Finite Group Databasebeta

← Group #10768910

Character table — Group #10768910

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order12222234444666121212124444661212121212124444444488881212121212121212121224242424242424241212121222244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-11-111111-1-1-1-1-11-1
χ101111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1-1-111111-11
χ111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-11-1-1-111-11
χ121111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-1111-1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-1111-111-1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-1-11-1-1111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-11-111111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-111111-11-1-1-1-1-11
χ17222222222-2-222222222-2-2-22222-2-2-2-2000000000000-2-2000000000000000000002-20000-22000000
χ18222222222-2-222222222-2-2-22222-2-2-2-2000000000000-2-200000000000000000000-2200002-2000000
χ192222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000000000-2200000000000000000000220000-2-2000000
χ202222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000000000-2200000000000000000000-2-2000022000000
χ21222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111111111111111-1-1-1-100000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1111100000000000000
χ25222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-122-2-222-2-222-2-2-11-1-1-1-11111-1-1-1-11111-1-11100000000000000
χ26222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-122-2-2-2-222-2-222-111111-1-1-1-11111-1-1-1-1-1-11100000000000000
χ27222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-2-22222-2-2-2-222-11-1-1-1-111111111-1-1-1-111-1-100000000000000
χ28222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-2-222-2-22222-2-2-111111-1-1-1-1-1-1-1-1111111-1-100000000000000
χ292222-2-2222222222222-2-22-2-2-2-2-22222000000000000-2-200000000000000000000002-200002-20000
χ302222-2-2222222222222-2-22-2-2-2-2-22222000000000000-2-20000000000000000000000-220000-220000
χ312222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-22-22-2000000002200000000000000002-22-200000000000000
χ322222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-2-22-2200000000220000000000000000-22-2200000000000000
χ332222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-22-2-22000000002-200000000000000002-2-2200000000000000
χ342222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-2-222-2000000002-20000000000000000-222-200000000000000
χ352222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-222000000000000-2200000000000000000000002-20000-220000
χ362222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-222000000000000-220000000000000000000000-2200002-20000
χ372222-2-2-122-2-2-1-1-1-1-1-1-1-22-22111111112-22-200000000-1-133−3−333−3−333−3−333−3−3-11-1100000000000000
χ382222-2-2-122-2-2-1-1-1-1-1-1-1-22-22111111112-22-200000000-1-1−3−333−3−333−3−333−3−333-11-1100000000000000
χ392222-2-2-122-2-2-1-1-1-1-1-1-1-22-2211111111-22-2200000000-1-133−3−333−3−3−3−333−3−3331-11-100000000000000
χ402222-2-2-122-2-2-1-1-1-1-1-1-1-22-2211111111-22-2200000000-1-1−3−333−3−33333−3−333−3−31-11-100000000000000
χ412222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-1112-2-2200000000-1133−3−3−3−33333−3−3−3−333-111-100000000000000
χ422222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-1112-2-2200000000-11−3−33333−3−3−3−33333−3−3-111-100000000000000
χ432222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111-222-200000000-1133−3−3−3−333−3−33333−3−31-1-1100000000000000
χ442222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111-222-200000000-11−3−33333−3−333−3−3−3−3331-1-1100000000000000
χ45444444-244-4-4-2-2-2-2-2-2-24-4-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ46444444-2-4-444-2-2-22222-44-4-4-2-222-2-2220000000000002-20000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-2-2-2-2-4-44-42222-2-2-2-2000000000000220000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-22222444-422-2-222-2-20000000000002-20000000000000000000000000000000000
χ4944-4-44-4400004-4-4000000004-40000000000000022−2200000000000022−2222−220000000000000000000000
χ5044-4-44-4400004-4-4000000004-400000000000000−2222000000000000−2222−22220000000000000000000000
χ5144-4-44-4-20000-222−2i3−2i32i32i30000-22−2i32i300000000000022−22000000000000−22−22i6−i6i6−i6000000000000000000
χ5244-4-44-4-20000-222−2i3−2i32i32i30000-22−2i32i3000000000000−22220000000000002−22−2−i6i6−i6i6000000000000000000
χ5344-4-44-4-20000-2222i32i3−2i3−2i30000-222i3−2i300000000000022−22000000000000−22−22−i6i6−i6i6000000000000000000
χ5444-4-44-4-20000-2222i32i3−2i3−2i30000-222i3−2i3000000000000−22220000000000002−22−2i6−i6i6−i6000000000000000000
χ5544-4-4-44400004-4-400000000-440000000000000000−2i22i200000000000000−2i22i22i2−2i2000000000000000000
χ5644-4-4-44400004-4-400000000-4400000000000000002i2−2i2000000000000002i2−2i2−2i22i2000000000000000000
χ5744-4-4-44-20000-222−2i3−2i32i32i300002-22i3−2i300000000000000−2i22i200000000006−6−66i2−i2−i2i2000000000000000000
χ5844-4-4-44-20000-222−2i3−2i32i32i300002-22i3−2i3000000000000002i2−2i20000000000−666−6−i2i2i2−i2000000000000000000
χ5944-4-4-44-20000-2222i32i3−2i3−2i300002-2−2i32i300000000000000−2i22i20000000000−666−6i2−i2−i2i2000000000000000000
χ6044-4-4-44-20000-2222i32i3−2i3−2i300002-2−2i32i3000000000000002i2−2i200000000006−6−66−i2i2i2−i2000000000000000000
χ614-44-4004004-4-44-40000000000004-40000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ624-44-4004004-4-44-40000000000004-4000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ634-44-400400-44-44-4000000000000-440000002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ644-44-400400-44-44-4000000000000-44000000−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ654-44-400-2004-42-2223−2323−2300000000-2223−2300002i−2i2i−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−ζ2200000000000000000000000000
χ664-44-400-2004-42-2223−2323−2300000000-2223−230000−2i2i−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+ζ2200000000000000000000000000
χ674-44-400-2004-42-22−2323−232300000000-22−232300002i−2i2i−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−ζ2200000000000000000000000000
χ684-44-400-2004-42-22−2323−232300000000-22−23230000−2i2i−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+ζ2200000000000000000000000000
χ694-44-400-200-442-2223−2323−23000000002-2−232300002i−2i−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+ζ2200000000000000000000000000
χ704-44-400-200-442-2223−2323−23000000002-2−23230000−2i2i2i−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−ζ2200000000000000000000000000
χ714-44-400-200-442-22−2323−2323000000002-223−2300002i−2i−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+ζ2200000000000000000000000000
χ724-44-400-200-442-22−2323−2323000000002-223−230000−2i2i2i−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−ζ2200000000000000000000000000
χ734-4-440044i−4i00-4-444i−4i−4i4i000000000000000000000000000000000000000000000000002i−2i00002-200
χ744-4-440044i−4i00-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000−2i2i0000-2200
χ754-4-44004−4i4i00-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000002i−2i0000-2200
χ764-4-44004−4i4i00-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000−2i2i00002-200
χ778-8-8800-48i−8i0044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ788-8-8800-4−8i8i0044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000

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