Finite Group Databasebeta

← Group #10828735

Character table — Group #10828735

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222222222444444444448888888888888888888888888888881212121216161616242424242424242424244848
order1222223444444666121212122246666121212122444444468888121212121212121212242424242424242444446121212444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111
χ51111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-11-1-1-1-111
χ61111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ911111111-1-11111111111-1-1-1-1-11111-1-111-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-1-111-111-1-11-1
χ1011111111-1-11111111111-1-1-1-1-11111-1-111-1-111-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-11-1-111-11
χ1111111111-1-11111111111-1-1-1-1-11111-1-111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-1-1-11111-11
χ1211111111-1-11111111111-1-1-1-1-11111-1-111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111111-1-1-1-11-1
χ1311111111-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1-1-1111-1
χ1411111111-1-11111111111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1111111-1-1-11
χ1511111111-1-11111111111-1-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-1-111111111-1-1-1-11111-111-111-111-1-1-1-1-1-11
χ1611111111-1-11111111111-1-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11-1-1111111-1
χ172222222-222-2-2-2222-2-2-2-2-2-22-2-222-2-22200000000-2000020000000000000000000000002-200002-20000
χ182222222-222-2-2-2222-2-2-2-2-2-22-2-222-2-22200000000-200002000000000000000000000000-220000-220000
χ192222222-2-2-2-2-2-2222-2-2-2-222-22222-2-2-2-20000000020000-20000000000000000000000002-20000-220000
χ202222222-2-2-2-2-2-2222-2-2-2-222-22222-2-2-2-20000000020000-2000000000000000000000000-2200002-20000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-2-2-2-2-111111111111111110000-1-1-1-1000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111111100001111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-12222-111111111-1-1-1-1-1-1-1-100001111000000000000
χ25222222-12-2-2222-1-1-1-1-1-1-1-2-2-211-1-1-1-11122-2-222-2-2122-2-21-1-1-1-11111-1-1-1-111110000-111-1000000000000
χ26222222-12-2-2222-1-1-1-1-1-1-1-2-2-211-1-1-1-11122-2-2-2-2221-2-22211111-1-1-1-11111-1-1-1-10000-111-1000000000000
χ27222222-12-2-2222-1-1-1-1-1-1-1-2-2-211-1-1-1-111-2-22222-2-21-2-2221-1-1-1-111111111-1-1-1-100001-1-11000000000000
χ28222222-12-2-2222-1-1-1-1-1-1-1-2-2-211-1-1-1-111-2-222-2-222122-2-211111-1-1-1-1-1-1-1-1111100001-1-11000000000000
χ292222-2-222222-2-222222222-2-222-2-2-2-22200000000-20000-2000000000000000022-2-2000000-2002000000
χ302222-2-222222-2-222222222-2-222-2-2-2-22200000000-20000-20000000000000000-2-222000000200-2000000
χ312222-2-222-2-22-2-22222222-222-2-2-2-2-2-2-2-200000000200002000000000000000022-2-2000000200-2000000
χ322222-2-222-2-22-2-22222222-222-2-2-2-2-2-2-2-2000000002000020000000000000000-2-222000000-2002000000
χ332222-2-22-222-222222-2-2-2-2-22-2-2-2-2-222222-22-2000020000-20000000000000000000022-2-2000000000000
χ342222-2-22-222-222222-2-2-2-2-22-2-2-2-2-22222-22-22000020000-200000000000000000000-2-222000000000000
χ352222-2-22-2-2-2-222222-2-2-2-22-2222-2-222-2-22-2-220000-200002000000000000000000002-22-2000000000000
χ362222-2-22-2-2-2-222222-2-2-2-22-2222-2-222-2-2-222-20000-20000200000000000000000000-22-22000000000000
χ372222-2-2-1-222-222-1-1-11111-22-21111-1-1-1-12-22-20000-10000133−3−333−3−333−3−333−3−30000-1-111000000000000
χ382222-2-2-1-222-222-1-1-11111-22-21111-1-1-1-12-22-20000-100001−3−333−3−333−3−333−3−3330000-1-111000000000000
χ392222-2-2-1-222-222-1-1-11111-22-21111-1-1-1-1-22-220000-10000133−3−333−3−3−3−333−3−333000011-1-1000000000000
χ402222-2-2-1-222-222-1-1-11111-22-21111-1-1-1-1-22-220000-100001−3−333−3−33333−3−333−3−3000011-1-1000000000000
χ412222-2-2-1-2-2-2-222-1-1-111112-22-1-111-1-1112-2-22000010000-133−3−3−3−33333−3−3−3−3330000-11-11000000000000
χ422222-2-2-1-2-2-2-222-1-1-111112-22-1-111-1-1112-2-22000010000-1−3−33333−3−3−3−33333−3−30000-11-11000000000000
χ432222-2-2-1-2-2-2-222-1-1-111112-22-1-111-1-111-222-2000010000-133−3−3−3−333−3−33333−3−300001-11-1000000000000
χ442222-2-2-1-2-2-2-222-1-1-111112-22-1-111-1-111-222-2000010000-1−3−33333−3−333−3−3−3−33300001-11-1000000000000
