Finite Group Databasebeta

← Group #10823404

Character table — Group #10823404

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111111122222222222233333333444444444444444466668888888888888888888812121212121212121212121216161616161616162424242424242424
order122222223444466666664444444444448888888812121212444444444444121212122424242424242424224488888888121212121212121222444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111
χ17222222222-2-2-2-222222222222222222-2-200000000-2-2-2-2-2-2-2-20000000022-2-20000000022-2-2000000000000000000000000
χ18222222222-2-2-2-2222222222222222-2-22200000000-2-2-2-2-2-2-2-200000000-2-22200000000-2-222000000000000000000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-200000000-2-2-2-222220000000022-2-200000000-2-222000000000000000000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000-2-2220000000022-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-100000000222222222222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-100000000222222222222-1-1-1-10000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-10000000000001111111100000000
χ2322222222-12222-1-1-1-1-1-1-1000000002222-2-2-2-2-2-2-2-2-1-1-1-1000022-2-222-2-2-1-1-1-111111111000000000000-1-111-1-11100000000
χ2422222222-12222-1-1-1-1-1-1-1000000002222-2-2-2-2-2-2-2-2-1-1-1-10000-2-222-2-222-1-1-1-11111111100000000000011-1-111-1-100000000
χ2522222222-12222-1-1-1-1-1-1-100000000-2-2-2-22222-2-2-2-2-1-1-1-100002222-2-2-2-21111-1-1-1-11111000000000000-1-1-1-1111100000000
χ2622222222-12222-1-1-1-1-1-1-100000000-2-2-2-22222-2-2-2-2-1-1-1-10000-2-2-2-222221111-1-1-1-111110000000000001111-1-1-1-100000000
χ2722222222-12222-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-22222-1-1-1-1000022-2-2-2-22211111111-1-1-1-1000000000000-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-100000000-2-2-2-2-2-2-2-22222-1-1-1-10000-2-22222-2-211111111-1-1-1-100000000000011-1-1-1-11100000000
χ2922-22-2-2-22222-2-22-2-222-2-22i2i2i2i−2i−2i−2i−2i000000000000-2-2222i2i−2i−2i00002i−2i0000000000000000000000000000002i−2i0000002-200
χ3022-22-2-2-22222-2-22-2-222-2-22i2i2i2i−2i−2i−2i−2i000000000000-2-2222i2i−2i−2i0000−2i2i000000000000000000000000000000−2i2i000000-2200
χ3122-22-2-2-22222-2-22-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000000-2-222−2i−2i2i2i00002i−2i0000000000000000000000000000002i−2i000000-2200
χ3222-22-2-2-22222-2-22-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000000-2-222−2i−2i2i2i0000−2i2i000000000000000000000000000000−2i2i0000002-200
χ3322-22-2-2-222-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000000022-2-2−2i−2i2i2i2-20000000000000000000000000000002-2000000002i−2i0000
χ3422-22-2-2-222-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000000022-2-2−2i−2i2i2i-22000000000000000000000000000000-2200000000−2i2i0000
χ3522-22-2-2-222-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i00000000000022-2-22i2i−2i−2i2-20000000000000000000000000000002-200000000−2i2i0000
χ3622-22-2-2-222-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i00000000000022-2-22i2i−2i−2i-22000000000000000000000000000000-22000000002i−2i0000
χ3722-2-22-22-22000022-2-2-2-222i2i−2i−2i2i2i−2i−2i2i−2i0022−2−2i2i2−i2−i200000000000000002i−2i0022−2−2i2i2−i2−i22-200i2i2−i2−i222−2−20000000000000000
χ3822-2-22-22-22000022-2-2-2-222i2i−2i−2i2i2i−2i−2i2i−2i00−2−222−i2−i2i2i200000000000000002i−2i00−2−222−i2−i2i2i22-200−i2−i2i2i2−2−2220000000000000000
χ3922-2-22-22-22000022-2-2-2-222i2i−2i−2i2i2i−2i−2i−2i2i0022−2−2−i2−i2i2i20000000000000000−2i2i0022−2−2−i2−i2i2i2-2200i2i2−i2−i2−2−2220000000000000000
