Finite Group Databasebeta

← Group #10770415

Character table — Group #10770415

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888888888888888816161616242424242424242448484848
order1222223446661212121244444661212121212122444444488881212121212121212121224242424242424246121212224444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ611111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111
χ91111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-11-11-11-11-11-11-1
χ101111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-1-11-11-11-11-11-11
χ111111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-11-11-11-11-1-11-11
χ121111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-11-111-11-1
χ131111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-1111-1-111-1-11-111-1
χ141111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-111-111-1-111-11-1-11
χ151111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-111-1-11
χ161111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-111-1-111-1-111-1
χ1722222222222222222-2-2-2-22222-2-2-2-2000000000000-2-200000000000000000000002200-2-20000
χ1822222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000000000-2-200220000
χ192222222-2-2222-2-2-2-2-222-2-222-2-222-2-2000000000000-2200000000000000000000002-200-220000
χ202222222-2-2222-2-2-2-2-222-2-222-2-222-2-2000000000000-220000000000000000000000-22002-20000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111111111111111-1-1-1-1000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-11111000000000000
χ25222222-1-2-2-1-1-11111-2-2-222-1-11111-1-12-22-222-2-222-2-2-11-1-1-1-11111-1-1-1-11111-1-111000000000000
χ26222222-1-2-2-1-1-11111-2-2-222-1-11111-1-12-22-2-2-222-2-222-111111-1-1-1-11111-1-1-1-1-1-111000000000000
χ27222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-22-2222-2-2-2-222-11-1-1-1-111111111-1-1-1-111-1-1000000000000
χ28222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-22-22-2-22222-2-2-111111-1-1-1-1-1-1-1-1111111-1-1000000000000
χ292222-2-22222222222-22-22-2-2-2-2-22222000000000000-2-2000000000000000000002200-2-2000000
χ302222-2-22222222222-22-22-2-2-2-2-22222000000000000-2-200000000000000000000-2-20022000000
χ312222-2-22222222222-2-22-22-2-2-2-2-2-2-2-22-2-22000000002200000000000000002-22-2000000000000
χ322222-2-22222222222-2-22-22-2-2-2-2-2-2-2-2-222-200000000220000000000000000-22-22000000000000
χ332222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-222-2-2000000002-200000000000000002-2-22000000000000
χ342222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-2-2-222000000002-20000000000000000-222-2000000000000
χ352222-2-22-2-2222-2-2-2-22-222-2-2-222-2-222000000000000-22000000000000000000002-200-22000000
χ362222-2-22-2-2222-2-2-2-22-222-2-2-222-2-222000000000000-2200000000000000000000-22002-2000000
χ372222-2-2-122-1-1-1-1-1-1-1-2-22-22111111112-2-2200000000-1-133−3−333−3−333−3−333−3−3-11-11000000000000
χ382222-2-2-122-1-1-1-1-1-1-1-2-22-22111111112-2-2200000000-1-1−3−333−3−333−3−333−3−333-11-11000000000000
χ392222-2-2-122-1-1-1-1-1-1-1-2-22-2211111111-222-200000000-1-133−3−333−3−3−3−333−3−3331-11-1000000000000
χ402222-2-2-122-1-1-1-1-1-1-1-2-22-2211111111-222-200000000-1-1−3−333−3−33333−3−333−3−31-11-1000000000000
χ412222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-11122-2-200000000-1133−3−3−3−33333−3−3−3−333-111-1000000000000
χ422222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-11122-2-200000000-11−3−33333−3−3−3−33333−3−3-111-1000000000000
χ432222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-111-2-22200000000-1133−3−3−3−333−3−33333−3−31-1-11000000000000
χ442222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-111-2-22200000000-11−3−33333−3−333−3−3−3−3331-1-11000000000000
χ45444444-244-2-2-2-2-2-2-24-4-4-4-4-2-2-2-222220000000000002200000000000000000000000000000000
χ46444444-2-4-4-2-2-22222-444-4-4-2-222-2-2220000000000002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-2-2-2-2-44-44-42222-2-2-2-20000000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-222224-444-422-2-222-2-20000000000002-200000000000000000000000000000000
χ494-44-40044-44-4-444-4-4000000000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ504-44-40044-44-4-444-4-400000000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ514-44-4004-444-4-4-4-444000000000000000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ524-44-4004-444-4-4-4-44400000000000000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ534-44-400-24-4-222-2-22200000000023−2323−2300002i−2i2i−2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ544-44-400-24-4-222-2-22200000000023−2323−230000−2i2i−2i2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ554-44-400-24-4-222-2-222000000000−2323−232300002i−2i2i−2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ564-44-400-24-4-222-2-222000000000−2323−23230000−2i2i−2i2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ574-44-400-2-44-22222-2-200000000023−23−232300002i−2i−2i2i000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ584-44-400-2-44-22222-2-200000000023−23−23230000−2i2i2i−2i000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ594-44-400-2-44-22222-2-2000000000−232323−2300002i−2i−2i2i000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ604-44-400-2-44-22222-2-2000000000−232323−230000−2i2i2i−2i000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ614-4-444-4400-44-40000000004-40000000000000000−2i22i200000000000000−2i22i2−2i22i20000000000000000
χ624-4-444-4400-44-40000000004-400000000000000002i2−2i2000000000000002i2−2i22i2−2i20000000000000000
χ634-4-444-4-2002-2223−2323−2300000-2223−2300000000000000−2i22i20000000000i6−i6i6−i6i2−i2i2−i20000000000000000
χ644-4-444-4-2002-2223−2323−2300000-2223−23000000000000002i2−2i20000000000−i6i6−i6i6−i2i2−i2i20000000000000000
χ654-4-444-4-2002-22−2323−232300000-22−232300000000000000−2i22i20000000000−i6i6−i6i6i2−i2i2−i20000000000000000
χ664-4-444-4-2002-22−2323−232300000-22−2323000000000000002i2−2i20000000000i6−i6i6−i6−i2i2−i2i20000000000000000
χ674-4-44-44400-44-4000000000-4400000000000000−2i22i2000000000000−2i22i22i2−2i200000000000000000000
χ684-4-44-44400-44-4000000000-44000000000000002i2−2i20000000000002i2−2i2−2i22i200000000000000000000
χ694-4-44-44-2002-2223−2323−23000002-2−2323000000000000−2i22i2000000000000i2−i2−i2i2−i6i6i6−i60000000000000000
χ704-4-44-44-2002-2223−2323−23000002-2−23230000000000002i2−2i2000000000000−i2i2i2−i2i6−i6−i6i60000000000000000
χ714-4-44-44-2002-22−2323−2323000002-223−23000000000000−2i22i2000000000000i2−i2−i2i2i6−i6−i6i60000000000000000
χ724-4-44-44-2002-22−2323−2323000002-223−230000000000002i2−2i2000000000000−i2i2i2−i2−i6i6i6−i60000000000000000
χ7388-8-800800-8-88000000000000000000000000000000000000000000000000000000000000000
χ7488-8-800-40044-443−43−434300000000000000000000000000000000000000000000000000000000000
χ7588-8-800-40044-4−434343−4300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.