Finite Group Databasebeta

← Group #10846245

Character table — Group #10846245

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444466666666666688888888888888881212121212121212121216161616161616161616242424244848
order122222223444466666664444888888881212121244448888888844441212121224242424242424242244448888441212121212121212224424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1-111-11
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-111-11
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-11-1
χ911111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1111-1-1-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-11111-1-111-1-1-11
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-22222000000000000-2-2220000000022-2-2-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-2-2-2000000000000-2-22200000000-2-2222200000000000000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-2222200000000000022-2-200000000-2-222-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-2-2-200000000000022-2-20000000022-2-22200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-10000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-1-1-1-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1000000000000-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-211111111000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-100000000000022-2-2-1-1-1-11111111100000000002-2-1-1-1-11111000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1000000000000-2-222-1-1-1-1111111110000000000-221111-1-1-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-100000000000022221111-1-1-1-111110000000000-2-2-1-111-1-111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000000000-2-2-2-21111-1-1-1-1111100000000002211-1-111-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-100000000000022-2-211111111-1-1-1-10000000000-22-1-11111-1-1000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000-2-22211111111-1-1-1-100000000002-211-1-1-1-111000000
χ29222-2-2-22-222-2-2222-2-2-2-2200002i2i−2i−2i00002-22-22i2i−2i−2i2222-2-2-2-2000000002i2i−2i−2i000000002i−2i00000000000000000000
χ30222-2-2-22-222-2-2222-2-2-2-2200002i2i−2i−2i00002-22-2−2i−2i2i2i-2-2-2-22222000000002i2i−2i−2i00000000−2i2i00000000000000000000
χ31222-2-2-22-222-2-2222-2-2-2-220000−2i−2i2i2i00002-22-22i2i−2i−2i-2-2-2-2222200000000−2i−2i2i2i000000002i−2i00000000000000000000
χ32222-2-2-22-222-2-2222-2-2-2-220000−2i−2i2i2i00002-22-2−2i−2i2i2i2222-2-2-2-200000000−2i−2i2i2i00000000−2i2i00000000000000000000
χ33222-2-2-22-22-222-222-2-2-2-22000000002i2i−2i−2i-22-222i2i−2i−2i000000000000000000002i2i−2i−2i0000−2i2i22-2-20000000000000000
χ34222-2-2-22-22-222-222-2-2-2-22000000002i2i−2i−2i-22-22−2i−2i2i2i000000000000000000002i2i−2i−2i00002i−2i-2-2220000000000000000
χ35222-2-2-22-22-222-222-2-2-2-2200000000−2i−2i2i2i-22-222i2i−2i−2i00000000000000000000−2i−2i2i2i0000−2i2i-2-2220000000000000000
χ36222-2-2-22-22-222-222-2-2-2-2200000000−2i−2i2i2i-22-22−2i−2i2i2i00000000000000000000−2i−2i2i2i00002i−2i22-2-20000000000000000
χ3722-222-2-2-2200002-2-2-222-22-200−i2i2−i2i2−i2i2−i2i200002-22-2−i2−i2i2i2−i2−i2i2i20000002-2−i2i2−i2i2−i2i2−i2i22-20000−i2i2−i2i20000000000000000
χ3822-222-2-2-2200002-2-2-222-22-200−i2i2−i2i2−i2i2−i2i20000-22-22i2i2−i2−i2i2i2−i2−i20000002-2−i2i2−i2i2−i2i2−i2i2-220000i2−i2i2−i20000000000000000
χ3922-222-2-2-2200002-2-2-222-22-200i2−i2i2−i2i2−i2i2−i200002-22-2i2i2−i2−i2i2i2−i2−i20000002-2i2−i2i2−i2i2−i2i2−i22-20000i2−i2i2−i20000000000000000
χ4022-222-2-2-2200002-2-2-222-22-200i2−i2i2−i2i2−i2i2−i20000-22-22−i2−i2i2i2−i2−i2i2i20000002-2i2−i2i2−i2i2−i2i2−i2-220000−i2i2−i2i20000000000000000
χ4122-222-2-2-2200002-2-2-222-2-2200−i2i2−i2i2i2−i2i2−i200002-22-2−i2−i2i2i2−i2−i2i2i2000000-22−i2i2−i2i2i2−i2i2−i2-220000i2−i2i2−i20000000000000000
χ4222-222-2-2-2200002-2-2-222-2-2200−i2i2−i2i2i2−i2i2−i20000-22-22i2i2−i2−i2i2i2−i2−i2000000-22−i2i2−i2i2i2−i2i2−i22-20000−i2i2−i2i20000000000000000
χ4322-222-2-2-2200002-2-2-222-2-2200i2−i2i2−i2−i2i2−i2i200002-22-2i2i2−i2−i2i2i2−i2−i2000000-22i2−i2i2−i2−i2i2−i2i2-220000−i2i2−i2i20000000000000000
χ4422-222-2-2-2200002-2-2-222-2-2200i2−i2i2−i2−i2i2−i2i20000-22-22−i2−i2i2i2−i2−i2i2i2000000-22i2−i2i2−i2−i2i2−i2i22-20000i2−i2i2−i20000000000000000
χ4522-2-2-22-22200002-222-2-2-2002-22−2−222−2−2200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i200002-2002−2−222−2−22002i−2i00−i2i2i2−i20000000000000000
χ4622-2-2-22-22200002-222-2-2-2002-22−2−222−2−220000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200002-2002−2−222−2−2200−2i2i00i2−i2−i2i20000000000000000
χ4722-2-2-22-22200002-222-2-2-2002-2−222−2−222−200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i200002-200−222−2−222−2002i−2i00i2−i2−i2i20000000000000000
χ4822-2-2-22-22200002-222-2-2-2002-2−222−2−222−20000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200002-200−222−2−222−200−2i2i00−i2i2i2−i20000000000000000
