Finite Group Databasebeta

← Group #10844748

Character table — Group #10844748

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444466666666666688888888888888881212121212121212121216161616161616161616242424244848
order1222222234444666666644448888888812121212444488888888444412121212242424242424242444444488882466121212121212444444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-1-11
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1-1111-1
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-1111-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-1-11
χ911111111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1011111111111111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-11-1-11111-1-111-1-11-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111111-111-1-1-1-111-1-111-11
χ1511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-11-1-11111-1-1-1-111-11
χ1611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11-111-1-1-1-11111-1-11-1
χ17222222222-2-2-2-2222222222-2-200000000-2-2-2-2222200000000000022-2-200000000-2-2-2-22200000000000000000000
χ18222222222-2-2-2-2222222222-2-200000000-2-2-2-2-2-2-2-200000000000022-2-2000000002222-2-200000000000000000000
χ19222222222-2-2-2-22222222-2-22200000000-2-2-2-22222000000000000-2-2220000000022-2-2-2-200000000000000000000
χ20222222222-2-2-2-22222222-2-22200000000-2-2-2-2-2-2-2-2000000000000-2-22200000000-2-2222200000000000000000000
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
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-100000000000022221111-1-1-1-111110000000000-2-211-1-111-1-1000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1000000000000-2-2-2-21111-1-1-1-11111000000000022-1-111-1-111000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-100000000000022-2-211111111-1-1-1-10000000000-2211-1-1-1-111000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1000000000000-2-22211111111-1-1-1-100000000002-2-1-11111-1-1000000
χ29222-2-2-22-222-2-222-2-2-22-220000000000002-2-2200002i2i2i2i−2i−2i−2i−2i002-20000000000000000000000000000002-22i−2i0000
χ30222-2-2-22-222-2-222-2-2-22-220000000000002-2-2200002i2i2i2i−2i−2i−2i−2i00-22000000000000000000000000000000-22−2i2i0000
χ31222-2-2-22-222-2-222-2-2-22-220000000000002-2-220000−2i−2i−2i−2i2i2i2i2i002-20000000000000000000000000000002-2−2i2i0000
χ32222-2-2-22-222-2-222-2-2-22-220000000000002-2-220000−2i−2i−2i−2i2i2i2i2i00-22000000000000000000000000000000-222i−2i0000
χ3322-2-2-22-22200002-22-2-22-22i−2i0022−2−2−i2−i2i2i200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i200002i−2i0022−2−2−i2−i2i2i200002-222−2−20000000000000000
χ3422-2-2-22-22200002-22-2-22-22i−2i0022−2−2−i2−i2i2i20000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i200002i−2i0022−2−2−i2−i2i2i20000-22−2−2220000000000000000
χ3522-2-2-22-22200002-22-2-22-22i−2i00−2−222i2i2−i2−i200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i200002i−2i00−2−222i2i2−i2−i200002-2−2−2220000000000000000
χ3622-2-2-22-22200002-22-2-22-22i−2i00−2−222i2i2−i2−i20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i200002i−2i00−2−222i2i2−i2−i20000-2222−2−20000000000000000
χ3722-2-2-22-22200002-22-2-22-2−2i2i0022−2−2i2i2−i2−i200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i20000−2i2i0022−2−2i2i2−i2−i20000-22−2−2220000000000000000
χ3822-2-2-22-22200002-22-2-22-2−2i2i0022−2−2i2i2−i2−i20000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i20000−2i2i0022−2−2i2i2−i2−i200002-222−2−20000000000000000
χ3922-2-2-22-22200002-22-2-22-2−2i2i00−2−222−i2−i2i2i200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i20000−2i2i00−2−222−i2−i2i2i20000-2222−2−20000000000000000
χ4022-2-2-22-22200002-22-2-22-2−2i2i00−2−222−i2−i2i2i20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i20000−2i2i00−2−222−i2−i2i2i200002-2−2−2220000000000000000
χ412-222-2-2-2220000-222-22-2-2002-2−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i2−22−22−22−20000002-2−i2i2−i2i2−i2i2−i2i22i−2i00002−22−20000000000000000
χ422-222-2-2-2220000-222-22-2-2002-2−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i−22−22−22−220000002-2−i2i2−i2i2−i2i2−i2i2−2i2i0000−22−220000000000000000
χ432-222-2-2-2220000-222-22-2-2002-2i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i−22−22−22−220000002-2i2−i2i2−i2i2−i2i2−i22i−2i0000−22−220000000000000000
χ442-222-2-2-2220000-222-22-2-2002-2i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i2−22−22−22−20000002-2i2−i2i2−i2i2−i2i2−i2−2i2i00002−22−20000000000000000
χ452-222-2-2-2220000-222-22-2-200-22−i2i2−i2i2i2−i2i2−i200002i−2i2i−2i2−22−22−22−2000000-22−i2i2−i2i2i2−i2i2−i2−2i2i0000−22−220000000000000000
χ462-222-2-2-2220000-222-22-2-200-22−i2i2−i2i2i2−i2i2−i20000−2i2i−2i2i−22−22−22−22000000-22−i2i2−i2i2i2−i2i2−i22i−2i00002−22−20000000000000000
χ472-222-2-2-2220000-222-22-2-200-22i2−i2i2−i2−i2i2−i2i200002i−2i2i−2i−22−22−22−22000000-22i2−i2i2−i2−i2i2−i2i2−2i2i00002−22−20000000000000000
χ482-222-2-2-2220000-222-22-2-200-22i2−i2i2−i2−i2i2−i2i20000−2i2i−2i2i2−22−22−22−2000000-22i2−i2i2−i2−i2i2−i2i22i−2i0000−22−220000000000000000
