Finite Group Databasebeta

← Group #10830651

Character table — Group #10830651

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666224444666688881212121244444444488121212121212121212122424242424242424444488884121212122224444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11111-1-111-1
χ911111111111111111111-1-11111-1-1-1-1111111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1-111-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-1111-1-111-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-111-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-111-1-11111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1111-1-111-1-1-1-11
χ17222222222-2-2-2-2222222222000022220000-2-2-2-22222-2000000-2-2000000000000000022-2-2000000000-2000000000
χ18222222222-2-2-2-2222222222000022220000-2-2-2-2-2-2-2-2-2000000-2-20000000000000000-2-2220000000002000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-222222000000220000000000000000-2-2-2-20000000002000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-2-2-2-2-220000002200000000000000002222000000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-100002-2-222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222211112222-1-1-1-10000-2-2-222-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1-10000-222-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-2-2-22-2222-2-222-2-2-2-220022-2-2000000002-22-2000000000000022-2-200000000000000002i2i−2i−2i00000000002i−2i000
χ30222-2-2-22-2222-2-222-2-2-2-220022-2-2000000002-22-2000000000000022-2-20000000000000000−2i−2i2i2i0000000000−2i2i000
χ31222-2-2-22-2222-2-222-2-2-2-2200-2-222000000002-22-20000000000000-2-22200000000000000002i2i−2i−2i0000000000−2i2i000
χ32222-2-2-22-2222-2-222-2-2-2-2200-2-222000000002-22-20000000000000-2-2220000000000000000−2i−2i2i2i00000000002i−2i000
χ3322-2-2-22-22200002-222-2-2-22-2000022-2-222−2−200002i2i−2i−2i000002−2000000000022−2−222−2−22i−2i00−i2i2−i2i2000000000000−i2i20
χ3422-2-2-22-22200002-222-2-2-22-2000022-2-222−2−20000−2i−2i2i2i000002−2000000000022−2−222−2−2−2i2i00i2−i2i2−i2000000000000i2−i20
χ3522-2-2-22-22200002-222-2-2-22-2000022-2-2−2−22200002i2i−2i−2i00000−220000000000−2−222−2−2222i−2i00i2−i2i2−i2000000000000i2−i20
χ3622-2-2-22-22200002-222-2-2-22-2000022-2-2−2−2220000−2i−2i2i2i00000−220000000000−2−222−2−222−2i2i00−i2i2−i2i2000000000000−i2i20
χ3722-2-2-22-22200002-222-2-2-2-220000-2-22222−2−200002i2i−2i−2i00000−22000000000022−2−2−2−222−2i2i00−i2i2−i2i2000000000000i2−i20
χ3822-2-2-22-22200002-222-2-2-2-220000-2-22222−2−20000−2i−2i2i2i00000−22000000000022−2−2−2−2222i−2i00i2−i2i2−i2000000000000−i2i20
χ3922-2-2-22-22200002-222-2-2-2-220000-2-222−2−22200002i2i−2i−2i000002−20000000000−2−22222−2−2−2i2i00i2−i2i2−i2000000000000−i2i20
χ4022-2-2-22-22200002-222-2-2-2-220000-2-222−2−2220000−2i−2i2i2i000002−20000000000−2−22222−2−22i−2i00−i2i2−i2i2000000000000i2−i20
χ412-2-22-222-22-22-22-2-22-2-222002-22-200002-22-2-2-22200000002-200002-22-200002-22-20000000000000002-20000000000
χ422-2-22-222-22-22-22-2-22-2-222002-22-20000-22-22-2-2220000000-2200002-22-20000-22-22000000000000000-220000000000
χ432-2-22-222-22-22-22-2-22-2-22200-22-2200002-22-2-2-2220000000-220000-22-2200002-22-2000000000000000-220000000000
χ442-2-22-222-22-22-22-2-22-2-22200-22-220000-22-22-2-22200000002-20000-22-220000-22-220000000000000002-20000000000
χ452-2-22-222-2-1-22-2211-111-1-1002-22-2−i3i3−i3i32-22-211-1-100000002-200−i3i3-11-11−i3−i3i3i3-11-11−i3i3−i3i3000000000−i3i3-110000000000
χ462-2-22-222-2-1-22-2211-111-1-1002-22-2−i3i3−i3i3-22-2211-1-10000000-2200−i3i3-11-11−i3−i3i3i31-11-1i3−i3i3−i3000000000i3−i31-10000000000
χ472-2-22-222-2-1-22-2211-111-1-1002-22-2i3−i3i3−i32-22-211-1-100000002-200i3−i3-11-11i3i3−i3−i3-11-11i3−i3i3−i3000000000i3−i3-110000000000
χ482-2-22-222-2-1-22-2211-111-1-1002-22-2i3−i3i3−i3-22-2211-1-10000000-2200i3−i3-11-11i3i3−i3−i31-11-1−i3i3−i3i3000000000−i3i31-10000000000
χ492-2-22-222-2-1-22-2211-111-1-100-22-22−i3i3−i3i32-22-211-1-10000000-2200−i3i31-11-1i3i3−i3−i3-11-11−i3i3−i3i3000000000i3−i31-10000000000
χ502-2-22-222-2-1-22-2211-111-1-100-22-22−i3i3−i3i3-22-2211-1-100000002-200−i3i31-11-1i3i3−i3−i31-11-1i3−i3i3−i3000000000−i3i3-110000000000
χ512-2-22-222-2-1-22-2211-111-1-100-22-22i3−i3i3−i32-22-211-1-10000000-2200i3−i31-11-1−i3−i3i3i3-11-11i3−i3i3−i3000000000−i3i31-10000000000