χ4922-2-2-22-22200002-222-2-2-200-222−2−22−222−200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000-22002−2−22−222−200−2i2i00i2−i2−i2i20000000000000000
χ5022-2-2-22-22200002-222-2-2-200-222−2−22−222−20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000-22002−2−22−222−2002i−2i00−i2i2i2−i20000000000000000
χ5122-2-2-22-22200002-222-2-2-200-22−222−22−2−2200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000-2200−222−22−2−2200−2i2i00−i2i2i2−i20000000000000000
χ5222-2-2-22-22200002-222-2-2-200-22−222−22−2−220000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000-2200−222−22−2−22002i−2i00i2−i2−i2i20000000000000000
χ532-2-22-222-22-2-222-2-2-22-222000000000000-222-200002-22-22-22-2002-200000000000000000000000000002-2002-20000
χ542-2-22-222-22-2-222-2-2-22-222000000000000-222-200002-22-22-22-200-220000000000000000000000000000-2200-220000
χ552-2-22-222-22-2-222-2-2-22-222000000000000-222-20000-22-22-22-22002-200000000000000000000000000002-200-220000
χ562-2-22-222-22-2-222-2-2-22-222000000000000-222-20000-22-22-22-2200-220000000000000000000000000000-22002-20000
χ572-2-2-22-2222-22-22-2-22-22-22000000000000-2-22200002-22-2-22-222-2000000000000000000000000002-2000000002-200
χ582-2-2-22-2222-22-22-2-22-22-22000000000000-2-22200002-22-2-22-22-2200000000000000000000000000-2200000000-2200
χ592-2-2-22-2222-22-22-2-22-22-22000000000000-2-2220000-22-222-22-22-2000000000000000000000000002-200000000-2200
χ602-2-2-22-2222-22-22-2-22-22-22000000000000-2-2220000-22-222-22-2-2200000000000000000000000000-22000000002-200
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000000002222000000000000000022-2-20000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000000022220000000000000000-2-2220000000000000000000000000000000000
χ63444-4-4-44-4-24-4-44-2-22222-200004i4i−4i−4i0000-22-2200000000000000000000−2i−2i2i2i000000000000000000000000000000
χ64444-4-4-44-4-24-4-44-2-22222-20000−4i−4i4i4i0000-22-22000000000000000000002i2i−2i−2i000000000000000000000000000000
χ65444-4-4-44-4-2-444-4-2-22222-2000000004i4i−4i−4i2-22-2000000000000000000000000−2i−2i2i2i00000000000000000000000000
χ66444-4-4-44-4-2-444-4-2-22222-200000000−4i−4i4i4i2-22-20000000000000000000000002i2i−2i−2i00000000000000000000000000
χ6744-444-4-4-4-20000-2222-2-224-400−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000-22i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ6844-444-4-4-4-20000-2222-2-224-4002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000-22−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ6944-444-4-4-4-20000-2222-2-22-4400−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002-2i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ7044-444-4-4-4-20000-2222-2-22-44002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000002-2−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ7144-4-4-44-44-20000-22-2-2222004-422−22−222222−22−222200000000000000000000-2200−222−2−222−200000000000000000000000000
χ7244-4-4-44-44-20000-22-2-2222004-4−222222−22−222222−2200000000000000000000-22002−2−222−2−2200000000000000000000000000
χ7344-4-4-44-44-20000-22-2-222200-4422−22−2222−222222−22000000000000000000002-200−222−22−2−2200000000000000000000000000
χ7444-4-4-44-44-20000-22-2-222200-44−222222−2222−22−2222000000000000000000002-2002−2−22−222−200000000000000000000000000
χ754-444-4-4-4440000-444-4-44-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ764-444-4-4-4440000-444-4-44-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ774-44-444-4-440000-44-444-4-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ784-44-444-4-440000-44-444-4-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ794-4-44-444-4444-4-4-4-4-44-4440000000000004-4-44000000000000000000000000000000000000000000000000000000
χ804-4-44-444-4-244-4-4222-22-2-2000000000000-222-20000000000000000000000000000000000000000000000−2i32i3000000
χ814-4-44-444-4-244-4-4222-22-2-2000000000000-222-200000000000000000000000000000000000000000000002i3−2i3000000
χ824-4-44-444-4-2-4-444222-22-2-20000000000002-2-22000000000000004-40000000000000000000000000000-2200000000
χ834-4-44-444-4-2-4-444222-22-2-20000000000002-2-2200000000000000-4400000000000000000000000000002-200000000
χ844-4-4-44-44444-44-4-4-44-44-4400000000000044-4-4000000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-24-44-422-22-22-2000000000000-2-22200000000000000000000000000000000000000000023−230000000000
χ864-4-4-44-444-24-44-422-22-22-2000000000000-2-222000000000000000000000000000000000000000000−23230000000000
χ874-4-4-44-444-2-44-4422-22-22-200000000000022-2-20000000000004-400000000000000000000000000-22000000000000
χ884-4-4-44-444-2-44-4422-22-22-200000000000022-2-2000000000000-44000000000000000000000000002-2000000000000
χ898-888-8-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-400004-44-4-4440000000000000000000000000000000000000000000000000000000000000000000000

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