χ4522-2-22-22-20022-2-2-22-2-222000002-22-2000000000002-2000000000002-22-200002i−2i2i−2i00000002i−2i0000000
χ4622-2-22-22-20022-2-2-22-2-222000002-22-2000000000002-2000000000002-22-20000−2i2i−2i2i0000000−2i2i0000000
χ4722-2-22-22-20022-2-2-22-2-222000002-22-200000000000-2200000000000-22-2200002i−2i2i−2i0000000−2i2i0000000
χ4822-2-22-22-20022-2-2-22-2-222000002-22-200000000000-2200000000000-22-220000−2i2i−2i2i00000002i−2i0000000
χ4922-2-2-222-2002-22-2-22-2-22200000-22-2200000000000002-200000000000002-22-22i−2i−2i2i0000000000002i−2i00
χ5022-2-2-222-2002-22-2-22-2-22200000-22-2200000000000002-200000000000002-22-2−2i2i2i−2i000000000000−2i2i00
χ5122-2-2-222-2002-22-2-22-2-22200000-22-220000000000000-220000000000000-22-222i−2i−2i2i000000000000−2i2i00
χ5222-2-2-222-2002-22-2-22-2-22200000-22-220000000000000-220000000000000-22-22−2i2i2i−2i0000000000002i−2i00
χ53444444-2-444-4-4-4-2-2-22222-4-4422-2-222-2-20000000020000-2000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2222244-4-2-2-2-2222200000000-200002000000000000000000000000000000000000
χ554444-4-4-24444-4-4-2-2-2-2-2-2-24-4-4-2-22222-2-200000000200002000000000000000000000000000000000000
χ564444-4-4-24-4-44-4-4-2-2-2-2-2-2-2-4442222222200000000-20000-2000000000000000000000000000000000000
χ5744-4-44-44400-4-44-4-4444-4-4000004-4-440000000000000000000000000000000000000000000000000000
χ5844-4-44-4-2400-4-4422-2-2-22200000-222-2000000000000000000000000000023−23−232300000000000000000000
χ5944-4-44-4-2400-4-4422-2-2-22200000-222-20000000000000000000000000000−232323−2300000000000000000000
χ6044-4-44-4-2-40044-422-222-2-200000-22-22000000000004-400000000000-22-22000000000000000000000000
χ6144-4-44-4-2-40044-422-222-2-200000-22-2200000000000-44000000000002-22-2000000000000000000000000
χ6244-4-4-444400-44-4-4-4444-4-400000-444-40000000000000000000000000000000000000000000000000000
χ6344-4-4-44-2400-44-422-2-2-222000002-2-2200000000000000000000000023−23−2323000000000000000000000000
χ6444-4-4-44-2400-44-422-2-2-222000002-2-22000000000000000000000000−232323−23000000000000000000000000
χ6544-4-4-44-2-4004-4422-222-2-2000002-22-200000000000004-40000000000000-22-2200000000000000000000
χ6644-4-4-44-2-4004-4422-222-2-2000002-22-20000000000000-4400000000000002-22-200000000000000000000
χ674-4-4400404i−4i0004-4-400000000000004i−4i00002i−2i2-20000002i−2i2i−2i2-22-20000000000000000000000000000
χ684-4-4400404i−4i0004-4-400000000000004i−4i0000−2i2i-22000000−2i2i−2i2i-22-220000000000000000000000000000
χ694-4-440040−4i4i0004-4-40000000000000−4i4i00002i−2i-220000002i−2i2i−2i-22-220000000000000000000000000000
χ704-4-440040−4i4i0004-4-40000000000000−4i4i0000−2i2i2-2000000−2i2i−2i2i2-22-20000000000000000000000000000
χ714-4-4400-204i−4i000-22223−2323−23000−2i32i30000−2i2i00002i−2i2-2000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1−31+3−1+31−30000000000000000000000000000
χ724-4-4400-204i−4i000-22223−2323−23000−2i32i30000−2i2i0000−2i2i-22000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111+3−1−31−3−1+30000000000000000000000000000
χ734-4-4400-204i−4i000-222−2323−23230002i3−2i30000−2i2i00002i−2i2-2000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1+31−3−1−31+30000000000000000000000000000
χ744-4-4400-204i−4i000-222−2323−23230002i3−2i30000−2i2i0000−2i2i-22000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111−3−1+31+3−1−30000000000000000000000000000
χ754-4-4400-20−4i4i000-22223−2323−230002i3−2i300002i−2i00002i−2i-22000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111+3−1−31−3−1+30000000000000000000000000000
χ764-4-4400-20−4i4i000-22223−2323−230002i3−2i300002i−2i0000−2i2i2-2000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1−31+3−1+31−30000000000000000000000000000
χ774-4-4400-20−4i4i000-222−2323−2323000−2i32i300002i−2i00002i−2i-22000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111−3−1+31+3−1−30000000000000000000000000000
χ784-4-4400-20−4i4i000-222−2323−2323000−2i32i300002i−2i0000−2i2i2-2000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1+31−3−1−31+30000000000000000000000000000
χ798-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000
χ818-88-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.