Finite Group Databasebeta

← Group #13150875

Character table — Group #13150875

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666666661212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222223666446612121212336666666666366666666612121212121212121212121212121212222222224444446666666666121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11-111-1-11-1-1-1-1-1-1-1-1-11-1111-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-111-11-1-1-1-1-1-1-1-1-11-1-1-1111
χ51111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-111-1-11-1-11
χ61111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-111-1
χ71111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-1-111111-1-1-1111-1
χ81111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-11-1-1-1-11111-1111-1-1-11
χ91111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11-1111-11-1-1-111-1-111-1-1111-1-11-1-1
χ101111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-11-1-1-1-11-111111-1-111-1-1-1-1-111-111
χ111111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-111-11-1-11-11-1-111-1-1111-11-1-1-111
χ121111-1-111111-1-1-111-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111-11-11-111-11-1-1-111-1-111-11-1111-1-1
χ131111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-1111-11-11-1-111-1-1-1-11111-11-1-11-1
χ141111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1-11-1-11-11-11111-1-1-1-111-1-11-111-11
χ151111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-11-1-111-1-11-1-11111-1-11-1-11-11-11
χ161111-1-11111-11-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-111-1-111-1-1-1-11111-1-1111-1-111-1-111-1-1-11111-1-1-111-11-11-1
χ172222222222222222222-1-1-1-1-1-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-100000000
χ182222222222222222222-1-1-1-1-1-1-1-1222-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111111100000000
χ19222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000002002202000000000-1000-1-1-1
χ20222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000-200-2-20-20000000001000111
χ212222222222-2-222-2-2-2-22-1-1-1-1-1-1-1-1222-122-1-1-1-1-1-1-11111-2-2-2-2111111112222-2-200000000-1-1-1-1111100000000
χ222222222222-2-222-2-2-2-22-1-1-1-1-1-1-1-1222-122-1-1-1-1-1-1-11111-2-2-2-211111111-2-2-2-222000000001111-1-1-1-100000000
χ232222222222-2-222-2-2-2-2-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000200-2-202000000000-100011-1
χ242222222222-2-222-2-2-2-2-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000-200220-20000000001000-1-11
χ252222-2-222222-2-2-222-2-22-1-1-11111-1222-1-2-2-1-11111-1-1-11122-2-2-1-1-1-1111122-2-22-200000000-1-111-1-11100000000
χ262222-2-222222-2-2-222-2-22-1-1-11111-1222-1-2-2-1-11111-1-1-11122-2-2-1-1-1-11111-2-222-220000000011-1-111-1-100000000
χ272222-2-222222-2-2-222-2-2-1222-2-2-2-22-1-1-1-111-1-11111-122-2-2-1-111-1-1-1-1111100000002002-20-2000000000-1000-111
χ282222-2-222222-2-2-222-2-2-1222-2-2-2-22-1-1-1-111-1-11111-122-2-2-1-111-1-1-1-111110000000-200-220200000000010001-1-1
χ292222-2-22222-22-2-2-2-2222-1-1-11111-1222-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-122-2-2-2200000000-1-11111-1-100000000
χ302222-2-22222-22-2-2-2-2222-1-1-11111-1222-1-2-2-1-11111-111-1-1-2-2221111-1-1-1-1-2-2222-20000000011-1-1-1-11100000000
χ312222-2-22222-22-2-2-2-222-1222-2-2-2-22-1-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-10000000200-220-2000000000-10001-11
χ322222-2-22222-22-2-2-2-222-1222-2-2-2-22-1-1-1-111-1-11111-1-2-22211-1-11111-1-1-1-10000000-2002-2020000000001000-11-1
χ332-2-222-22-2-22002-2000022-2-222-2-22-2-2222-2-2-222-2-2200000000000000002-22-200000000002-22-2000000000000
χ342-2-222-22-2-22002-2000022-2-222-2-22-2-2222-2-2-222-2-220000000000000000-22-220000000000-22-22000000000000
χ352-2-222-22-2-22002-200002-111-1-111-1-2-22-12-211-1-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i32-22-20000000000-11-11−i3i3−i3i300000000
χ362-2-222-22-2-22002-200002-111-1-111-1-2-22-12-211-1-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3-22-2200000000001-11-1i3−i3i3−i300000000
χ372-2-222-22-2-22002-200002-111-1-111-1-2-22-12-211-1-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i32-22-20000000000-11-11i3−i3i3−i300000000
χ382-2-222-22-2-22002-200002-111-1-111-1-2-22-12-211-1-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3-22-2200000000001-11-1−i3i3−i3i300000000
χ392-2-22-222-2-2200-22000022-2-2-2-2222-2-222-22-2-2-2-222200000000000000002-2-2200000000002-2-22000000000000
χ402-2-22-222-2-2200-22000022-2-2-2-2222-2-222-22-2-2-2-22220000000000000000-222-20000000000-222-2000000000000
χ412-2-22-222-2-2200-2200002-11111-1-1-1-2-22-1-221111-1-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i32-2-220000000000-111-1−i3i3i3−i300000000
χ422-2-22-222-2-2200-2200002-11111-1-1-1-2-22-1-221111-1-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3-222-200000000001-1-11i3−i3−i3i300000000
