Finite Group Databasebeta

← Group #13165970

Character table — Group #13165970

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222266666688889999121212121212121212121212121212121212121212121212121216161616161616161616161616161616242424242424242454545454545472727272108108
order12443333666612121212121212122444443612128888666688121212121212121212121212121212121212121233336666121212121212121224242424242424248888882424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511-1-111111111-1-1-1-1-1-1-1-1-1ii−i−i111-1-1ii−i−i-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−i1-1
χ611-1-111111111-1-1-1-1-1-1-1-1-1ii−i−i111-1-1−i−iii-1-1-1-1i−i1111iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−ii-1-111−i−iii-11
χ711-1-111111111-1-1-1-1-1-1-1-1-1−i−iii111-1-1ii−i−i-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiiii−i-1-111ii−i−i-11
χ811-1-111111111-1-1-1-1-1-1-1-1-1−i−iii111-1-1−i−iii-1-1-1-1−ii1111−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii1-1
χ922222222222222222222200002-1-1-1-1222222220022220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-100
χ1022222222222222222222200002-1-1-1-1-2-2-2-222220022220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-20000111100
χ1122222-1-1-12-1-1-122-1-1-1-1-1-1222222222200002-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1000000000000
χ1222222-1-1-12-1-1-122-1-1-1-1-1-12-2-2-2-22222200002-1-1-1-2-22-1-1-1-2-2111111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1-2111-2111000000000000
χ132222-12-1-1-12-1-1-1-122-1-1-1-122222222220000-12-1-122-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1000000000000
χ142222-12-1-1-12-1-1-1-122-1-1-1-12-2-2-2-2222220000-12-1-1-2-2-12-1-111-2-2111111-2-21111-12-1-1-12-1-1-1-122-1-1-1-11-2111-211000000000000
χ152222-1-12-1-1-12-1-1-1-1-122-1-122222222220000-1-12-122-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1000000000000
χ162222-1-12-1-1-12-1-1-1-1-122-1-12-2-2-2-2222220000-1-12-1-2-2-1-12-11111-2-2111111-2-211-1-12-1-1-12-1-1-1-1-122-1-111-2111-21000000000000
χ172222-1-1-12-1-1-12-1-1-1-1-1-12222222222220000-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12000000000000
χ182222-1-1-12-1-1-12-1-1-1-1-1-1222-2-2-2-2222220000-1-1-12-2-2-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2000000000000
χ1922-2-222222222-2-2-2-2-2-2-2-2-200002-1-1112i2i−2i−2i-2-2-2-20022220000000000000000-1-1-1-1-1-1-1-111111111000000002i−2i0000−i−iii00
χ2022-2-222222222-2-2-2-2-2-2-2-2-200002-1-111−2i−2i2i2i-2-2-2-20022220000000000000000-1-1-1-1-1-1-1-11111111100000000−2i2i0000ii−i−i00
χ2122-2-22-1-1-12-1-1-1-2-2111111-22i2i−2i−2i222-2-20000-21112i−2i2-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-12-1-1-1-2-21111112i−i−i−i−2iiii000000000000
χ2222-2-22-1-1-12-1-1-1-2-2111111-2−2i−2i2i2i222-2-20000-2111−2i2i2-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-12-1-1-1-2-2111111−2iiii2i−i−i−i000000000000
