Finite Group Databasebeta

← Group #14512413

Character table — Group #14512413

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111444455555555555566666688881212242424242424303030303030303030303030303030303030323232324040404040404040404040404848606060606060
order12445102020224488888888244444361212881020202020202444448888888888881530606066121224242424242424244040444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111-1-111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ4111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-11-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ511111111-1-1-1-1iiii−i−i−i−i111111111111111111-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11ii−i−i-1-1
χ611111111-1-1-1-1iiii−i−i−i−i11-1-1-1-11111-1-111-1-1-1-1-11111-1ii−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1−i−iii11
χ711111111-1-1-1-1−i−i−i−iiiii111111111111111111-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11−i−iii-1-1
χ811111111-1-1-1-1−i−i−i−iiiii11-1-1-1-11111-1-111-1-1-1-1-11111-1−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1ii−i−i11
χ911-1-111-1-111-1-1ii−i−iii−i−i-11ii−i−i11-1-1i−i-11ii−i−i-1ii−i−i1i−ii−i11-1-111-1-111-1-111-1-1ii−i−iii−i−ii−i1-11-1i−i
χ1011-1-111-1-111-1-1ii−i−iii−i−i-11−i−iii11-1-1−ii-11−i−iii-1−i−iii1i−ii−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i−ii-11-11−ii
χ1111-1-111-1-111-1-1−i−iii−i−iii-11ii−i−i11-1-1i−i-11ii−i−i-1ii−i−i1−ii−ii-1-111-1-11111-1-111-1-1−i−iii−i−iiii−i-11-11i−i
χ1211-1-111-1-111-1-1−i−iii−i−iii-11−i−iii11-1-1−ii-11−i−iii-1−i−iii1−ii−ii11-1-111-1-111-1-111-1-1−i−iii−i−iii−ii1-11-1−ii
χ1311-1-111-1-1-1-11111-1-1-1-111-11ii−i−i11-1-1i−i-11ii−i−i1−i−iii-11-1-11−i−iiiii−i−i11-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ1411-1-111-1-1-1-11111-1-1-1-111-11−i−iii11-1-1−ii-11−i−iii1ii−i−i-11-1-11ii−i−i−i−iii11-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ1511-1-111-1-1-1-111-1-11111-1-1-11ii−i−i11-1-1i−i-11ii−i−i1−i−iii-1-111-1ii−i−i−i−iii11-1-1-1-111-1-11111-1-1i−ii−i−ii−ii
χ1611-1-111-1-1-1-111-1-11111-1-1-11−i−iii11-1-1−ii-11−i−iii1ii−i−i-1-111-1−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−ii−iii−ii−i
χ1722222222222222222222220000-1-1-1-100220000200002222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222222222222-2-2-2-2-2-2-2-2220000-1-1-1-100220000200002-2-2-2-200000000-1-1-1-1-1-1-1-11111111100000000
χ1922222222-2-2-2-22i2i2i2i−2i−2i−2i−2i220000-1-1-1-100220000-20000-22i2i−2i−2i00000000-1-1-1-11111−i−i−i−iiiii00000000
χ2022222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i220000-1-1-1-100220000-20000-2−2i−2i2i2i00000000-1-1-1-11111iiii−i−i−i−i00000000
