Finite Group Databasebeta

← Group #11774059

Character table — Group #11774059

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222244444444444444444466668888888888888888888888121212121212121212121212121224242424242424242424242424242424363636367272
order122222334444666666666636666666661212121212121212444444121212121212121212121212121212121212121244888812121212121212124488121212122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1ii−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−iii−i−ii−i
χ1011111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1−i−iii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii−i−iii−ii
χ1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1ii−i−i1111-1-1-1-1-11−ii-1-111ii−i−i−i−iiiii−i−i−ii
χ1211111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1−i−iii1111-1-1-1-1-11i−i-1-111−i−iiiii−i−i−i−iiii−i
χ1311111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11ii−i−i-1-1-1-11111-11i−i-1-111ii−i−iii−i−i−i−iii−ii
χ1411111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11−i−iii-1-1-1-11111-11−ii-1-111−i−iii−i−iiiii−i−ii−i
χ1511111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-11ii−i−i-1-1-1-111111-1−ii11-1-1ii−i−i−i−iii−i−iiii−i
χ1611111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-11−i−iii-1-1-1-111111-1i−i11-1-1−i−iiiii−i−iii−i−i−ii
χ172222222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022220000000000220000-1-1-1-1-1-1-1-1000000
χ182222222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1000022-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000-2-2000011111111000000
χ192222222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-2-21111-2-2-2-21111-1-1-1-111110022220000000000-2-20000-1-1-1-11111000000
χ202222222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-2-21111-2-2-2-21111-1-1-1-1111100-2-2-2-200000000002200001111-1-1-1-1000000
χ212222222-1-2-2-2-22222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100002-211-1-122-2-211111111-1-1-1-1002i2i−2i−2i00000000002i−2i0000−i−iii−i−iii000000
χ222222222-1-2-2-2-22222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100002-211-1-122-2-211111111-1-1-1-100−2i−2i2i2i0000000000−2i2i0000ii−i−iii−i−i000000
χ232222222-1-2-2-2-22222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-22-1-111-2-222-1-1-1-111111111002i2i−2i−2i0000000000−2i2i0000−i−iiiii−i−i000000
χ242222222-1-2-2-2-22222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-211110000-22-1-111-2-222-1-1-1-11111111100−2i−2i2i2i00000000002i−2i0000ii−i−i−i−iii000000
χ25222222-122222-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-12200-1-1-1-100000000000000
χ26222222-122222-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-211111111-1-1-1-11111220000-1-1-1-1-1-1-1-1-2-200111100000000000000
χ27222222-122222-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000011111111-2-200111100000000000000
χ28222222-122222-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-211111111-1-1-1-11111-2-20000111111112200-1-1-1-100000000000000
χ29222222-12-2-2-2-2-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-11111-2-2-2-222-2-22-2-2-222-1-11111111111-1-1-1-12-20000-1-1-1-111112-200-1-11100000000000000
χ30222222-12-2-2-2-2-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-11111-2-2-2-222-2-2-2222-2-211-1-1-1-1-1-1111111112-20000-1-1-1-11111-220011-1-100000000000000
χ31222222-12-2-2-2-2-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-11111-2-2-2-2-2-2222-2-2-222-1-11111111111-1-1-1-1-2200001111-1-1-1-1-220011-1-100000000000000
χ32222222-12-2-2-2-2-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-11111-2-2-2-2-2-222-2222-2-211-1-1-1-1-1-111111111-2200001111-1-1-1-12-200-1-11100000000000000