χ522-2-22-222-2-1-22-2211-111-1-100-22-22i3−i3i3−i3-22-2211-1-100000002-200i3−i31-11-1−i3−i3i3i31-11-1−i3i3−i3i3000000000i3−i3-110000000000
χ532-2-2-22-22222-2-22-2-2-222-22000000000000002-2-222-22-202-200000000002-22-200000000002-200000000002-20000000
χ542-2-2-22-22222-2-22-2-2-222-22000000000000002-2-222-22-20-220000000000-22-2200000000002-20000000000-220000000
χ552-2-2-22-22222-2-22-2-2-222-22000000000000002-2-22-22-2202-200000000002-22-20000000000-220000000000-220000000
χ562-2-2-22-22222-2-22-2-2-222-22000000000000002-2-22-22-220-220000000000-22-220000000000-2200000000002-20000000
χ572-2-2-22-2222-222-2-2-2-222-22002-2-2200000000-222-22-22-20000000002-2-2200000000000000-220000000000002-200000
χ582-2-2-22-2222-222-2-2-2-222-22002-2-2200000000-222-2-22-220000000002-2-22000000000000002-2000000000000-2200000
χ592-2-2-22-2222-222-2-2-2-222-2200-222-200000000-222-22-22-2000000000-222-200000000000000-22000000000000-2200000
χ602-2-2-22-2222-222-2-2-2-222-2200-222-200000000-222-2-22-22000000000-222-2000000000000002-20000000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-2000022220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-4-44-44-4-44444-4-4-4-4400000000000000-44-440000000000000000000000000000000000000000000000000000
χ64444-4-4-44-4-244-4-4-2-22222-20044-4-400000000-22-220000000000000-2-22200000000000000000000000000000000000
χ65444-4-4-44-4-244-4-4-2-22222-200-4-44400000000-22-22000000000000022-2-200000000000000000000000000000000000
χ66444-4-4-44-4-2-4-444-2-22222-2000000000000002-22-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ67444-4-4-44-4-2-4-444-2-22222-2000000000000002-22-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6844-444-4-4-4400004-4-4-444-400000000000000000000000000000000000000000000000000022−22−2222000000000000000
χ6944-444-4-4-4400004-4-4-444-4000000000000000000000000000000000000000000000000000−222222−22000000000000000
χ7044-4-4-44-44-20000-22-2-22224-40000-2-2222222−22−22000000000000022−220000000000−2−222−2−22200000000000000000000000
χ7144-4-4-44-44-20000-22-2-22224-40000-2-222−22−2222220000000000000−2222000000000022−2−222−2−200000000000000000000000
χ7244-4-4-44-44-20000-22-2-2222-44000022-2-22222−22−220000000000000−22220000000000−2−22222−2−200000000000000000000000
χ7344-4-4-44-44-20000-22-2-2222-44000022-2-2−22−222222000000000000022−22000000000022−2−2−2−22200000000000000000000000
χ744-444-4-4-4440000-44-44-44-40000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ754-444-4-4-4440000-44-44-44-4000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ764-44-444-4-440000-444-44-4-4000000000022−22−2222000000000000000000000000022−22−2222000000000000000000000000000
χ774-44-444-4-440000-444-44-4-40000000000−222222−220000000000000000000000000−222222−22000000000000000000000000000
χ784-44-444-4-4-200002-2-22-222000000−2i32i32i3−2i322−22−22220000000000000000000000000−222−2−i6i6i6−i600000000000000000000000
χ794-44-444-4-4-200002-2-22-222000000−2i32i32i3−2i3−222222−2200000000000000000000000002−2−22i6−i6−i6i600000000000000000000000
χ804-44-444-4-4-200002-2-22-2220000002i3−2i3−2i32i322−22−22220000000000000000000000000−222−2i6−i6−i6i600000000000000000000000
χ814-44-444-4-4-200002-2-22-2220000002i3−2i3−2i32i3−222222−2200000000000000000000000002−2−22−i6i6i6−i600000000000000000000000
χ824-4-44-444-444-44-4-4-44-4-4440000000000000044-4-40000000000000000000000000000000000000000000000000000
χ834-4-44-444-4-24-44-422-222-2-2000000−2i32i3−2i32i30000-2-222000000000002i3−2i3000000000000000000000000000000000000000
χ844-4-44-444-4-24-44-422-222-2-20000002i3−2i32i3−2i30000-2-22200000000000−2i32i3000000000000000000000000000000000000000
χ854-4-4-44-444-24-4-44222-2-22-200000000000000-222-2000004-40000000000-22-220000000000000000000000000000000
χ864-4-4-44-444-24-4-44222-2-22-200000000000000-222-200000-4400000000002-22-20000000000000000000000000000000
χ874-4-4-44-444-2-444-4222-2-22-2004-4-44000000002-2-220000000000000-222-200000000000000000000000000000000000
χ884-4-4-44-444-2-444-4222-2-22-200-444-4000000002-2-2200000000000002-2-2200000000000000000000000000000000000
χ8988-888-8-8-8-40000-4444-4-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-888-8-8-88-400004-44-44-440000000000000000000000000000000000000000000000000000000000000000000000

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