Finite Group Databasebeta

← Group #10696468

Character table — Group #10696468

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222444444444444448888888888888888888888888816161616161624242424484848484848
order122222223666666644444412121212121212128888888812122424242424242424242424242424242444121212128888222244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-11-1-1-11
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ922222222222222222-2-2-2-22-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-20000000000
χ1022222222222222222-2-2-2-22-2-2-2-2-2-2-2-200000000220000000000000000-22-2-2220000000000
χ112222222222222222-22-22-2-222-2-222-2-200000000-2-20000000000000000000000000002000-2
χ122222222222222222-22-22-2-222-2-222-2-200000000-2-2000000000000000000000000000-20002
χ132222222222222222-2-22-22-2-2-222-2-22200000000-2-2000000000000000000000000002000-20
χ142222222222222222-2-22-22-2-2-222-2-22200000000-2-200000000000000000000000000-200020
χ1522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ1722222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ1822222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ1922222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-13333−3−3−3−33333−3−3−3−32-2-1-1110000000000
χ2022222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-13333−3−3−3−3−3−3−3−33333-2211-1-10000000000
χ2122222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-1−3−3−3−333333333−3−3−3−3-2211-1-10000000000
χ2222222222-1-1-1-1-1-1-1-12-2-2-2-221111111100000000-1-1−3−3−3−33333−3−3−3−333332-2-1-1110000000000
χ232-2-22-2-2222-2-2222-2-2222-2-2-22222-2-2-2-2000000002-200000000000000000000002i2i−2i−2i000000
χ242-2-22-2-2222-2-2222-2-2222-2-2-22222-2-2-2-2000000002-20000000000000000000000−2i−2i2i2i000000
χ252-2-22-2-2222-2-2222-2-22-2-222-2-2-2-2-22222000000002-200000000000000000000000000002-200
χ262-2-22-2-2222-2-2222-2-22-2-222-2-2-2-2-22222000000002-20000000000000000000000000000-2200
χ272-2-22-2-2222-2-2222-2-2-22-2-22222-2-2-2-222000022-2-2-220000000022-2-222-2-20000000000000000
χ282-2-22-2-2222-2-2222-2-2-22-2-22222-2-2-2-2220000-2-222-2200000000-2-222-2-2220000000000000000
χ292-2-22-2-2222-2-2222-2-2-2-222-22-2-22222-2-222-2-20000-2222-2-222-2-2000000000000000000000000
χ302-2-22-2-2222-2-2222-2-2-2-222-22-2-22222-2-2-2-2220000-22-2-222-2-222000000000000000000000000
χ312-2-22-2-222-111-1-1-111-22-2-222-1-11111-1-1000022-2-21-133−3−3−3−333-1-111-1-111003−33−30000000000
χ322-2-22-2-222-111-1-1-111-22-2-222-1-11111-1-1000022-2-21-1−3−33333−3−3-1-111-1-11100−33−330000000000
χ332-2-22-2-222-111-1-1-111-22-2-222-1-11111-1-10000-2-2221-133−3−3−3−33311-1-111-1-100−33−330000000000
χ342-2-22-2-222-111-1-1-111-22-2-222-1-11111-1-10000-2-2221-1−3−33333−3−311-1-111-1-1003−33−30000000000
χ352-2-22-2-222-111-1-1-111-2-222-2211-1-1-1-11122-2-200001-1-1-111-1-11133−3−3−3−33300−333−30000000000
χ362-2-22-2-222-111-1-1-111-2-222-2211-1-1-1-11122-2-200001-1-1-111-1-111−3−33333−3−3003−3−330000000000
χ372-2-22-2-222-111-1-1-111-2-222-2211-1-1-1-111-2-22200001-111-1-111-1-133−3−3−3−333003−3−330000000000
χ382-2-22-2-222-111-1-1-111-2-222-2211-1-1-1-111-2-22200001-111-1-111-1-1−3−33333−3−300−333−30000000000
χ3944444444-2-2-2-2-2-2-2-2-44-44-4-4-2-222-2-222000000002200000000000000000000000000000000
