Finite Group Databasebeta

← Group #10768840

Character table — Group #10768840

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order1222222234466612121212244466661212121224444444688881212121212121212122424242424242424612121244444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1111-1-1111-1-1-111-1-111111-1-1-1-11111-1-1-1-111-1-11-11-11-11-111-1-11-1
χ101111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1111-1-1111-1-1-111-1-111111-1-1-1-11111-1-1-1-111-1-1-11-11-11-11-1-111-11
χ111111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1111-1-11-1-111-1-1-1111-1-1-1-11111-1-1-1-1111111-1-11-11-11-11-1-1-111-11
χ121111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-1111-1-11-1-111-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-11-11-11-1111-1-11-1
χ131111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-111-111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1111-11-1-11-11-1-1111-1
χ141111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-111-111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-111-11-111-11-111-1-1-11
χ151111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-111-111-1-1-111-111-1-11-1-1-1-111111111-1-1-1-1-1-1111-11-1-11-1111-1-1-11
χ161111-1-1111-1-1111-1-1-1-1-1-111-1-111-1-111-111-1-1-111-111-1-11-1-1-1-111111111-1-1-1-1-1-111-11-111-11-1-1-1111-1
χ17222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-20000000020000-20000000000000000000000002-2-22000000
χ18222222222-2-2222-2-2-2-22-2-2-22222-2-2-2-20000000020000-2000000000000000000000000-222-2000000
χ1922222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-2-2-2-2-11111111111111111-1-1-1-100000000000000
χ2122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-2-2-2-2-1-1-1-1-1-1-1-1-111111111111100000000000000
χ2222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-12222-111111111-1-1-1-1-1-1-1-1111100000000000000
χ23222222-2-22222222222-2-22-222-2-2-2-22200000000-20000-20000000000000000000022-2-20000000000
χ24222222-2-22222222222-2-22-222-2-2-2-22200000000-20000-200000000000000000000-2-2220000000000
χ25222222-2-22-2-2222-2-2-2-2-22-2222-2-222-2-222-2-20000-20000200000000000000002-22-200000000000000
χ26222222-2-22-2-2222-2-2-2-2-22-2222-2-222-2-2-2-2220000-2000020000000000000000-22-2200000000000000
χ27222222-2-2-1-2-2-1-1-11111-22-22-1-111-1-11122-2-2000010000-133−3−333−3−333−3−333−3−3-11-1100000000000000
χ28222222-2-2-1-2-2-1-1-11111-22-22-1-111-1-11122-2-2000010000-1−3−333−3−333−3−333−3−333-11-1100000000000000
χ29222222-2-2-1-2-2-1-1-11111-22-22-1-111-1-111-2-222000010000-133−3−333−3−3−3−333−3−3331-11-100000000000000
χ30222222-2-2-1-2-2-1-1-11111-22-22-1-111-1-111-2-222000010000-1−3−333−3−33333−3−333−3−31-11-100000000000000
χ312222-2-2222222222222-22-2-2-2-22222-2-200000000-20000-200000000000000000000000022-2-2000000
χ322222-2-2222222222222-22-2-2-2-22222-2-200000000-20000-2000000000000000000000000-2-222000000
χ332222-2-222-1-2-2-1-1-11111-2-22211-1-111-1-12-2-2222-2-2122-2-2-1-1-1-1-11111-1-1-1-11111-1-11100000000000000
χ342222-2-222-1-2-2-1-1-11111-2-22211-1-111-1-12-2-22-2-2221-2-222-11111-1-1-1-11111-1-1-1-1-1-11100000000000000
χ352222-2-222-1-2-2-1-1-11111-2-22211-1-111-1-1-222-222-2-21-2-222-1-1-1-1-111111111-1-1-1-111-1-100000000000000
χ362222-2-222-1-2-2-1-1-11111-2-22211-1-111-1-1-222-2-2-222122-2-2-11111-1-1-1-1-1-1-1-1111111-1-100000000000000
χ372222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-22-22-2000020000200000000000000002-2-2200000000000000
χ382222-2-2-2-222222222222-2-22-2-2-2-2-2-2-2-2-22-2200002000020000000000000000-222-200000000000000
χ392222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-222220000000020000-2000000000000000000002-2-220000000000
χ402222-2-2-2-22-2-2222-2-2-2-2222-2-2-2-2-222220000000020000-200000000000000000000-222-20000000000
χ412222-2-2-2-2-122-1-1-1-1-1-1-12-2-22111111112-22-20000-10000-133−3−3−3−33333−3−3−3−333-111-100000000000000
χ422222-2-2-2-2-122-1-1-1-1-1-1-12-2-22111111112-22-20000-10000-1−3−33333−3−3−3−33333−3−3-111-100000000000000
