Finite Group Databasebeta

← Group #13172116

Character table — Group #13172116

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order122233366666666623336666666666644366666666666666624444121212121212121222224444666612121212121212121212121212121212446666121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1-1-111-1-111111-1-1-111111111-1-1-1-1-11-1-1-1-111-1-1-1-1-11-1
χ31111111111111111111111111111111111111111111111111-1111-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1-111-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-1-11-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-111111-11
χ71111111111111111111111111111111-1-11111111111111111-111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-111-111
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-111-1-1-1-1111111-11-1-1-1-111-1-1-1-111-1-1-1111-1-1-1-11111-11-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-1111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-111111-1-11111-1-111-1-1-1-1-1-11-111-1-111-1-111-1-1111-111-1-111-1-1111-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-1-111-1-111-1-111-1-11111-11-1-111-1-111-1-111-1-11-111-1-111-1-1-1-11-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-111-1-1-1-111111111-1-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-111-1-111-1-1-1-11111-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-11111-1-11111-1-111-1111-1-1-1-111-1-1-111
χ17222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12220200002222222200002-1-1-1-1-1-12000000-1-1-1-1-1-100-1-1-1-1000000000
χ18222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-2-2020000-2-222-2-2-2-200002-1-1-1-111-2000000-1-11111001111000000000
χ19222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2220-2000022-2-2-2-2-2-20000-21111-1-1200000011-1-1-1-1001111000000000
χ20222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-20-20000-2-2-2-222220000-2111111-200000011111100-1-1-1-1000000000
χ21222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-1111122-20-2000022-2-222-2-200002-1-1-11-11-200000011-1-11100-1-111000000000
χ22222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-111112-220-20000-2-2-2-2-2-22200002-1-1-111-120000001111-1-10011-1-1000000000
χ23222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-22-20200002222-2-2220000-2111-1-11-2000000-1-1-1-1110011-1-1000000000
χ24222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2-22020000-2-22222-2-20000-2111-11-12000000-1-111-1-100-1-111000000000
χ2522222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-120022-1-12200-1-100002200-12-1-120002-1-1-1-1-1-1-10000020000-1-100000-10
χ2622222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-1-2002-2-1-12200110000-2-2001-211-20002-1-1-1-1-11100000-20000110000010
χ2722222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1200-2211-2-200-1-10000-2-200-12-1-12000-211111-1-100000-20000110000010
χ2822222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-200-2-211-2-20011000022001-211-2000-211111110000020000-1-100000-10
χ2922222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-11111200-2-2-1-12200110000-2-200-12-1-1-2000-21-1-1111100000200001100000-10
χ3022222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-11111-200-22-1-12200-1-1000022001-2112000-21-1-111-1-100000-20000-1-10000010
χ3122222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-111112002-211-2-2001100002200-12-1-1-20002-111-1-11100000-20000-1-10000010
χ3222222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111-2002211-2-200-1-10000-2-2001-21120002-111-1-1-1-100000200001100000-10
χ332222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10222022-1-1-1-100000000220000022-1-12-1-1-1-100-1-1-1-120000000-1-100-100
χ342222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10-2-22022-1-11100000000-2-200000-2-21-12-1-1-1-1001111-200000001100100
χ352222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1022-20-2-211-1-100000000-2-20000022-11-2111100-1-1-1-1-200000001100100
χ362222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-2-20-2-21111000000002200000-2-211-2111100111120000000-1-100-100
χ372222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-1111102-2-2022-1-1-1-10000000022000002-211-2-1-11100-1-111-20000000-1-100100
χ382222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-22-2022-1-11100000000-2-200000-22-11-2-1-1110011-1-1200000001100-100
χ392222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-1111102-220-2-211-1-100000000-2-2000002-21-1211-1-100-1-111200000001100-100
χ402222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110-2220-2-21111000000002200000-22-1-1211-1-10011-1-1-20000000-1-100100
χ4122-2-2222-22-2-2-222-2-20222002-22-2-2-22-2-22i−2i2000000002-2-20000000002i−2i2i−2i00002-200000000000000002i−2i00000000002-20000002i−2i000
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χ5144444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-14000-40000002200000000-2-2112000000000-1-10000000000000000000
χ5244444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-40004000000-2-20000000022-1-1-2000000000110000000000000000000
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χ574444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-2441-2-211-2-2-2-2111111100040-2-2-2-200000000000000000000-2-21111000000000000000000000
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χ1018-88-8-4-4-4-44-44-44444022200-2-2-222-2-22-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-4-44-44-44444022200-2-2-222-2-22-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-484-8-88444-4-402-4-400-2-444-2244-400200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4444-4444-4-40222−4i34i3-22-2-2-22-2-2200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4444-4444-4-402224i3−4i3-22-2-2-22-2-2200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).