χ2122-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i-220000-1-11100-220000-2000022i−2i2i−2i00000000-1-111-1-111−i−iii−i−iii00000000
χ2222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i-220000-1-11100-220000-200002−2i2i−2i2i00000000-1-111-1-111ii−i−iii−i−i00000000
χ2322-2-222-2-2-2-22222-2-2-2-222-220000-1-11100-22000020000-22-2-2200000000-1-11111-1-1-1-11111-1-100000000
χ2422-2-222-2-2-2-222-2-22222-2-2-220000-1-11100-22000020000-2-222-200000000-1-11111-1-111-1-1-1-11100000000
χ252-22i−2i2-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i-11i−i00001+i−1−i1−i−1+i01+i−1−i1−i−1+i000002−2i2−i22−2i2−i2-11i−i1-1i−iζ−ζζ3−ζ3ζ−ζζ3−ζ300000000
χ262-22i−2i2-22i−2i2-22i−2i2ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i-11i−i0000−1−i1+i−1+i1−i0−1−i1+i−1+i1−i00000−22−i2i2−22−i2i2-11i−i1-1i−iζ−ζζ3−ζ3ζ−ζζ3−ζ300000000
χ272-22i−2i2-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i-11i−i00001+i−1−i1−i−1+i01+i−1−i1−i−1+i00000−22−i2i2−22−i2i2-11i−i1-1i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ300000000
χ282-22i−2i2-22i−2i2-22i−2i−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i-11i−i0000−1−i1+i−1+i1−i0−1−i1+i−1+i1−i000002−2i2−i22−2i2−i2-11i−i1-1i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ300000000
χ292-22i−2i2-22i−2i-22−2i2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ001+i−1−i1−i−1+i-11i−i00001+i−1−i1−i−1+i0−1−i1+i−1+i1−i00000i2−i2−22−i2i22−2-11i−i-11−iiζ3−ζ3−ζζ−ζ3ζ3ζ−ζ00000000
χ302-22i−2i2-22i−2i-22−2i2i2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ00−1−i1+i−1+i1−i-11i−i0000−1−i1+i−1+i1−i01+i−1−i1−i−1+i00000−i2i22−2i2−i2−22-11i−i-11−iiζ3−ζ3−ζζ−ζ3ζ3ζ−ζ00000000
χ312-22i−2i2-22i−2i-22−2i2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ001+i−1−i1−i−1+i-11i−i00001+i−1−i1−i−1+i0−1−i1+i−1+i1−i00000−i2i22−2i2−i2−22-11i−i-11−ii−ζ3ζ3ζ−ζζ3−ζ3−ζζ00000000
χ322-22i−2i2-22i−2i-22−2i2i−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ00−1−i1+i−1+i1−i-11i−i0000−1−i1+i−1+i1−i01+i−1−i1−i−1+i00000i2−i2−22−i2i22−2-11i−i-11−ii−ζ3ζ3ζ−ζζ3−ζ3−ζζ00000000
χ332-2−2i2i2-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i-11−ii00001−i−1+i1+i−1−i01−i−1+i1+i−1−i00000−22i2−i2−22i2−i2-11−ii1-1−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ00000000
χ342-2−2i2i2-2−2i2i2-2−2i2i2ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i-11−ii0000−1+i1−i−1−i1+i0−1+i1−i−1−i1+i000002−2−i2i22−2−i2i2-11−ii1-1−iiζ3−ζ3ζ−ζζ3−ζ3ζ−ζ00000000
χ352-2−2i2i2-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i-11−ii00001−i−1+i1+i−1−i01−i−1+i1+i−1−i000002−2−i2i22−2−i2i2-11−ii1-1−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ00000000