χ432222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-22-220000-10000-133−3−3−3−333−3−33333−3−31-1-1100000000000000
χ442222-2-2-2-2-122-1-1-1-1-1-1-12-2-2211111111-22-220000-10000-1−3−33333−3−333−3−3−3−3331-1-1100000000000000
χ4544444444-2-4-4-2-2-222224-4-4-4-2-2-2-2222200000000-2000020000000000000000000000000000000000
χ46444444-4-4-244-2-2-2-2-2-2-2-4-44-4-2-22222-2-2000000002000020000000000000000000000000000000000
χ474444-4-444-244-2-2-2-2-2-2-2-44-4-422-2-2-2-222000000002000020000000000000000000000000000000000
χ484444-4-4-4-4-2-4-4-2-2-22222444-42222-2-2-2-200000000-2000020000000000000000000000000000000000
χ4944-4-44-4004004-4-4000000004-400000000002-22-20000002-22-22-22-200000000000000000000000000
χ5044-4-44-4004004-4-4000000004-40000000000-22-22000000-22-22-22-2200000000000000000000000000
χ5144-4-44-400-200-2222323−23−230000-22000023−2300002-22-2000000−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000000000
χ5244-4-44-400-200-2222323−23−230000-22000023−230000-22-220000001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000000000
χ5344-4-44-400-200-222−23−2323230000-220000−232300002-22-2000000−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000000000
χ5444-4-44-400-200-222−23−2323230000-220000−23230000-22-220000001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000000000
χ5544-4-4-44004004-4-400000000-4400000000002-2-220000002-22-2-22-2200000000000000000000000000
χ5644-4-4-44004004-4-400000000-440000000000-222-2000000-22-222-22-200000000000000000000000000
χ5744-4-4-4400-200-2222323−23−2300002-20000−232300002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+300000000000000000000000000
χ5844-4-4-4400-200-2222323−23−2300002-20000−23230000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−300000000000000000000000000
χ5944-4-4-4400-200-222−23−23232300002-2000023−2300002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−300000000000000000000000000
χ6044-4-4-4400-200-222−23−23232300002-2000023−230000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+300000000000000000000000000
χ614-44-4000044-4-4-444-44-40000000000000000000000000000000000000000000000000000002i−2i2i−2i00
χ624-44-4000044-4-4-444-44-4000000000000000000000000000000000000000000000000000000−2i2i−2i2i00
χ634-44-400004-44-4-44-44-440000000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ644-44-400004-44-4-44-44-44000000000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ654-4-44004-4400-44-400000000004-4000000000000000−2i22i20000000000000−2i22i2−2i22i2000000000000000000
χ664-4-44004-4400-44-400000000004-40000000000000002i2−2i200000000000002i2−2i22i2−2i2000000000000000000
χ674-4-44004-4-2002-2223−23−2323000000-2223−230000000000000−2i22i2000000000i6−i6i6−i6i2−i2i2−i2000000000000000000
χ684-4-44004-4-2002-2223−23−2323000000-2223−2300000000000002i2−2i2000000000−i6i6−i6i6−i2i2−i2i2000000000000000000
χ694-4-44004-4-2002-22−232323−23000000-22−23230000000000000−2i22i2000000000−i6i6−i6i6i2−i2i2−i2000000000000000000
χ704-4-44004-4-2002-22−232323−23000000-22−232300000000000002i2−2i2000000000i6−i6i6−i6−i2i2−i2i2000000000000000000
χ714-4-4400-44400-44-40000000000-440000000000000−2i22i200000000000−2i22i22i2−2i20000000000000000000000
χ724-4-4400-44400-44-40000000000-4400000000000002i2−2i2000000000002i2−2i2−2i22i20000000000000000000000
χ734-4-4400-44-2002-2223−23−23230000002-2−232300000000000−2i22i200000000000i2−i2−i2i2i6−i6−i6i6000000000000000000
χ744-4-4400-44-2002-2223−23−23230000002-2−2323000000000002i2−2i200000000000−i2i2i2−i2−i6i6i6−i6000000000000000000
χ754-4-4400-44-2002-22−232323−230000002-223−2300000000000−2i22i200000000000i2−i2−i2i2−i6i6i6−i6000000000000000000
χ764-4-4400-44-2002-22−232323−230000002-223−23000000000002i2−2i200000000000−i2i2i2−i2i6−i6−i6i6000000000000000000
χ778-88-80000-48-844-4-44-44000000000000000000000000000000000000000000000000000000000000
χ788-88-80000-4-8844-44-44-4000000000000000000000000000000000000000000000000000000000000

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