χ332222-2-22222-2-2-2-2-2-22222222-2-22-2-2-2-22222-2-222-2-222220000000000000022-2-20000-2-2000022-2-222-2-20000000000000000000000
χ342222-2-22222-2-2-2-2-2-22222222-2-22-2-2-2-22222-2-222-2-2-2-2-2-20000000000000022-2-20000220000-2-222-2-2220000000000000000000000
χ352222-2-222-2-222-2-2-2-22222222-2-22-2-2-2-222-2-222-2-22222-2-200000000000000-2-2220000-22000022-2-2-2-2220000000000000000000000
χ362222-2-222-2-222-2-2-2-22222222-2-22-2-2-2-222-2-222-2-222-2-22200000000000000-2-22200002-20000-2-22222-2-20000000000000000000000
χ372222-2-2-1222-2-21111222-1-1-1-1-2-2-11111-1-1-1-11122-2-22222000000−i3i3−i3i3−i3−i3i3i3-1-111−i3−i3i3i3-2-20000-1-111-1-1110000−i3i3−i3i300000000000000
χ382222-2-2-1222-2-21111222-1-1-1-1-2-2-11111-1-1-1-11122-2-22222000000i3−i3i3−i3i3i3−i3−i3-1-111i3i3−i3−i3-2-20000-1-111-1-1110000i3−i3i3−i300000000000000
χ392222-2-2-1222-2-21111222-1-1-1-1-2-2-11111-1-1-1-11122-2-2-2-2-2-2000000−i3i3−i3i3−i3−i3i3i3-1-111−i3−i3i3i322000011-1-111-1-10000i3−i3i3−i300000000000000
χ402222-2-2-1222-2-21111222-1-1-1-1-2-2-11111-1-1-1-11122-2-2-2-2-2-2000000i3−i3i3−i3i3i3−i3−i3-1-111i3i3−i3−i322000011-1-111-1-10000−i3i3−i3i300000000000000
χ412222-2-2-12-2-2221111222-1-1-1-1-2-2-11111-1-111-1-1-2-22222-2-2000000−i3i3i3−i3i3i3−i3−i311-1-1−i3−i3i3i3-220000-1-11111-1-10000−i3i3i3−i300000000000000
χ422222-2-2-12-2-2221111222-1-1-1-1-2-2-11111-1-111-1-1-2-22222-2-2000000i3−i3−i3i3−i3−i3i3i311-1-1i3i3−i3−i3-220000-1-11111-1-10000i3−i3−i3i300000000000000
χ432222-2-2-12-2-2221111222-1-1-1-1-2-2-11111-1-111-1-1-2-222-2-222000000−i3i3i3−i3i3i3−i3−i311-1-1−i3−i3i3i32-2000011-1-1-1-1110000i3−i3−i3i300000000000000
χ442222-2-2-12-2-2221111222-1-1-1-1-2-2-11111-1-111-1-1-2-222-2-222000000i3−i3−i3i3−i3−i3i3i311-1-1i3i3−i3−i32-2000011-1-1-1-1110000−i3i3i3−i300000000000000
χ452-2-222-2222i−2i2i−2i22-2-2-22-2-2-2222-2-222-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i0000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ462-2-222-2222i−2i2i−2i22-2-2-22-2-2-2222-2-222-2-22-22i−2i2i−2i2i−2i2i−2i0000000000000000002i−2i2i−2i00000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ472-2-222-222−2i2i−2i2i22-2-2-22-2-2-2222-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i00000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ482-2-222-222−2i2i−2i2i22-2-2-22-2-2-2222-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000−2i2i−2i2i0000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ492-2-22-22222i−2i−2i2i-2-222-22-2-2-222-22-2-2-2222-22i−2i−2i2i2i−2i−2i2i0000000000000000002i−2i−2i2i0000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ502-2-22-22222i−2i−2i2i-2-222-22-2-2-222-22-2-2-2222-22i−2i−2i2i2i−2i−2i2i0000000000000000002i−2i−2i2i000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ512-2-22-2222−2i2i2i−2i-2-222-22-2-2-222-22-2-2-2222-2−2i2i2i−2i−2i2i2i−2i000000000000000000−2i2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ522-2-22-2222−2i2i2i−2i-2-222-22-2-2-222-22-2-2-2222-2−2i2i2i−2i−2i2i2i−2i000000000000000000−2i2i2i−2i0000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ532-2-22-222-12i−2i−2i2i-2-2221-11-2-22-11-1111-1-1-112i−2i−2i2i−iii−i000000−i3i33−30000−i3i3−i3i3−iii−i3−33−3002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ542-2-22-222-12i−2i−2i2i-2-2221-11-2-22-11-1111-1-1-112i−2i−2i2i−iii−i000000−i3i33−30000−i3i3−i3i3−iii−i3−33−300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ552-2-22-222-12i−2i−2i2i-2-2221-11-2-22-11-1111-1-1-112i−2i−2i2i−iii−i000000i3−i3−330000i3−i3i3−i3−iii−i−33−33002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ562-2-22-222-12i−2i−2i2i-2-2221-11-2-22-11-1111-1-1-112i−2i−2i2i−iii−i000000i3−i3−330000i3−i3i3−i3−iii−i−33−3300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ572-2-22-222-1−2i2i2i−2i-2-2221-11-2-22-11-1111-1-1-11−2i2i2i−2ii−i−ii000000−i3i3−330000−i3i3−i3i3i−i−ii−33−3300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ582-2-22-222-1−2i2i2i−2i-2-2221-11-2-22-11-1111-1-1-11−2i2i2i−2ii−i−ii000000−i3i3−330000−i3i3−i3i3i−i−ii−33−33002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ592-2-22-222-1−2i2i2i−2i-2-2221-11-2-22-11-1111-1-1-11−2i2i2i−2ii−i−ii000000i3−i33−30000i3−i3i3−i3i−i−ii3−33−300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