χ362-2−2i2i2-2−2i2i2-2−2i2i−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i-11−ii0000−1+i1−i−1−i1+i0−1+i1−i−1−i1+i00000−22i2−i2−22i2−i2-11−ii1-1−ii−ζ3ζ3−ζζ−ζ3ζ3−ζζ00000000
χ372-2−2i2i2-2−2i2i-222i−2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3001−i−1+i1+i−1−i-11−ii00001−i−1+i1+i−1−i0−1+i1−i−1−i1+i00000i2−i22−2−i2i2−22-11−ii-11i−iζ−ζ−ζ3ζ3−ζζζ3−ζ300000000
χ382-2−2i2i2-2−2i2i-222i−2i2ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ300−1+i1−i−1−i1+i-11−ii0000−1+i1−i−1−i1+i01−i−1+i1+i−1−i00000−i2i2−22i2−i22−2-11−ii-11i−iζ−ζ−ζ3ζ3−ζζζ3−ζ300000000
χ392-2−2i2i2-2−2i2i-222i−2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3001−i−1+i1+i−1−i-11−ii00001−i−1+i1+i−1−i0−1+i1−i−1−i1+i00000−i2i2−22i2−i22−2-11−ii-11i−i−ζζζ3−ζ3ζ−ζ−ζ3ζ300000000
χ402-2−2i2i2-2−2i2i-222i−2i−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ300−1+i1−i−1−i1+i-11−ii0000−1+i1−i−1−i1+i01−i−1+i1+i−1−i00000i2−i22−2−i2i2−22-11−ii-11i−i−ζζζ3−ζ3ζ−ζ−ζ3ζ300000000
χ4133333333333333333333-1-111110000-1-1-1-11111-11111-1-1-1-1-1111111110000000000000000-1-1-1-1-1-1-1-1
χ4233333333333333333333-1-1-1-1-1-1000011-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111
χ43333333333333-3-3-3-3-3-3-3-3-1-111110000-1-1-1-11111-11111-11111-1-1-1-1-1-1-1-10000000000000000-1-11111-1-1
χ44333333333333-3-3-3-3-3-3-3-3-1-1-1-1-1-1000011-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000011-1-1-1-111
χ4533333333-3-3-3-33i3i3i3i−3i−3i−3i−3i-1-111110000-1-1-1-111111-1-1-1-11−i−iiiiiii−i−i−i−i0000000000000000-1-1−i−iii11
χ4633333333-3-3-3-33i3i3i3i−3i−3i−3i−3i-1-1-1-1-1-1000011-1-1-1-1-1-1111111−i−iii−i−i−i−iiiii000000000000000011ii−i−i-1-1
χ4733333333-3-3-3-3−3i−3i−3i−3i3i3i3i3i-1-111110000-1-1-1-111111-1-1-1-11ii−i−i−i−i−i−iiiii0000000000000000-1-1ii−i−i11
χ4833333333-3-3-3-3−3i−3i−3i−3i3i3i3i3i-1-1-1-1-1-1000011-1-1-1-1-1-1111111ii−i−iiiii−i−i−i−i000000000000000011−i−iii-1-1
χ4933-3-333-3-333-3-33i3i−3i−3i3i3i−3i−3i1-1ii−i−i0000−ii1-1ii−i−i1ii−i−i-1−ii−ii11-1-111-1-10000000000000000−ii-11-11−ii
χ5033-3-333-3-333-3-33i3i−3i−3i3i3i−3i−3i1-1−i−iii0000i−i1-1−i−iii1−i−iii-1−ii−ii-1-111-1-1110000000000000000i−i1-11-1i−i
χ5133-3-333-3-333-3-3−3i−3i3i3i−3i−3i3i3i1-1ii−i−i0000−ii1-1ii−i−i1ii−i−i-1i−ii−i-1-111-1-1110000000000000000−ii1-11-1−ii
χ5233-3-333-3-333-3-3−3i−3i3i3i−3i−3i3i3i1-1−i−iii0000i−i1-1−i−iii1−i−iii-1i−ii−i11-1-111-1-10000000000000000i−i-11-11i−i
χ5333-3-333-3-3-3-33333-3-3-3-3331-1ii−i−i0000−ii1-1ii−i−i-1−i−iii1-111-1−i−iiiii−i−i0000000000000000−iii−i−iii−i
χ5433-3-333-3-3-3-33333-3-3-3-3331-1−i−iii0000i−i1-1−i−iii-1ii−i−i1-111-1ii−i−i−i−iii0000000000000000i−i−iii−i−ii
χ5533-3-333-3-3-3-333-3-33333-3-31-1ii−i−i0000−ii1-1ii−i−i-1−i−iii11-1-11ii−i−i−i−iii0000000000000000−ii−iii−ii−i