χ2322-2-2-12-1-1-12-1-111-2-21111-22i2i−2i−2i222-2-200001-2112i−2i-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-1-12-1-111-2-21111−i2i−i−ii−2iii000000000000
χ2422-2-2-12-1-1-12-1-111-2-21111-2−2i−2i2i2i222-2-200001-211−2i2i-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i-12-1-1-12-1-111-2-21111i−2iii−i2i−i−i000000000000
χ2522-2-2-1-12-1-1-12-11111-2-211-22i2i−2i−2i222-2-2000011-212i−2i-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii-1-12-1-1-12-11111-2-211−i−i2i−iii−2ii000000000000
χ2622-2-2-1-12-1-1-12-11111-2-211-2−2i−2i2i2i222-2-2000011-21−2i2i-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i-1-12-1-1-12-11111-2-211ii−2ii−i−i2i−i000000000000
χ2722-2-2-1-1-12-1-1-12111111-2-2-22i2i−2i−2i222-2-20000111-22i−2i-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i-1-1-12-1-1-12111111-2-2−i−i−i2iiii−2i000000000000
χ2822-2-2-1-1-12-1-1-12111111-2-2-2−2i−2i2i2i222-2-20000111-2−2i2i-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i-1-1-12-1-1-12111111-2-2iii−2i−i−i−i2i000000000000
χ292-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i01+i−1−i1−i−1+i0-11i−i2ζ3−2ζ32ζ−2ζ00000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i-1-1-1-11111i−ii−ii−ii−i0000000000i2−i22−2ζ3−ζ3ζ−ζ00
χ302-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i01+i−1−i1−i−1+i0-11i−i−2ζ32ζ3−2ζ2ζ00000000001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i-1-1-1-11111i−ii−ii−ii−i0000000000−i2i2−22−ζ3ζ3−ζζ00
χ312-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i0−1−i1+i−1+i1−i0-11i−i2ζ3−2ζ32ζ−2ζ0000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i-1-1-1-11111i−ii−ii−ii−i0000000000−i2i2−22ζ3−ζ3ζ−ζ00
χ322-22i−2i2222-2-2-2-22i−2i2i−2i2i−2i2i−2i0−1−i1+i−1+i1−i0-11i−i−2ζ32ζ3−2ζ2ζ0000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i-1-1-1-11111i−ii−ii−ii−i0000000000i2−i22−2−ζ3ζ3−ζζ00
χ332-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i01−i−1+i1+i−1−i0-11−ii2ζ−2ζ2ζ3−2ζ300000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i-1-1-1-11111−ii−ii−ii−ii0000000000i2−i2−22ζ−ζζ3−ζ300
χ342-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i01−i−1+i1+i−1−i0-11−ii−2ζ2ζ−2ζ32ζ300000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i-1-1-1-11111−ii−ii−ii−ii0000000000−i2i22−2−ζζ−ζ3ζ300
χ352-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i0−1+i1−i−1−i1+i0-11−ii2ζ−2ζ2ζ3−2ζ30000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i-1-1-1-11111−ii−ii−ii−ii0000000000−i2i22−2ζ−ζζ3−ζ300
χ362-2−2i2i2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i0−1+i1−i−1−i1+i0-11−ii−2ζ2ζ−2ζ32ζ30000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i-1-1-1-11111−ii−ii−ii−ii0000000000i2−i2−22−ζζ−ζ3ζ300
χ3733333333333333333333-11111-100003333-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-1-1-111110000-1-1
χ3833333333333333333333-11111-10000-3-3-3-3-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-111-1-1-1-1000011
