Finite Group Databasebeta

← Group #10697550

Character table — Group #10697550

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212444488881212121212121212121224242424242424248824242424224488882224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ92222222222-2-222222222-2-2-22222-2-2-2-200000000-2-2000000000000000000000022-2-200000000
χ102222222222-2-222222222-2-2-22222-2-2-2-200000000-2-20000000000000000000000-2-22200000000
χ112222222-2-2-222-2222-2-2-2-2-22-222-2-2-2-222000000002-20000000000000000000000000000002-200
χ122222222-2-2-222-2222-2-2-2-2-22-222-2-2-2-222000000002-2000000000000000000000000000000-2200
χ132222222-2-2-2-2-2-2222-2-2-2-22-2222-2-222-2-222-2-20000-222222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-2-2-2-22-2222-2-222-2-2-2-2220000-22-2-2-2-2222200000000000000000000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-1-1-111112-22-1-111-1-11122-2-200001-1-1-1-1-111113333−3−3−3−30033−3−3000000000000
χ20222222-1-2-2-2-2-2-2-1-1-111112-22-1-111-1-11122-2-200001-1-1-1-1-11111−3−3−3−3333300−3−333000000000000
χ21222222-1-2-2-2-2-2-2-1-1-111112-22-1-111-1-111-2-22200001-11111-1-1-1-13333−3−3−3−300−3−333000000000000
χ22222222-1-2-2-2-2-2-2-1-1-111112-22-1-111-1-111-2-22200001-11111-1-1-1-1−3−3−3−333330033−3−3000000000000
χ232222-2-2222-222-2222-2-2-2-2-2-22-2-222-2-222000022-2-2-220000000022-2-222-2-2000000000000000000
χ242222-2-2222-222-2222-2-2-2-2-2-22-2-222-2-2220000-2-222-2200000000-2-222-2-222000000000000000000
χ252222-2-2222-2-2-2-2222-2-2-2-222-2-2-22222-2-2000000002-2000000000000000000000000002i2i−2i−2i0000
χ262222-2-2222-2-2-2-2222-2-2-2-222-2-2-22222-2-2000000002-200000000000000000000000000−2i−2i2i2i0000
χ272222-2-22-2-2222222222222-2-2-2-2-2-2222200000000-2-2000000000000000000000000000000002-2
χ282222-2-22-2-2222222222222-2-2-2-2-2-2222200000000-2-200000000000000000000000000000000-22
χ292222-2-22-2-22-2-222222222-222-2-2-2-2-2-2-2-2000000002200000000000000002-22-22-2000000000000
χ302222-2-22-2-22-2-222222222-222-2-2-2-2-2-2-2-200000000220000000000000000-22-22-22000000000000
χ312222-2-2-122-222-2-1-1-11111-2-2211-1-111-1-1000022-2-21-133−3−333−3−3-1-111-1-111003−3−33000000000000
χ322222-2-2-122-222-2-1-1-11111-2-2211-1-111-1-1000022-2-21-1−3−333−3−333-1-111-1-11100−333−3000000000000
χ332222-2-2-122-222-2-1-1-11111-2-2211-1-111-1-10000-2-2221-133−3−333−3−311-1-111-1-100−333−3000000000000
χ342222-2-2-122-222-2-1-1-11111-2-2211-1-111-1-10000-2-2221-1−3−333−3−33311-1-111-1-1003−3−33000000000000
χ352222-2-2-1-2-22-2-22-1-1-1-1-1-1-1-2221111111100000000-1-133−3−3−3−33333−3−3−3−333-221-11-1000000000000
χ362222-2-2-1-2-22-2-22-1-1-1-1-1-1-1-2221111111100000000-1-133−3−3−3−333−3−33333−3−32-2-11-11000000000000
χ372222-2-2-1-2-22-2-22-1-1-1-1-1-1-1-2221111111100000000-1-1−3−33333−3−333−3−3−3−3332-2-11-11000000000000
χ382222-2-2-1-2-22-2-22-1-1-1-1-1-1-1-2221111111100000000-1-1−3−33333−3−3−3−33333−3−3-221-11-1000000000000
χ392-22-22-222-2200-22-2-222-2-20002-22-2000000002−22−200000000002−22−22−22−2000000002i−2i−i2i2−i2i20000
χ402-22-22-222-2200-22-2-222-2-20002-22-2000000002−22−200000000002−22−22−22−200000000−2i2ii2−i2i2−i20000
χ412-22-22-222-2200-22-2-222-2-20002-22-200000000−22−220000000000−22−22−22−22000000002i−2ii2−i2i2−i20000
χ422-22-22-222-2200-22-2-222-2-20002-22-200000000−22−220000000000−22−22−22−2200000000−2i2i−i2i2−i2i20000