χ492-2-22-222-222-22-2-22-2-2-22200000000000022-2-200002-2-22-222-22i−2i00000000000000000000000000002i−2i0000002i−2i00
χ502-2-22-222-222-22-2-22-2-2-22200000000000022-2-200002-2-22-222-2−2i2i0000000000000000000000000000−2i2i000000−2i2i00
χ512-2-22-222-222-22-2-22-2-2-22200000000000022-2-20000-222-22-2-222i−2i00000000000000000000000000002i−2i000000−2i2i00
χ522-2-22-222-222-22-2-22-2-2-22200000000000022-2-20000-222-22-2-22−2i2i0000000000000000000000000000−2i2i0000002i−2i00
χ532-2-2-22-222222-2-2-2-222-2-2200002i−2i−2i2i00002-22-22-2-22−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i0000002-20000000000000000000000
χ542-2-2-22-222222-2-2-2-222-2-2200002i−2i−2i2i00002-22-2-222-22i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i000000-220000000000000000000000
χ552-2-2-22-222222-2-2-2-222-2-220000−2i2i2i−2i00002-22-22-2-222i−2i−2i2i2i−2i−2i2i00000000−2i2i2i−2i0000002-20000000000000000000000
χ562-2-2-22-222222-2-2-2-222-2-220000−2i2i2i−2i00002-22-2-222-2−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i000000-220000000000000000000000
χ572-2-2-22-2222-2-222-2-222-2-22000000002-2-22-22-222-2-22000000000000000000002-2-2200-22002-2-220000000000000000
χ582-2-2-22-2222-2-222-2-222-2-22000000002-2-22-22-22-222-2000000000000000000002-2-22002-200-222-20000000000000000
χ592-2-2-22-2222-2-222-2-222-2-2200000000-222-2-22-222-2-2200000000000000000000-222-200-2200-222-20000000000000000
χ602-2-2-22-2222-2-222-2-222-2-2200000000-222-2-22-22-222-200000000000000000000-222-2002-2002-2-220000000000000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-244-4-40000000022220000000000000000-2-2220000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444000000002222000000000000000022-2-20000000000000000000000000000000000
χ63444-4-4-44-44-444-44-4-4-44-44000000000000-444-4000000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-24-4-44-2222-22-2000000000000-222-2000000000000004-4000000000000000000000000000000-22000000
χ65444-4-4-44-4-24-4-44-2222-22-2000000000000-222-200000000000000-440000000000000000000000000000002-2000000
χ66444-4-4-44-4-2-444-4-2222-22-20000000000002-2-220000000000000000000000000000000000000000000023−2300000000
χ67444-4-4-44-4-2-444-4-2222-22-20000000000002-2-2200000000000000000000000000000000000000000000−232300000000
χ6844-444-4-4-44000044-44-4-4-4000000000000000000002222−22−22−22−222222000000000000000000000000000000000000000000
χ6944-444-4-4-44000044-44-4-4-400000000000000000000−22−2222222222−22−22000000000000000000000000000000000000000000
χ7044-4-4-44-44-20000-22-222-224i−4i002222−22−22−2i2−2i22i22i200000000000000000000−2i2i00−2−222i2i2−i2−i200000000000000000000000000
χ7144-4-4-44-44-20000-22-222-224i−4i00−22−2222222i22i2−2i2−2i200000000000000000000−2i2i0022−2−2−i2−i2i2i200000000000000000000000000
χ7244-4-4-44-44-20000-22-222-22−4i4i002222−22−222i22i2−2i2−2i2000000000000000000002i−2i00−2−222−i2−i2i2i200000000000000000000000000
χ7344-4-4-44-44-20000-22-222-22−4i4i00−22−222222−2i2−2i22i22i2000000000000000000002i−2i0022−2−2i2i2−i2−i200000000000000000000000000
χ744-444-4-4-44-200002-2-22-222004-4−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000-22i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ754-444-4-4-44-200002-2-22-222004-42i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000-22−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ764-444-4-4-44-200002-2-22-22200-44−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000002-2i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ774-444-4-4-44-200002-2-22-22200-442i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000002-2−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ784-44-444-4-440000-4-4-4444-400000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ794-44-444-4-440000-4-4-4444-4000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ804-4-44-444-44-44-44-44-4-4-444000000000000-4-444000000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-24-44-42-2222-2-2000000000000-2-2220000000000004i−4i0000000000000000000000000000−2i2i0000000000
χ824-4-44-444-4-24-44-42-2222-2-2000000000000-2-222000000000000−4i4i00000000000000000000000000002i−2i0000000000
χ834-4-44-444-4-2-44-442-2222-2-200000000000022-2-20000000000000000000000000000000000000000−2i32i3000000000000
χ844-4-44-444-4-2-44-442-2222-2-200000000000022-2-200000000000000000000000000000000000000002i3−2i3000000000000
χ854-4-4-44-444-244-4-422-2-222-200004i−4i−4i4i0000-22-2200000000000000000000−2i2i2i−2i000000000000000000000000000000
χ864-4-4-44-444-244-4-422-2-222-20000−4i4i4i−4i0000-22-22000000000000000000002i−2i−2i2i000000000000000000000000000000
χ874-4-4-44-444-2-4-44422-2-222-2000000004-4-442-22-2000000000000000000000000-222-200000000000000000000000000
χ884-4-4-44-444-2-4-44422-2-222-200000000-444-42-22-20000000000000000000000002-2-2200000000000000000000000000
χ8988-888-8-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-888-8-8-40000444-4-4-440000000000000000000000000000000000000000000000000000000000000000000000

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