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χ64444444-2-2-4-4-4-4-2-2-2-2-2-2-2-2-2-21-2-21111111222222220000-44-2-22222-2-21111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ814-44-400-2400002i3−2i3−2i32i3-4-442-22-20022i3−2i3−2i32i32-200000000004i−4i00000000000000000000000000000000−2i2i−23230000000000000000000000
χ824-44-400-2400002i3−2i3−2i32i3-4-442-22-20022i3−2i3−2i32i32-20000000000−4i4i000000000000000000000000000000002i−2i23−230000000000000000000000
χ834-4-444-44-24i−4i4i−4i44-4-42-22-4-44-2-222-2-222-224i−4i4i−4i−2i2i−2i2i000000000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ844-4-444-44-2−4i4i−4i4i44-4-42-22-4-44-2-222-2-222-22−4i4i−4i4i2i−2i2i−2i0000000000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ854-4-444-4-244i−4i4i−4i-2-222-44-422-2-24-42-2-222-22−2i2i−2i2i4i−4i4i−4i000000000000000000−2i2i−2i2i0000000000000000000000000000000000000000
χ864-4-444-4-24−4i4i−4i4i-2-222-44-422-2-24-42-2-222-222i−2i2i−2i−4i4i−4i4i0000000000000000002i−2i2i−2i0000000000000000000000000000000000000000
χ874-4-444-4-2-24i−4i4i−4i-2-2222-2222-21-22-111-1-11-1−2i2i−2i2i−2i2i−2i2i000000000000003-3-33i−ii−i3i−3i−3i3i000000000000000000000000000000000000
χ884-4-444-4-2-24i−4i4i−4i-2-2222-2222-21-22-111-1-11-1−2i2i−2i2i−2i2i−2i2i00000000000000-333-3i−ii−i−3i3i3i−3i000000000000000000000000000000000000
χ894-4-444-4-2-2−4i4i−4i4i-2-2222-2222-21-22-111-1-11-12i−2i2i−2i2i−2i2i−2i000000000000003-3-33−ii−ii−3i3i3i−3i000000000000000000000000000000000000
χ904-4-444-4-2-2−4i4i−4i4i-2-2222-2222-21-22-111-1-11-12i−2i2i−2i2i−2i2i−2i00000000000000-333-3−ii−ii3i−3i−3i3i000000000000000000000000000000000000
χ914-4-44-44-244i−4i−4i4i22-2-2-44-422-2-2-44222-2-2-22−2i2i2i−2i4i−4i−4i4i000000000000000000−2i2i2i−2i0000000000000000000000000000000000000000
χ924-4-44-44-24−4i4i4i−4i22-2-2-44-422-2-2-44222-2-2-222i−2i−2i2i−4i4i4i−4i0000000000000000002i−2i−2i2i0000000000000000000000000000000000000000
χ934-4-44-44-2-24i−4i−4i4i22-2-22-2222-212-2-1-1-1111-1−2i2i2i−2i−2i2i2i−2i000000−2i32i323−230000i3−i3i3−i3i−i−ii−33−33000000000000000000000000000000000000
χ944-4-44-44-2-24i−4i−4i4i22-2-22-2222-212-2-1-1-1111-1−2i2i2i−2i−2i2i2i−2i0000002i3−2i3−23230000−i3i3−i3i3i−i−ii3−33−3000000000000000000000000000000000000
χ954-4-44-44-2-2−4i4i4i−4i22-2-22-2222-212-2-1-1-1111-12i−2i−2i2i2i−2i−2i2i000000−2i32i3−23230000i3−i3i3−i3−iii−i3−33−3000000000000000000000000000000000000
χ964-4-44-44-2-2−4i4i4i−4i22-2-22-2222-212-2-1-1-1111-12i−2i−2i2i2i−2i−2i2i0000002i3−2i323−230000−i3i3−i3i3−iii−i−33−33000000000000000000000000000000000000
χ9788-8-8008-400000000-4448-8-8-400-40000440000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-40000−4i34i3−4i34i3-444-44420022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-400004i3−4i34i3−4i3-444-4442002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8008-40000000044-4-88-8-400400004-40000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-800-4-40000−4i34i34i3−4i344-44-44200-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-800-4-400004i3−4i3−4i34i344-44-44200-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000000000000000000

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