χ4022-2-22-22-22000022-2-2-2-222i2i−2i−2i2i2i−2i−2i−2i2i00−2−222i2i2−i2−i20000000000000000−2i2i00−2−222i2i2−i2−i2-2200−i2−i2i2i222−2−20000000000000000
χ4122-2-22-22-22000022-2-2-2-22−2i−2i2i2i−2i−2i2i2i2i−2i0022−2−2i2i2−i2−i200000000000000002i−2i0022−2−2i2i2−i2−i2-2200−i2−i2i2i2−2−2220000000000000000
χ4222-2-22-22-22000022-2-2-2-22−2i−2i2i2i−2i−2i2i2i2i−2i00−2−222−i2−i2i2i200000000000000002i−2i00−2−222−i2−i2i2i2-2200i2i2−i2−i222−2−20000000000000000
χ4322-2-22-22-22000022-2-2-2-22−2i−2i2i2i−2i−2i2i2i−2i2i0022−2−2−i2−i2i2i20000000000000000−2i2i0022−2−2−i2−i2i2i22-200−i2−i2i2i222−2−20000000000000000
χ4422-2-22-22-22000022-2-2-2-22−2i−2i2i2i−2i−2i2i2i−2i2i00−2−222i2i2−i2−i20000000000000000−2i2i00−2−222i2i2−i2−i22-200i2i2−i2−i2−2−2220000000000000000
χ452-22-22-2-2222-22-2-2222-2-2-22i−2i2i−2i2i−2i2i−2i000000002-22-22-22-22i−2i2i−2i00000000000000002-22-2000000002i−2i2i−2i0000000000000000
χ462-22-22-2-2222-22-2-2222-2-2-22i−2i2i−2i2i−2i2i−2i00000000-22-222-22-22i−2i2i−2i0000000000000000-22-2200000000−2i2i−2i2i0000000000000000
χ472-22-22-2-2222-22-2-2222-2-2-2−2i2i−2i2i−2i2i−2i2i000000002-22-22-22-2−2i2i−2i2i00000000000000002-22-200000000−2i2i−2i2i0000000000000000
χ482-22-22-2-2222-22-2-2222-2-2-2−2i2i−2i2i−2i2i−2i2i00000000-22-222-22-2−2i2i−2i2i0000000000000000-22-22000000002i−2i2i−2i0000000000000000
χ492-22-22-2-222-22-22-2222-2-2-22i−2i2i−2i2i−2i2i−2i00002-22-20000-22-22−2i2i−2i2i0000000000002-22-2000000002i−2i2i−2i00000000000000000000
χ502-22-22-2-222-22-22-2222-2-2-22i−2i2i−2i2i−2i2i−2i0000-22-220000-22-22−2i2i−2i2i000000000000-22-2200000000−2i2i−2i2i00000000000000000000
χ512-22-22-2-222-22-22-2222-2-2-2−2i2i−2i2i−2i2i−2i2i00002-22-20000-22-222i−2i2i−2i0000000000002-22-200000000−2i2i−2i2i00000000000000000000
χ522-22-22-2-222-22-22-2222-2-2-2−2i2i−2i2i−2i2i−2i2i0000-22-220000-22-222i−2i2i−2i000000000000-22-22000000002i−2i2i−2i00000000000000000000
χ532-2-2222-2-220000-22-2-222-22-2-222-2-22002i−2i2−2−22i2−i2−i2i20000000000000000002i−2i2−2−22i2−i2−i2i2002i−2i2−2−22−i2i2i2−i20000000000000000
χ542-2-2222-2-220000-22-2-222-22-2-222-2-22002i−2i−222−2−i2i2i2−i20000000000000000002i−2i−222−2−i2i2i2−i2002i−2i−222−2i2−i2−i2i20000000000000000
χ552-2-2222-2-220000-22-2-222-22-2-222-2-2200−2i2i2−2−22−i2i2i2−i2000000000000000000−2i2i2−2−22−i2i2i2−i200−2i2i2−2−22i2−i2−i2i20000000000000000
χ562-2-2222-2-220000-22-2-222-22-2-222-2-2200−2i2i−222−2i2−i2−i2i2000000000000000000−2i2i−222−2i2−i2−i2i200−2i2i−222−2−i2i2i2−i20000000000000000
χ572-2-2222-2-220000-22-2-222-2-222-2-222-2002i−2i2−2−22i2−i2−i2i20000000000000000002i−2i2−2−22i2−i2−i2i200−2i2i−222−2i2−i2−i2i20000000000000000
χ582-2-2222-2-220000-22-2-222-2-222-2-222-2002i−2i−222−2−i2i2i2−i20000000000000000002i−2i−222−2−i2i2i2−i200−2i2i2−2−22−i2i2i2−i20000000000000000
χ592-2-2222-2-220000-22-2-222-2-222-2-222-200−2i2i2−2−22−i2i2i2−i2000000000000000000−2i2i2−2−22−i2i2i2−i2002i−2i−222−2−i2i2i2−i20000000000000000
χ602-2-2222-2-220000-22-2-222-2-222-2-222-200−2i2i−222−2i2−i2−i2i2000000000000000000−2i2i−222−2i2−i2−i2i2002i−2i2−2−22i2−i2−i2i20000000000000000
χ612-2-2-2-222222-2-22-2-2-22-2222-22-2-22-22000000000000-222-22-2-22002-20000000000000000000000000000002-200002-2000000
χ622-2-2-2-222222-2-22-2-2-22-2222-22-2-22-22000000000000-222-22-2-2200-22000000000000000000000000000000-220000-22000000
χ632-2-2-2-222222-2-22-2-2-22-222-22-222-22-2000000000000-222-2-222-2002-20000000000000000000000000000002-20000-22000000
χ642-2-2-2-222222-2-22-2-2-22-222-22-222-22-2000000000000-222-2-222-200-22000000000000000000000000000000-2200002-2000000
χ652-2-2-2-22222-222-2-2-2-22-2222-22-2-22-220000000000002-2-22-222-20000002-20000000000000000000000000000002-20000002-2