χ3933333333333333333333-1-1-1-1-1-100003333-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1000011
χ4033333333333333333333-1-1-1-1-1-10000-3-3-3-3-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000111111111111110000-1-1
χ4133-3-333333333-3-3-3-3-3-3-3-31ii−i−i-100003i3i−3i−3i1111−ii-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−i−i−i−iiiii−ii11-1-10000-11
χ4233-3-333333333-3-3-3-3-3-3-3-31ii−i−i-10000−3i−3i3i3i1111−ii-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−i−i−i−iiiiii−i-1-11100001-1
χ4333-3-333333333-3-3-3-3-3-3-3-31−i−iii-100003i3i−3i−3i1111i−i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000iiii−i−i−i−i−ii-1-11100001-1
χ4433-3-333333333-3-3-3-3-3-3-3-31−i−iii-10000−3i−3i3i3i1111i−i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii0000000000000000iiii−i−i−i−ii−i11-1-10000-11
χ4544444-2-2-24-2-2-244-2-2-2-2-2-2400004-2-2-2-200004-2-2-2004-2-2-20000000000000000-2111-2111-2-211111100000000000000000000
χ464444-24-2-2-24-2-2-2-244-2-2-2-2400004-2-2-2-20000-24-2-200-24-2-200000000000000001-2111-21111-2-2111100000000000000000000
χ474444-2-24-2-2-24-2-2-2-2-244-2-2400004-2-2-2-20000-2-24-200-2-24-2000000000000000011-2111-211111-2-21100000000000000000000
χ484444-2-2-24-2-2-24-2-2-2-2-2-244400004-2-2-2-20000-2-2-2400-2-2-240000000000000000111-2111-2111111-2-200000000000000000000
χ4944-4-44-2-2-24-2-2-2-4-4222222-400004-2-2220000-4222004-2-2-20000000000000000-2111-211122-1-1-1-1-1-100000000000000000000
χ5044-4-4-24-2-2-24-2-222-4-42222-400004-2-22200002-42200-24-2-200000000000000001-2111-211-1-122-1-1-1-100000000000000000000
χ5144-4-4-2-24-2-2-24-22222-4-422-400004-2-222000022-4200-2-24-2000000000000000011-2111-21-1-1-1-122-1-100000000000000000000
χ5244-4-4-2-2-24-2-2-24222222-4-4-400004-2-2220000222-400-2-2-240000000000000000111-2111-2-1-1-1-1-1-12200000000000000000000
χ534-44i−4i4444-4-4-4-44i−4i4i−4i4i−4i4i−4i0000001-1−ii4ζ3−4ζ34ζ−4ζ000000000000000000000000001111-1-1-1-1−ii−ii−ii−ii00000000000000−ζ3ζ3−ζζ00
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χ714-4−4i4i-2-2-24222-42i−2i2i−2i2i−2i−4i4i02−2i−2+2i2+2i−2−2i0-22−2i2i00000000000000−1+i1−i−1+i1−i−1+i1−i2−2i−2+2i−1−i1+i−1−i1+i−1−i1+i2+2i−2−2i111-2-1-1-12i−ii−ii−i−2i2i00000000000000000000
χ724-4−4i4i-2-2-24222-42i−2i2i−2i2i−2i−4i4i0−2+2i2−2i−2−2i2+2i0-22−2i2i000000000000001−i−1+i1−i−1+i1−i−1+i−2+2i2−2i1+i−1−i1+i−1−i1+i−1−i−2−2i2+2i111-2-1-1-12i−ii−ii−i−2i2i00000000000000000000
χ7366666-3-3-36-3-3-366-3-3-3-3-3-3-22222-200000000-2111-2-2-211122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000-2111-2111000000000000
χ7466666-3-3-36-3-3-366-3-3-3-3-3-3-2-2-2-2-2-200000000-211122-2111-2-2111111-2-211111100000000000000002-1-1-12-1-1-1000000000000
χ756666-36-3-3-36-3-3-3-366-3-3-3-3-22222-2000000001-211-2-21-211-1-122-1-1-1-1-1-122-1-1-1-100000000000000001-2111-211000000000000
χ766666-36-3-3-36-3-3-3-366-3-3-3-3-2-2-2-2-2-2000000001-211221-21111-2-2111111-2-211110000000000000000-12-1-1-12-1-1000000000000