χ5633-3-333-3-3-3-333-3-33333-3-31-1−i−iii0000i−i1-1−i−iii-1ii−i−i11-1-11−i−iiiii−i−i0000000000000000i−ii−i−ii−ii
χ574444-1-1-1-1000000000000444444444444-1-1-1-1-1-1000000000000000000-1-1-1-1000000000000-1-1000000
χ584444-1-1-1-100000000000044-4-4-4-44444-4-4-1-11111000000000000000000-1-1-1-100000000000011000000
χ5944-4-4-1-111000000000000-444i4i−4i−4i44-4-44i−4i1-1−i−iii000000000000000000-1-111000000000000−ii000000
χ6044-4-4-1-111000000000000-44−4i−4i4i4i44-4-4−4i4i1-1ii−i−i000000000000000000-1-111000000000000i−i000000
χ614-44i−4i4-44i−4i4-44i−4i4ζ−4ζ4ζ3−4ζ34ζ−4ζ4ζ3−4ζ30000001-1−ii000000000000000000000000001-1−ii-11−ii−ζζ−ζ3ζ3−ζζ−ζ3ζ300000000
χ624-44i−4i4-44i−4i4-44i−4i−4ζ4ζ−4ζ34ζ3−4ζ4ζ−4ζ34ζ30000001-1−ii000000000000000000000000001-1−ii-11−iiζ−ζζ3−ζ3ζ−ζζ3−ζ300000000
χ634-44i−4i4-44i−4i-44−4i4i4ζ3−4ζ3−4ζ4ζ−4ζ34ζ34ζ−4ζ0000001-1−ii000000000000000000000000001-1−ii1-1i−i−ζ3ζ3ζ−ζζ3−ζ3−ζζ00000000
χ644-44i−4i4-44i−4i-44−4i4i−4ζ34ζ34ζ−4ζ4ζ3−4ζ3−4ζ4ζ0000001-1−ii000000000000000000000000001-1−ii1-1i−iζ3−ζ3−ζζ−ζ3ζ3ζ−ζ00000000
χ654-4−4i4i4-4−4i4i4-4−4i4i4ζ3−4ζ34ζ−4ζ4ζ3−4ζ34ζ−4ζ0000001-1i−i000000000000000000000000001-1i−i-11i−i−ζ3ζ3−ζζ−ζ3ζ3−ζζ00000000
χ664-4−4i4i4-4−4i4i4-4−4i4i−4ζ34ζ3−4ζ4ζ−4ζ34ζ3−4ζ4ζ0000001-1i−i000000000000000000000000001-1i−i-11i−iζ3−ζ3ζ−ζζ3−ζ3ζ−ζ00000000
χ674-4−4i4i4-4−4i4i-444i−4i4ζ−4ζ−4ζ34ζ3−4ζ4ζ4ζ3−4ζ30000001-1i−i000000000000000000000000001-1i−i1-1−ii−ζζζ3−ζ3ζ−ζ−ζ3ζ300000000
χ684-4−4i4i4-4−4i4i-444i−4i−4ζ4ζ4ζ3−4ζ34ζ−4ζ−4ζ34ζ30000001-1i−i000000000000000000000000001-1i−i1-1−iiζ−ζ−ζ3ζ3−ζζζ3−ζ300000000
χ698888-2-2-2-2000000000000880000-4-4-4-400-2-20000000000000000000000111100000000000000000000
χ7088-8-8-2-222000000000000-880000-4-444002-2000000000000000000000011-1-100000000000000000000
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χ738-8−8i8i-222i−2i000000000000004−4i−4+4i4+4i−4−4i-44−4i4i0000−1+i1−i−1−i1+i0000000000000000001-1i−i00000000000000000000
χ748-8−8i8i-222i−2i00000000000000−4+4i4−4i−4−4i4+4i-44−4i4i00001−i−1+i1+i−1−i0000000000000000001-1i−i00000000000000000000
χ7512121212-3-3-3-3000000000000-4-444440000-4-411-1-1-1-1000000000000000000000000000000000011000000
χ7612121212-3-3-3-3000000000000-4-4-4-4-4-40000441111110000000000000000000000000000000000-1-1000000
χ771212-12-12-3-3330000000000004-44i4i−4i−4i0000−4i4i-11−i−iii0000000000000000000000000000000000i−i000000
χ781212-12-12-3-3330000000000004-4−4i−4i4i4i00004i−4i-11ii−i−i0000000000000000000000000000000000−ii000000
χ7916-1616i−16i-44−4i4i0000000000000000004-4−4i4i00000000000000000000000000-11i−i00000000000000000000
χ8016-16−16i16i-444i−4i0000000000000000004-44i−4i00000000000000000000000000-11−ii00000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.