Finite Group Databasebeta

← Group #10849416

Character table — Group #10849416

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666666644444444441212121212121212121212121212121212121212121212121212121244444444441212121212121212222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-111-1111111-1-1
χ91111111-1-1-1-111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-11-1-11-111-1-11-1
χ101111111-1-1-1-111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-1-111-1-11-111-11-1-111-11
χ111111111-1-1-1-111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111-1-111-1-11-1-1111-1-1-11
χ121111111-1-1-1-111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1-11111-111-1-1-1111-1
χ131111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1111-1-1-1-111-11-1-11-1-1-111-11
χ141111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-1111-111-1111-1-11-1
χ151111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-1-11-1-11-1-1111-1
χ161111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-111-111-111-1-1-11
χ17222222222-2-2-2-2-2-222222222-200000000-2-2-2-200000000000000002222-2-2-2-22-22-20000002-22-20000000000000000
χ18222222222-2-2-2-2-2-222222222-200000000-2-2-2-200000000000000002222-2-2-2-2-22-22000000-22-220000000000000000
χ192222222-2-222-2-2-2-22222222-2200000000-2-2-2-20000000000000000-2-2-2-222222-2-220000002-2-220000000000000000
χ202222222-2-222-2-2-2-22222222-2200000000-2-2-2-20000000000000000-2-2-2-22222-222-2000000-222-20000000000000000
χ21222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ22222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ23222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-1-1-1-122220000-2-2-1-1-1-11111000000000000
χ24222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-2-2-2-20000221111-1-1-1-1000000000000
χ25222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-1-1-1-111112-22-2000000-11-11−i3i3−i3i3000000000000
χ26222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-1-1-1-11111-22-220000001-11-1i3−i3i3−i3000000000000
χ27222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-1-1-1-111112-22-2000000-11-11i3−i3i3−i3000000000000
χ28222222-122-2-2-2-2-2-2-1-1-1-1-1-1-12-2000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-1-1-1-11111-22-220000001-11-1−i3i3−i3i3000000000000
χ29222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-12-2-22000000-111-1−i3i3i3−i3000000000000
χ30222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-222-20000001-1-11i3−i3−i3i3000000000000
χ31222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-12-2-22000000-111-1i3−i3−i3i3000000000000
χ32222222-1-2-222-2-2-2-2-1-1-1-1-1-1-1-22000000001111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-222-20000001-1-11−i3i3i3−i3000000000000
χ33222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-200002-2-1-111-1-111000000000000
χ34222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2220000-2211-1-111-1-1000000000000
χ35222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-11111111122-2-20000-22-1-11111-1-1000000000000
χ36222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-111111111-2-22200002-211-1-1-1-111000000000000
χ372222-2-222222-222-22-2-2-2-222-2-20000000022-2-2000000000000000022-2-222-2-200000000000000000002-20-22000000
χ382222-2-222222-222-22-2-2-2-222-2-20000000022-2-2000000000000000022-2-222-2-20000000000000000000-2202-2000000
χ392222-2-2222-2-22-2-222-2-2-2-222-2200000000-2-222000000000000000022-2-2-2-222000022-2-20000000000200-200000000
χ402222-2-2222-2-22-2-222-2-2-2-222-2200000000-2-222000000000000000022-2-2-2-2220000-2-2220000000000-200200000000
χ412222-2-22-2-2222-2-222-2-2-2-2222-200000000-2-2220000000000000000-2-22222-2-2000022-2-20000000000-200200000000
χ422222-2-22-2-2222-2-222-2-2-2-2222-200000000-2-2220000000000000000-2-22222-2-20000-2-2220000000000200-200000000
χ432222-2-22-2-2-2-2-222-22-2-2-2-222220000000022-2-20000000000000000-2-222-2-2220000000000000000000220-2-2000000
χ442222-2-22-2-2-2-2-222-22-2-2-2-222220000000022-2-20000000000000000-2-222-2-2220000000000000000000-2-2022000000
χ452-2-222-220000-22-22222-2-2-2-200000022-2-22-22-20000000022-2-222-2-20000000000002i−2i2i−2i0000000000000000002i−2i00
χ462-2-222-220000-22-22222-2-2-2-200000022-2-22-22-20000000022-2-222-2-2000000000000−2i2i−2i2i000000000000000000−2i2i00
χ472-2-222-220000-22-22222-2-2-2-2000000-2-2222-22-200000000-2-222-2-2220000000000002i−2i2i−2i000000000000000000−2i2i00
χ482-2-222-220000-22-22222-2-2-2-2000000-2-2222-22-200000000-2-222-2-222000000000000−2i2i−2i2i0000000000000000002i−2i00
χ492-2-22-2220000-2-2222-2-222-2-20022-2-20000-222-222-2-222-2-2000000000000000000002i−2i−2i2i00000000000000002i−2i0000
χ502-2-22-2220000-2-2222-2-222-2-20022-2-20000-222-222-2-222-2-200000000000000000000−2i2i2i−2i0000000000000000−2i2i0000
χ512-2-22-2220000-2-2222-2-222-2-200-2-2220000-222-2-2-222-2-222000000000000000000002i−2i−2i2i0000000000000000−2i2i0000
χ522-2-22-2220000-2-2222-2-222-2-200-2-2220000-222-2-2-222-2-22200000000000000000000−2i2i2i−2i00000000000000002i−2i0000
χ534444-4-4-24444-444-4-22222-2-2-4-400000000-2-2220000000000000000-2-222-2-222000000000000000000000000000000
χ544444-4-4-244-4-44-4-44-22222-2-2-440000000022-2-20000000000000000-2-22222-2-2000000000000000000000000000000
χ554444-4-4-2-4-4444-4-44-22222-2-24-40000000022-2-2000000000000000022-2-2-2-222000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-444-4-22222-2-24400000000-2-222000000000000000022-2-222-2-2000000000000000000000000000000