χ776666-3-36-3-3-36-3-3-3-3-366-3-3-22222-20000000011-21-2-211-21-1-1-1-122-1-1-1-1-1-122-1-1000000000000000011-2111-21000000000000
χ786666-3-36-3-3-36-3-3-3-3-366-3-3-2-2-2-2-2-20000000011-212211-211111-2-2111111-2-2110000000000000000-1-12-1-1-12-1000000000000
χ796666-3-3-36-3-3-36-3-3-3-3-3-366-22222-200000000111-2-2-2111-2-1-1-1-1-1-122-1-1-1-1-1-1220000000000000000111-2111-2000000000000
χ806666-3-3-36-3-3-36-3-3-3-3-3-366-2-2-2-2-2-200000000111-222111-2111111-2-2111111-2-20000000000000000-1-1-12-1-1-12000000000000
χ8166-6-66-3-3-36-3-3-3-6-633333322i2i−2i−2i-2000000002-1-1-1−2i2i-21112i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000000000−2iiii2i−i−i−i000000000000
χ8266-6-66-3-3-36-3-3-3-6-63333332−2i−2i2i2i-2000000002-1-1-12i−2i-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000000002i−i−i−i−2iiii000000000000
χ8366-6-6-36-3-3-36-3-333-6-6333322i2i−2i−2i-200000000-12-1-1−2i2i1-211−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000000000i−2iii−i2i−i−i000000000000
χ8466-6-6-36-3-3-36-3-333-6-633332−2i−2i2i2i-200000000-12-1-12i−2i1-211ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000000000−i2i−i−ii−2iii000000000000
χ8566-6-6-3-36-3-3-36-33333-6-63322i2i−2i−2i-200000000-1-12-1−2i2i11-21−i−i−i−i2i2i−i−iiiii−2i−2iii0000000000000000ii−2ii−i−i2i−i000000000000
χ8666-6-6-3-36-3-3-36-33333-6-6332−2i−2i2i2i-200000000-1-12-12i−2i11-21iiii−2i−2iii−i−i−i−i2i2i−i−i0000000000000000−i−i2i−iii−2ii000000000000
χ8766-6-6-3-3-36-3-3-36333333-6-622i2i−2i−2i-200000000-1-1-12−2i2i111-2−i−i−i−i−i−i2i2iiiiiii−2i−2i0000000000000000iii−2i−i−i−i2i000000000000
χ8866-6-6-3-3-36-3-3-36333333-6-62−2i−2i2i2i-200000000-1-1-122i−2i111-2iiiiii−2i−2i−i−i−i−i−i−i2i2i0000000000000000−i−i−i2iiii−2i000000000000
χ898-88i−8i8-4-4-4-84448i−8i−4i4i−4i4i−4i4i0000002-2−2i2i0000000000000000000000000000002-1-1-1-2111−2i2ii−ii−ii−i00000000000000000000
χ908-88i−8i-48-4-44-844−4i4i8i−8i−4i4i−4i4i0000002-2−2i2i000000000000000000000000000000-12-1-11-211i−i−2i2ii−ii−i00000000000000000000
χ918-88i−8i-4-48-444-84−4i4i−4i4i8i−8i−4i4i0000002-2−2i2i000000000000000000000000000000-1-12-111-21i−ii−i−2i2ii−i00000000000000000000
χ928-88i−8i-4-4-48444-8−4i4i−4i4i−4i4i8i−8i0000002-2−2i2i000000000000000000000000000000-1-1-12111-2i−ii−ii−i−2i2i00000000000000000000
χ938-8−8i8i8-4-4-4-8444−8i8i4i−4i4i−4i4i−4i0000002-22i−2i0000000000000000000000000000002-1-1-1-21112i−2i−ii−ii−ii00000000000000000000
χ948-8−8i8i-48-4-44-8444i−4i−8i8i4i−4i4i−4i0000002-22i−2i000000000000000000000000000000-12-1-11-211−ii2i−2i−ii−ii00000000000000000000
χ958-8−8i8i-4-48-444-844i−4i4i−4i−8i8i4i−4i0000002-22i−2i000000000000000000000000000000-1-12-111-21−ii−ii2i−2i−ii00000000000000000000
χ968-8−8i8i-4-4-48444-84i−4i4i−4i4i−4i−8i8i0000002-22i−2i000000000000000000000000000000-1-1-12111-2−ii−ii−ii2i−2i00000000000000000000

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