Finite Group Databasebeta

← Group #11781404

Character table — Group #11781404

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
χ92222222-22-222222222222-2222-2-22-2-222222-2-2000000-2-2-2-2-2000000000000000022-2-200000000000022-2-2000000000000
χ102222222-22-222222222222-2222-2-22-2-222222-2-2000000-2-2-2-2-20000000000000000-2-222000000000000-2-222000000000000
χ11222222-22-22222222-2-2-2-22-2222-2-2-222-2-2-2-2-222222200-222-2-200000000000000000000-2-22222-2-2-2-2000000000000000000
χ12222222-22-22222222-2-2-2-22-2222-2-2-222-2-2-2-2-222-2-2-2-200-222-2-20000000000000000000022-2-2-2-22222000000000000000000
χ13222222-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-20000002-2-22200000000000000000000000000000000000000002i2i−2i−2i0000
χ14222222-2-2-2-2222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-20000002-2-2220000000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222-12222222-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000-1-1-1-1000000002-1-10
χ1622222-12222222-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-122000022-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000111100000000-2110
χ1722222-12222222-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-21111111111112222000000000000-1-1-1-100000000-2110
χ1822222-12222222-1-1-12222-12-1-1-122-1-1-1-1-1-1-1-1220000-2-2-1-1-1-1-1-2-2-2-2111111111111-2-2-2-20000000000001111000000002-1-10
χ1922222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-111-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i322-2-2000000000000-1-111000000000−i3i30
χ2022222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-111-1-1-1-1-1-2-2000000111110000−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3-2-22200000000000011-1-1000000000i3−i30
χ2122222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-111-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i322-2-2000000000000-1-111000000000i3−i30
χ2222222-12-22-2222-1-1-12222-1-2-1-1-1-2-2-111-1-1-1-1-1-2-2000000111110000i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3-2-22200000000000011-1-1000000000−i3i30
χ232222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-1222-1-12-1-1-1-12222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1000022-1-1-1-1-1-1-1-1220000-1-1-1-100000000
χ242222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-1222-1-12-1-1-1-12222-2-22-1-1-1-11111-2-21111-2-21111000022-1-1-1-1-1-1-1-1-2-20000111100000000
χ252222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-1222-1-12-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000-2-211111111-2-20000111100000000
χ262222-122222-1-1-1222-1-1-1-1-12-1-1-1-1-1222-1-12-1-1-1-1-2-2-2-2-2-22-1-1-1-11111-2-21111-2-211110000-2-211111111220000-1-1-1-100000000
χ272222-12-22-22-1-1-12221111-1-2-1-1-111-22211-211-1-1222200-2-1-11133−3−30033−3−30033−3−30000-2-2-1-1-1-1111100000033−3−300000000
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χ302222-12-22-22-1-1-12221111-1-2-1-1-111-22211-211-1-1-2-2-2-200-2-1-111−3−33300−3−33300−3−3330000221111-1-1-1-100000033−3−300000000
χ312-22-2220-2022-2-2-2-220000202-2-20002-2000002-22i2i−2i−2i−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002i2i−2i−2i00002−200002−22−200000000
χ322-22-2220-2022-2-2-2-220000202-2-20002-2000002-22i2i−2i−2ii2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002i2i−2i−2i0000−220000−22−2200000000
χ332-22-2220-2022-2-2-2-220000202-2-20002-2000002-2−2i−2i2i2i−i2i202-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000−2i−2i2i2i0000−220000−22−2200000000
χ342-22-2220-2022-2-2-2-220000202-2-20002-2000002-2−2i−2i2i2ii2−i202-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000−2i−2i2i2i00002−200002−22−200000000
χ352-22-2-120-202-111-2-223−33−3-10-1113−302-23−303−3-112i2i−2i−2i−i2i20-113−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000−i−iii−i3−i3i3i32−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
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χ382-22-2-120-202-111-2-223−33−3-10-1113−302-23−303−3-11−2i−2i2i2ii2−i20-113−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000ii−i−ii3i3−i3−i32−20000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
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χ402-22-2-120-202-111-2-22−33−33-10-111−3302-2−330−33-112i2i−2i−2ii2−i20-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000−i−iiii3i3−i3−i3−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ412-22-2-120-202-111-2-22−33−33-10-111−3302-2−330−33-11−2i−2i2i2i−i2i20-11−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000ii−i−i−i3−i3i3i3−220000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ422-22-2-120-202-111-2-22−33−33-10-111−3302-2−330−33-11−2i−2i2i2ii2−i20-11−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000ii−i−i−i3−i3i3i32−20000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ432-2-222220-20-22-22-2-222-2-220-22-200-200-2-222200−i2i2−i2i2000000000000000000000002i−2i00−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i0000002−22−20000
χ442-2-222220-20-22-22-2-222-2-220-22-200-200-2-222200−i2i2−i2i200000000000000000000000−2i2i00−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i000000−22−220000
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χ604444-2-2-44-44-2-2-2-2-2-222221-4111222-2-2-1-12-1-1-2-2000000211-1-1−23−2323230033−3−30033−3−300000000000000000000000000000000
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χ854-4-444-240-40-44-4-22244-4-4-202-220020022-2-2-200000000000000000000000000000−4i4i000000000000002i−2i00000000000000
χ864-4-444-2-4040-44-4-222-4-444-202-2200-200-2-222200000000000000000000000000000004-400000000000000-22000000000000
χ874-4-444-2-4040-44-4-222-4-444-202-2200-200-2-22220000000000000000000000000000000-44000000000000002-2000000000000
χ884-4-44-2440-402-224-4-4-2-222-202-2200-400224-2-200−2i22i2−2i22i2000000000000000000000000000−2i22i2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ894-4-44-2440-402-224-4-4-2-222-202-2200-400224-2-2002i2−2i22i2−2i20000000000000000000000000002i2−2i2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ904-4-44-24-40402-224-4-422-2-2-202-2200400-2-2-42200−2i22i2−2i22i20000000000000000000000000002i2−2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ914-4-44-24-40402-224-4-422-2-2-202-2200400-2-2-422002i2−2i22i2−2i2000000000000000000000000000−2i22i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ9288-8-88-40000-8-884-440000-4044-400000000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4000044-44-4443−43−434320-2-220000023−230−23230000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4000044-44-44−434343−4320-2-2200000−2323023−230000000000000000000000000000000000000000000000000000000000000
χ958-8-88-4-480-804-44-444-4-44420-22-200400-2-2-4220000000000000000000000000000000000000000000000000000000000000
χ968-8-88-4-4-80804-44-44444-4-420-22-200-400224-2-20000000000000000000000000000000000000000000000000000000000000

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