χ662-2-2-2-22222-222-2-2-2-22-2222-22-2-22-220000000000002-2-22-222-2000000-22000000000000000000000000000000-22000000-22
χ672-2-2-2-22222-222-2-2-2-22-222-22-222-22-20000000000002-2-222-2-220000002-20000000000000000000000000000002-2000000-22
χ682-2-2-2-22222-222-2-2-2-22-222-22-222-22-20000000000002-2-222-2-22000000-22000000000000000000000000000000-220000002-2
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-20000000044-4-4000000002222000000000000-2-222000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-2-2-2-2-2-2-200000000-4-44400000000222200000000000022-2-2000000000000000000000000000000000000
χ71444-4-44-4-4400004-44-4-44-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ72444-4-44-4-4400004-44-4-44-4-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000
χ7344-44-4-4-44-244-4-4-222-2-2220000000000000000000022-2-2000000004i−4i000000000000000000000000000000−2i2i0000000000
χ7444-44-4-4-44-244-4-4-222-2-2220000000000000000000022-2-200000000−4i4i0000000000000000000000000000002i−2i0000000000
χ7544-44-4-4-44-2-4-444-222-2-22200000000000000000000-2-22200004-4000000000000000000000000000000-2200000000000000
χ7644-44-4-4-44-2-4-444-222-2-22200000000000000000000-2-2220000-440000000000000000000000000000002-200000000000000
χ7744-4-44-44-4-20000-2-22222-2000000004i−4i002222−22−222i22i2−2i2−2i20000000000000000−2i2i00−2−222−i2−i2i2i20000000000000000000000000000
χ7844-4-44-44-4-20000-2-22222-2000000004i−4i00−22−222222−2i2−2i22i22i20000000000000000−2i2i0022−2−2i2i2−i2−i20000000000000000000000000000
χ7944-4-44-44-4-20000-2-22222-200000000−4i4i002222−22−22−2i2−2i22i22i200000000000000002i−2i00−2−222i2i2−i2−i20000000000000000000000000000
χ8044-4-44-44-4-20000-2-22222-200000000−4i4i00−22−2222222i22i2−2i2−2i200000000000000002i−2i0022−2−2−i2−i2i2i20000000000000000000000000000
χ814-444-4-44-440000-4-44-44-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ824-444-4-44-440000-4-44-44-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-44-44-4-44-24-44-42-2-2-222200000000000000004-44-4-22-2200000000000000000000-22-220000000000000000000000000000
χ844-44-44-4-44-24-44-42-2-2-22220000000000000000-44-44-22-22000000000000000000002-22-20000000000000000000000000000
χ854-44-44-4-44-2-44-442-2-2-22220000000000004-44-400002-22-20000000000000000-22-2200000000000000000000000000000000
χ864-44-44-4-44-2-44-442-2-2-2222000000000000-44-4400002-22-200000000000000002-22-200000000000000000000000000000000
χ874-4-4444-4-4-200002-222-2-2200000000004i−4i22−22−22222i2−2i2−2i22i2000000000000000000−2i2i−222−2−i2i2i2−i20000000000000000000000000000
χ884-4-4444-4-4-200002-222-2-2200000000004i−4i−222222−22−2i22i22i2−2i2000000000000000000−2i2i2−2−22i2−i2−i2i20000000000000000000000000000
χ894-4-4444-4-4-200002-222-2-220000000000−4i4i22−22−2222−2i22i22i2−2i20000000000000000002i−2i−222−2i2−i2−i2i20000000000000000000000000000
χ904-4-4444-4-4-200002-222-2-220000000000−4i4i−222222−222i2−2i2−2i22i20000000000000000002i−2i2−2−22−i2i2i2−i20000000000000000000000000000
χ914-4-4-4-4444-24-4-44222-22-2-2000000000000000000002-2-220000004-4000000000000000000000000000000-22000000000000
χ924-4-4-4-4444-24-4-44222-22-2-2000000000000000000002-2-22000000-440000000000000000000000000000002-2000000000000
χ934-4-4-4-4444-2-444-4222-22-2-200000000000000000000-222-200000000004-4000000000000000000000000000000-2200000000
χ944-4-4-4-4444-2-444-4222-22-2-200000000000000000000-222-20000000000-440000000000000000000000000000002-200000000
χ95888-8-88-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-8-88-8-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000000000

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