χ4044444444-2-2-2-2-2-2-2-2-4-44-44-422-2-222-2-2000000002200000000000000000000000000000000
χ414444-4-4-4-44444-4-4-4-400000000000000000000000000000000000000000000002i−2i2i−2i000000
χ424444-4-4-4-44444-4-4-4-40000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ4344-4-44-44-444-4-44-44-4000000000000002-22-20000002-22-22-22-2000000000000000000000000
χ4444-4-44-44-444-4-44-44-400000000000000-22-22000000-22-22-22-22000000000000000000000000
χ4544-4-44-44-4-2-222-22-220000000023−230023−232-22-2000000−1+31−3−1+31−3−1−31+3−1−31+3000000000000000000000000
χ4644-4-44-44-4-2-222-22-220000000023−230023−23-22-220000001−3−1+31−3−1+31+3−1−31+3−1−3000000000000000000000000
χ4744-4-44-44-4-2-222-22-2200000000−232300−23232-22-2000000−1−31+3−1−31+3−1+31−3−1+31−3000000000000000000000000
χ4844-4-44-44-4-2-222-22-2200000000−232300−2323-22-220000001+3−1−31+3−1−31−3−1+31−3−1+3000000000000000000000000
χ4944-4-4-44-4444-4-4-44-440000000000000000002-22-200000000002-22-22-22-20000000000000000
χ5044-4-4-44-4444-4-4-44-44000000000000000000-22-220000000000-22-22-22-220000000000000000
χ5144-4-4-44-44-2-2222-22-200000023−230023−230000002-22-20000000000−1+31−3−1+31−3−1−31+3−1−31+30000000000000000
χ5244-4-4-44-44-2-2222-22-200000023−230023−23000000-22-2200000000001−3−1+31−3−1+31+3−1−31+3−1−30000000000000000
χ5344-4-4-44-44-2-2222-22-2000000−232300−23230000002-22-20000000000−1−31+3−1−31+3−1+31−3−1+31−30000000000000000
χ5444-4-4-44-44-2-2222-22-2000000−232300−2323000000-22-2200000000001+3−1−31+3−1−31−3−1+31−3−1+30000000000000000
χ554-44-44-4-444-44-4-444-40000000000000000002-2-2200000000002-2-222-2-220000000000000000
χ564-44-44-4-444-44-4-444-4000000000000000000-222-20000000000-222-2-222-20000000000000000
χ574-44-44-4-44-22-222-2-2200000023−2300−23230000002-2-220000000000−1+31−31−3−1+3−1−31+31+3−1−30000000000000000
χ584-44-44-4-44-22-222-2-2200000023−2300−2323000000-222-200000000001−3−1+3−1+31−31+3−1−3−1−31+30000000000000000
χ594-44-44-4-44-22-222-2-22000000−23230023−230000002-2-220000000000−1−31+31+3−1−3−1+31−31−3−1+30000000000000000
χ604-44-44-4-44-22-222-2-22000000−23230023−23000000-222-200000000001+3−1−3−1−31+31−3−1+3−1+31−30000000000000000
χ614-44-4-444-44-44-44-4-44000000000000002-2-220000002-2-222-2-22000000000000000000000000
χ624-44-4-444-44-44-44-4-4400000000000000-222-2000000-222-2-222-2000000000000000000000000
χ634-44-4-444-4-22-22-222-20000000023−2300−23232-2-22000000−1+31−31−3−1+3−1−31+31+3−1−3000000000000000000000000
χ644-44-4-444-4-22-22-222-20000000023−2300−2323-222-20000001−3−1+3−1+31−31+3−1−3−1−31+3000000000000000000000000
χ654-44-4-444-4-22-22-222-200000000−23230023−232-2-22000000−1−31+31+3−1−3−1+31−31−3−1+3000000000000000000000000
χ664-44-4-444-4-22-22-222-200000000−23230023−23-222-20000001+3−1−3−1−31+31−3−1+3−1+31−3000000000000000000000000
χ674-4-4444-4-44-4-44-4-44400000000000000000000000000000000000000000000002-2-22000000
χ684-4-4444-4-44-4-44-4-4440000000000000000000000000000000000000000000000-222-2000000
χ694-4-44-4-444-222-2-2-222444-4-4-4-2-2-2-2222200000000-2200000000000000000000000000000000
χ704-4-44-4-444-222-2-2-2224-4-444-42222-2-2-2-200000000-2200000000000000000000000000000000
χ718888-8-8-8-8-4-4-4-4444400000000000000000000000000000000000000000000000000000000
χ728-8-8888-8-8-444-444-4-400000000000000000000000000000000000000000000000000000000

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