χ5744-4-4004004i−4i0000-400004-4002-22-22i−2i2i−2i00002-22-22-22-22i−2i2i−2i2i−2i2i−2i00004i−4i00000000000000000000000000000000
χ5844-4-4004004i−4i0000-400004-400-22-22−2i2i−2i2i0000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00004i−4i00000000000000000000000000000000
χ5944-4-400400−4i4i0000-400004-4002-22-2−2i2i−2i2i00002-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000−4i4i00000000000000000000000000000000
χ6044-4-400400−4i4i0000-400004-400-22-222i−2i2i−2i0000-22-22-22-222i−2i2i−2i2i−2i2i−2i0000−4i4i00000000000000000000000000000000
χ6144-4-400-2004i−4i00002−2i32i3−2i32i3-22002-22-22i−2i2i−2i0000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i32ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000−2i2i23−23000000000000000000000000000000
χ6244-4-400-2004i−4i00002−2i32i3−2i32i3-2200-22-22−2i2i−2i2i00001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000−2i2i23−23000000000000000000000000000000
χ6344-4-400-2004i−4i000022i3−2i32i3−2i3-22002-22-22i−2i2i−2i0000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i32ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000−2i2i−2323000000000000000000000000000000
χ6444-4-400-2004i−4i000022i3−2i32i3−2i3-2200-22-22−2i2i−2i2i00001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ70000−2i2i−2323000000000000000000000000000000
χ6544-4-400-200−4i4i00002−2i32i3−2i32i3-22002-22-2−2i2i−2i2i0000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ1100002i−2i−2323000000000000000000000000000000
χ6644-4-400-200−4i4i00002−2i32i3−2i32i3-2200-22-222i−2i2i−2i00001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i32ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ1100002i−2i−2323000000000000000000000000000000
χ6744-4-400-200−4i4i000022i3−2i32i3−2i3-22002-22-2−2i2i−2i2i0000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ700002i−2i23−23000000000000000000000000000000
χ6844-4-400-200−4i4i000022i3−2i32i3−2i3-2200-22-222i−2i2i−2i00001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i32ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ700002i−2i23−23000000000000000000000000000000
χ694-44-40044i−4i000000-40000-44002-2-222i−2i−2i2i00002-2-222-2-222i−2i−2i2i2i−2i−2i2i4i−4i000000000000000000000000000000000000
χ704-44-40044i−4i000000-40000-4400-222-2−2i2i2i−2i0000-222-2-222-2−2i2i2i−2i−2i2i2i−2i4i−4i000000000000000000000000000000000000
χ714-44-4004−4i4i000000-40000-44002-2-22−2i2i2i−2i00002-2-222-2-22−2i2i2i−2i−2i2i2i−2i−4i4i000000000000000000000000000000000000
χ724-44-4004−4i4i000000-40000-4400-222-22i−2i−2i2i0000-222-2-222-22i−2i−2i2i2i−2i−2i2i−4i4i000000000000000000000000000000000000
χ734-44-400-24i−4i0000002−2i32i32i3−2i32-2002-2-222i−2i−2i2i0000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i32ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ11−2i2i23−230000000000000000000000000000000000
χ744-44-400-24i−4i0000002−2i32i32i3−2i32-200-222-2−2i2i2i−2i00001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ11−2i2i23−230000000000000000000000000000000000
χ754-44-400-24i−4i00000022i3−2i3−2i32i32-2002-2-222i−2i−2i2i0000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i32ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ7−2i2i−23230000000000000000000000000000000000
χ764-44-400-24i−4i00000022i3−2i3−2i32i32-200-222-2−2i2i2i−2i00001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ7−2i2i−23230000000000000000000000000000000000
χ774-44-400-2−4i4i0000002−2i32i32i3−2i32-2002-2-22−2i2i2i−2i0000−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ112i−2i−23230000000000000000000000000000000000
χ784-44-400-2−4i4i0000002−2i32i32i3−2i32-200-222-22i−2i−2i2i00001−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i32ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ112i−2i−23230000000000000000000000000000000000
χ794-44-400-2−4i4i00000022i3−2i3−2i32i32-2002-2-22−2i2i2i−2i0000−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ72i−2i23−230000000000000000000000000000000000
χ804-44-400-2−4i4i00000022i3−2i3−2i32i32-200-222-22i−2i−2i2i00001+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i32ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ72i−2i23−230000000000000000000000000000000000
χ814-4-444-4400004-44-4444-4-4-4-40000000000-44-44000000000000000000000000000000000000000000000000000000
χ824-4-444-4-200004-44-4-2-2-2222200000000002-22-200000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000
χ834-4-444-4-200004-44-4-2-2-2222200000000002-22-2000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000
χ844-4-444-4-20000-44-44-2-2-2222200000044-4-4-22-2200000000-2-222-2-22200000000000000000000000000000000000000
χ854-4-444-4-20000-44-44-2-2-22222000000-4-444-22-220000000022-2-222-2-200000000000000000000000000000000000000
χ864-4-44-444000044-4-44-4-444-4-400000000004-4-44000000000000000000000000000000000000000000000000000000
χ874-4-44-44-2000044-4-4-222-2-2220000000000-222-2−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000
χ884-4-44-44-2000044-4-4-222-2-2220000000000-222-22i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000
χ894-4-44-44-20000-4-444-222-2-2220044-4-400002-2-22-2-222-2-2220000000000000000000000000000000000000000000000
χ904-4-44-44-20000-4-444-222-2-22200-4-44400002-2-2222-2-222-2-20000000000000000000000000000000000000000000000

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