χ432-22-2-2222-2-20022-2-2-2-222000-222-2000000002−2−2200000000002−2−222−2−220000002-2002−2−220000
χ442-22-2-2222-2-20022-2-2-2-222000-222-2000000002−2−2200000000002−2−222−2−22000000-2200−222−20000
χ452-22-2-2222-2-20022-2-2-2-222000-222-200000000−222−20000000000−222−2−222−20000002-200−222−20000
χ462-22-2-2222-2-20022-2-2-2-222000-222-200000000−222−20000000000−222−2−222−2000000-22002−2−220000
χ47444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-2-2-2222200000000220000000000000000000000000000000000
χ48444444-2-4-4-444-4-2-2-22222-44-4-2-22222-2-200000000-220000000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-2222244-422-2-2-2-22200000000-220000000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-2-2-2-2-24-4-42222-2-2-2-200000000220000000000000000000000000000000000
χ514-44-44-44-44-40044-4-4-4-4440004-4-44000000000000000000000000000000000000000000000000
χ524-44-44-4-24-4400-4-222-2-222000-22-220000000022−2222−220000000000−22−22−22−22000000000000000000
χ534-44-44-4-24-4400-4-222-2-222000-22-2200000000−2222−222200000000002−22−22−22−2000000000000000000
χ544-44-44-4-2-44-4004-22222-2-2000-222-200000000000000000000006−66−6−66−66000000000000000000
χ554-44-44-4-2-44-4004-22222-2-2000-222-20000000000000000000000−66−666−66−6000000000000000000
χ564-44-4-444-44400-44-4-444-4-4000-44-44000000000000000000000000000000000000000000000000
χ574-44-4-44-24-4-4004-22222-2-20002-2-220000000022−22−22220000000000−222−2−222−2000000000000000000
χ584-44-4-44-24-4-4004-22222-2-20002-2-2200000000−222222−2200000000002−2−222−2−22000000000000000000
χ594-44-4-44-2-44400-4-222-2-2220002-22-200000000000000000000006−6−66−666−6000000000000000000
χ604-44-4-44-2-44400-4-222-2-2220002-22-20000000000000000000000−666−66−6−66000000000000000000
χ614-4-440040004-40-44-400000000000004-42-22-20000002-22-22-22-200000000000000000000000000
χ624-4-440040004-40-44-400000000000004-4-22-22000000-22-22-22-2200000000000000000000000000
χ634-4-44004000-440-44-40000000000000-442-2-220000002-22-2-22-2200000000000000000000000000
χ644-4-44004000-440-44-40000000000000-44-222-2000000-22-222-22-200000000000000000000000000
χ654-4-4400-20004-402-2223−2323−23000000023−23-222-22-2000000−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000000000
χ664-4-4400-20004-402-2223−2323−23000000023−23-22-22-220000001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000000000
χ674-4-4400-20004-402-22−2323−23230000000−2323-222-22-2000000−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000000000
χ684-4-4400-20004-402-22−2323−23230000000−2323-22-22-220000001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000000000
χ694-4-4400-2000-4402-2223−2323−230000000−23232-22-2-22000000−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000000000
χ704-4-4400-2000-4402-2223−2323−230000000−23232-2-222-20000001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000000000
χ714-4-4400-2000-4402-22−2323−2323000000023−232-22-2-22000000−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000000000
χ724-4-4400-2000-4402-22−2323−2323000000023−232-2-222-20000001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000000000
χ7388-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ7488-8-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ7588-8-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000

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