-2-2-2-2-2222222200-222-2-20000000000000000-2-200002222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-22-2-2-2-2-2-2-2222-2-2-2-200-222-2-20000000000000000220000-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-2220000000000000000002i2i−2i−2i000000000000002i2i−2i−2i00000000
χ14222222-2-2-2-2222222-2-2-2-222222-2-222-2-2-2-2-2-2-2-20000002-2-222000000000000000000−2i−2i2i2i00000000000000−2i−2i2i2i00000000
χ1522222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-1000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000-1-1-1-100002-1-10
χ1622222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-1000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000000011110000-2110
χ1722222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-10000-2-2-1-1-1-1-1-2-2-2-211111111111100222200000000000000-1-1-1-10000-2110
χ1822222-12222222-1-1-12222-12-1-1-1-1-122-1-1-1-1-122-10000-2-2-1-1-1-1-1-2-2-2-211111111111100-2-2-2-200000000000000111100002-1-10
χ1922222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-21000000-111-1-10000333333−3−3−3−3−3−3002i2i−2i−2i00000000000000−i−iii00000−i3i30
χ2022222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-21000000-111-1-10000333333−3−3−3−3−3−300−2i−2i2i2i00000000000000ii−i−i00000i3−i30
χ2122222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-21000000-111-1-10000−3−3−3−3−3−3333333002i2i−2i−2i00000000000000−i−iii00000i3−i30
χ2222222-1-2-2-2-2222-1-1-1-2-2-2-2-12-1-1-1112211111-2-21000000-111-1-10000−3−3−3−3−3−333333300−2i−2i2i2i00000000000000ii−i−i00000−i3i30
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1220000-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-122222-2-22-1-1-1-11111-2-21111-2-21111220000-1-1-1-1-1-1-1-1-2-21111000000000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-2-2-2222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2000011111111-2-21111000000000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-122-1-1-1-12-1-1-1-12-2-2-2-2-2-22-1-1-1-11111-2-21111-2-21111-2-200001111111122-1-1-1-1000000000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-12222200-2-1-11133−3−30033−3−30033−3−3-2-20000-1-1-1-111110033−3−3000000000000
χ282222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-12222200-2-1-111−3−33300−3−33300−3−333-2-20000-1-1-1-1111100−3−333000000000000
χ292222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-12-2-2-2-200-2-1-11133−3−30033−3−30033−3−32200001111-1-1-1-100−3−333000000000000
χ302222-12-22-22-1-1-12221111-1-2-1-1-1-221111-211-1-12-2-2-2-200-2-1-111−3−33300−3−33300−3−3332200001111-1-1-1-10033−3−3000000000000
χ3122-2-22220-202-2-22-2-222-2-2202-2-2200022-2-2-200022−2−2000000000000000000000002−22−22−222−2−222−2−20000002−22−22-2000000
χ3222-2-22220-202-2-22-2-222-2-2202-2-2200022-2-2-200022−2−2000000000000000000000002−2−22−2222−2−222−2−2000000−22−22-22000000
χ3322-2-22220-202-2-22-2-222-2-2202-2-2200022-2-2-2000−2−22200000000000000000000000−222−22−2−2−222−2−2220000002−22−2-22000000
χ3422-2-22220-202-2-22-2-222-2-2202-2-2200022-2-2-2000−2−22200000000000000000000000−22−22−22−2−222−2−222000000−22−222-2000000
χ3522-2-222-20202-2-22-2-2-2-222202-2-2-2000-2-222200022−2−200000000000000000000000−22−i2i2i2−i222−2−2−2−222000000−i2i2i2−i2002i−2i0000
χ3622-2-222-20202-2-22-2-2-2-222202-2-2-2000-2-222200022−2−200000000000000000000000−22i2−i2−i2i222−2−2−2−222000000i2−i2−i2i200−2i2i0000
χ3722-2-222-20202-2-22-2-2-2-222202-2-2-2000-2-2222000−2−222000000000000000000000002−2−i2i2i2−i2−2−22222−2−2000000−i2i2i2−i200−2i2i0000
χ3822-2-222-20202-2-22-2-2-2-222202-2-2-2000-2-2222000−2−222000000000000000000000002−2i2−i2−i2i2−2−22222−2−2000000i2−i2−i2i2002i−2i0000
χ392-2-22220-202-22-2-22-2000020-22-20-200000002-222i−2i2i−2i−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002i−2i2i−2i00002−22−22−2000000000000
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χ412-2-22220-202-22-2-22-2000020-22-20-200000002-22−2i2i−2i2i−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000−2i2i−2i2i0000−22−22−22000000000000
χ422-2-22220-202-22-2-22-2000020-22-20-200000002-22−2i2i−2i2ii2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000−2i2i−2i2i00002−22−22−2000000000000
χ432-2-22-120-2021-11-22-23−33−3-101-110-23−33−303−3-1122i−2i2i−2i−i2i20-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000−ii−ii−i3i3−i3i32−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ442-2-22-120-2021-11-22-23−33−3-101-110-23−33−303−3-1122i−2i2i−2ii2−i20-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000−ii−ii−i3i3−i3i3−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ452-2-22-120-2021-11-22-23−33−3-101-110-23−33−303−3-112−2i2i−2i2i−i2i20-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000i−ii−ii3−i3i3−i3−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ462-2-22-120-2021-11-22-23−33−3-101-110-23−33−303−3-112−2i2i−2i2ii2−i20-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000i−ii−ii3−i3i3−i32−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ472-2-22-120-2021-11-22-2−33−33-101-110-2−33−330−33-1122i−2i2i−2i−i2i20-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000−ii−iii3−i3i3−i32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ482-2-22-120-2021-11-22-2−33−33-101-110-2−33−330−33-1122i−2i2i−2ii2−i20-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000−ii−iii3−i3i3−i3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ492-2-22-120-2021-11-22-2−33−33-101-110-2−33−330−33-112−2i2i−2i2i−i2i20-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000i−ii−i−i3i3−i3i3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
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χ614444-2-2-4-4-4-4-2-2-2-2-2-222221411122-2-2-1-12-1-1222000000-2-1-11100002323−3−3−3−3−23−23333300000000000000000000000000000000
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χ884-4-44-2-20-4042-222-2223−2323−2310-11-10223−23−330−33-22-20000−2i22i201-1−332ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000000000000000
χ894-4-44-2-20-4042-222-2223−2323−2310-11-10223−23−330−33-22-200002i2−2i201-1−33−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000000000000000
χ904-4-44-2-20-4042-222-22−2323−232310-11-102−23233−303−3-22-20000−2i22i201-13−32ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000000000000000
χ914-4-44-2-20-4042-222-22−2323−232310-11-102−23233−303−3-22-200002i2−2i201-13−3−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000000000000000
χ9288-8-8-4-480-80-444-444-4-444202-2-2-4000224-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-8080-444-44444-4-4202-2-24000-2-2-42200000000000000000000000000000000000000000000000000000000000000
χ948-88-88-40000-8-8844-40000-4044-400000000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4000044-444-443−43−434320-2-220000−2323023−2300000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4000044-444-4−434343−4320-2-22000023−230−232300000000000000000000000000000000000000000000000000000000000000

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