χ432-2-22-222-2-2200-2200002-11111-1-1-1-2-22-1-221111-1-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i32-2-220000000000-111-1i3−i3−i3i300000000
χ442-2-22-222-2-2200-2200002-11111-1-1-1-2-22-1-221111-1-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3-222-200000000001-1-11−i3i3i3−i300000000
χ45444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000
χ464444444444-4-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-21-2-2111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ474444-4-444444-4-4-444-4-4-2-2-2-22222-2-2-2-212211-1-1-1-11-2-222-2-2221111-1-1-1-1000000000000000000000000000000
χ484444-4-44444-44-4-4-4-444-2-2-2-22222-2-2-2-212211-1-1-1-1122-2-222-2-2-1-1-1-11111000000000000000000000000000000
χ4944-4-40044-4-400000000444-40000-44-4-44004-40000-40000000000000000000000000000000000000000000000
χ5044-4-40044-4-4000000004-2-22−2i32i3−2i32i324-4-4-200-22−2i32i3−2i32i320000000000000000000000000000000000000000000000
χ5144-4-40044-4-4000000004-2-222i3−2i32i3−2i324-4-4-200-222i3−2i32i3−2i320000000000000000000000000000000000000000000000
χ5244-4-40044-4-400000000-244-40000-4-222-200-2200002000023−230023−2323−230000000000000000000000000000000000
χ5344-4-40044-4-400000000-244-40000-4-222-200-22000020000−232300−2323−23230000000000000000000000000000000000
χ5444-4-40044-4-400000000-2-2-22−2i32i3−2i32i32-2221001-1i3−i3i3−i3-1000023−2300−33−333i−3i3i−3i000000000000000000000000000000
χ5544-4-40044-4-400000000-2-2-22−2i32i3−2i32i32-2221001-1i3−i3i3−i3-10000−2323003−33−3−3i3i−3i3i000000000000000000000000000000
χ5644-4-40044-4-400000000-2-2-222i3−2i32i3−2i32-2221001-1−i3i3−i3i3-1000023−2300−33−33−3i3i−3i3i000000000000000000000000000000
χ5744-4-40044-4-400000000-2-2-222i3−2i32i3−2i32-2221001-1−i3i3−i3i3-10000−2323003−33−33i−3i3i−3i000000000000000000000000000000
χ584-44-4004-44-40000000044-440000-4-44-4400-440000-40000000000000000000000000000000000000000000000
χ594-44-4004-44-4000000004-22-2−2i32i32i3−2i32-44-4-2002-2−2i32i32i3−2i320000000000000000000000000000000000000000000000
χ604-44-4004-44-4000000004-22-22i3−2i3−2i32i32-44-4-2002-22i3−2i3−2i32i320000000000000000000000000000000000000000000000
χ614-44-4004-44-400000000-24-440000-42-22-2002-20000200000023−23000023−23−2323000000000000000000000000000000
χ624-44-4004-44-400000000-24-440000-42-22-2002-200002000000−23230000−232323−23000000000000000000000000000000
χ634-44-4004-44-400000000-2-22-2−2i32i32i3−2i322-22100-11i3−i3−i3i3-100000023−233i−3i−3i3i−333−3000000000000000000000000000000
χ644-44-4004-44-400000000-2-22-2−2i32i32i3−2i322-22100-11i3−i3−i3i3-1000000−2323−3i3i3i−3i3−3−33000000000000000000000000000000
χ654-44-4004-44-400000000-2-22-22i3−2i3−2i32i322-22100-11−i3i3i3−i3-100000023−23−3i3i3i−3i−333−3000000000000000000000000000000
χ664-44-4004-44-400000000-2-22-22i3−2i3−2i32i322-22100-11−i3i3i3−i3-1000000−23233i−3i−3i3i3−3−33000000000000000000000000000000
χ674-4-444-44-4-44004-40000-24-4-444-4-4422-2-2-2222-2-222-20000000000000000000000000000000000000000000000
χ684-4-444-44-4-44004-40000-2-222-2-222-222-21-22-1-111-1-11−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000
χ694-4-444-44-4-44004-40000-2-222-2-222-222-21-22-1-111-1-112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000
χ704-4-44-444-4-4400-440000-24-4-4-4-444422-2-22-22222-2-2-20000000000000000000000000000000000000000000000
χ714-4-44-444-4-4400-440000-2-22222-2-2-222-212-2-1-1-1-1111−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000
χ724-4-44-444-4-4400-440000-2-22222-2-2-222-212-2-1-1-1-11112i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000
χ73666666-3-3-3-366-3-3-3-3-3-3000000000000000000000000000000000000000000002022002000000000-10-1-1-1000
χ74666666-3-3-3-366-3-3-3-3-3-300000000000000000000000000000000000000000000-20-2-200-200000000010111000
χ75666666-3-3-3-3-6-6-3-333330000000000000000000000000000000000000000000020-2-2002000000000-1011-1000
χ76666666-3-3-3-3-6-6-3-3333300000000000000000000000000000000000000000000-202200-200000000010-1-11000
χ776666-6-6-3-3-3-36-633-3-33300000000000000000000000000000000000000000000202-200-2000000000-10-111000
χ786666-6-6-3-3-3-36-633-3-33300000000000000000000000000000000000000000000-20-22002000000000101-1-1000
χ796666-6-6-3-3-3-3-663333-3-30000000000000000000000000000000000000000000020-2200-2000000000-101-11000
χ806666-6-6-3-3-3-3-663333-3-300000000000000000000000000000000000000000000-202-200200000000010-11-1000
χ811212-12-1200-6-66600000063−6300000000000000000000000000000000000000000000000000000000000000000000
χ821212-12-1200-6-666000000−636300000000000000000000000000000000000000000000000000000000000000000000
χ8312-1212-1200-66-66000063−630000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-1200-66-660000−63630000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-121212-12-666-600-66000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-1212-666-6006-6000000000000000000000000000000000000000000000000000000000000000000000000

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