Finite Group Databasebeta

← Group #10826270

Character table — Group #10826270

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order122222223444466666662244446666888812121212222222444881212121212121212121224242424242424244444888846612122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111-1
χ911111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-111-1-111-1-1-111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-111-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11-1-111111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-111-1-111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-111-1-1-1-11-1-111-1-11
χ17222222222-2-2-2-2222222222000022220000-2-2-2-2222200-20000-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-2222222222000022220000-2-2-2-2-2-2-2-200-20000-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-222220020000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-2-2-2-2-20020000220000000000000000222200000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-1-10000-2-22-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222211112222-1-1-1-1000022-2-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-1000022-22222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ2922-22-2-2-222-22-222-2-2-2-2220022-2-2000022-2-2-2-22200002-2000000022-2-2000022-2-200000000000002-2000000000000
χ3022-22-2-2-222-22-222-2-2-2-2220022-2-20000-2-222-2-2220000-22000000022-2-20000-2-2220000000000000-22000000000000
χ3122-22-2-2-222-22-222-2-2-2-22200-2-222000022-2-2-2-2220000-220000000-2-222000022-2-20000000000000-22000000000000
χ3222-22-2-2-222-22-222-2-2-2-22200-2-2220000-2-222-2-22200002-20000000-2-2220000-2-22200000000000002-2000000000000
χ3322-22-2-2-22-1-22-22-11111-1-10022-2-2−i3−i3i3i322-2-211-1-100002-200000−i3i3-1-111−i3−i3i3i3-1-111−i3−i3i3i3000000000-11−i3i30000000000
χ3422-22-2-2-22-1-22-22-11111-1-10022-2-2−i3−i3i3i3-2-22211-1-10000-2200000−i3i3-1-111−i3−i3i3i311-1-1i3i3−i3−i30000000001-1i3−i30000000000
χ3522-22-2-2-22-1-22-22-11111-1-10022-2-2i3i3−i3−i322-2-211-1-100002-200000i3−i3-1-111i3i3−i3−i3-1-111i3i3−i3−i3000000000-11i3−i30000000000
χ3622-22-2-2-22-1-22-22-11111-1-10022-2-2i3i3−i3−i3-2-22211-1-10000-2200000i3−i3-1-111i3i3−i3−i311-1-1−i3−i3i3i30000000001-1−i3i30000000000
χ3722-22-2-2-22-1-22-22-11111-1-100-2-222−i3−i3i3i322-2-211-1-10000-2200000−i3i311-1-1i3i3−i3−i3-1-111−i3−i3i3i30000000001-1i3−i30000000000
χ3822-22-2-2-22-1-22-22-11111-1-100-2-222−i3−i3i3i3-2-22211-1-100002-200000−i3i311-1-1i3i3−i3−i311-1-1i3i3−i3−i3000000000-11−i3i30000000000
χ3922-22-2-2-22-1-22-22-11111-1-100-2-222i3i3−i3−i322-2-211-1-10000-2200000i3−i311-1-1−i3−i3i3i3-1-111i3i3−i3−i30000000001-1−i3i30000000000
χ4022-22-2-2-22-1-22-22-11111-1-100-2-222i3i3−i3−i3-2-22211-1-100002-200000i3−i311-1-1−i3−i3i3i311-1-1−i3−i3i3i3000000000-11i3−i30000000000
χ412-22-2-22-222-2-222-222-2-2-22002-22-2000000002-22-200000000000002-22-2000000000000000022-2-2000002-200000000
χ422-22-2-22-222-2-222-222-2-2-22002-22-2000000002-22-200000000000002-22-20000000000000000-2-22200000-2200000000
χ432-22-2-22-222-2-222-222-2-2-2200-22-22000000002-22-20000000000000-22-22000000000000000022-2-200000-2200000000
χ442-22-2-22-222-2-222-222-2-2-2200-22-22000000002-22-20000000000000-22-220000000000000000-2-222000002-200000000
χ452-2-2222-2-220000-22-22-22-22-200002-22-2−i2i2−i2i2000022-2-200000−i2i20000000000−i2i2−i2i2−i2i2−i2i22-200−i2i2−i2i2000000000000−i2i20
χ462-2-2222-2-220000-22-22-22-22-200002-22-2−i2i2−i2i20000-2-22200000−i2i20000000000−i2i2−i2i2−i2i2−i2i2-2200i2−i2i2−i2000000000000i2−i20
χ472-2-2222-2-220000-22-22-22-22-200002-22-2i2−i2i2−i2000022-2-200000i2−i20000000000i2−i2i2−i2i2−i2i2−i22-200i2−i2i2−i2000000000000i2−i20
χ482-2-2222-2-220000-22-22-22-22-200002-22-2i2−i2i2−i20000-2-22200000i2−i20000000000i2−i2i2−i2i2−i2i2−i2-2200−i2i2−i2i2000000000000−i2i20
χ492-2-2222-2-220000-22-22-22-2-220000-22-22−i2i2−i2i2000022-2-200000i2−i20000000000−i2i2−i2i2i2−i2i2−i2-2200−i2i2−i2i2000000000000i2−i20
χ502-2-2222-2-220000-22-22-22-2-220000-22-22−i2i2−i2i20000-2-22200000i2−i20000000000−i2i2−i2i2i2−i2i2−i22-200i2−i2i2−i2000000000000−i2i20
χ512-2-2222-2-220000-22-22-22-2-220000-22-22i2−i2i2−i2000022-2-200000−i2i20000000000i2−i2i2−i2−i2i2−i2i2-2200i2−i2i2−i2000000000000−i2i20
χ522-2-2222-2-220000-22-22-22-2-220000-22-22i2−i2i2−i20000-2-22200000−i2i20000000000i2−i2i2−i2−i2i2−i2i22-200−i2i2−i2i2000000000000i2−i20
χ532-2-2-22-22222-2-22-2-2-222-22002-2-2200000000-222-22-22-20000000002-2-22000000000000002-2000000000000002-2000
χ542-2-2-22-22222-2-22-2-2-222-22002-2-2200000000-222-2-22-220000000002-2-2200000000000000-2200000000000000-22000
χ552-2-2-22-22222-2-22-2-2-222-2200-222-200000000-222-22-22-2000000000-222-2000000000000002-200000000000000-22000
χ562-2-2-22-22222-2-22-2-2-222-2200-222-200000000-222-2-22-22000000000-222-200000000000000-22000000000000002-2000
χ572-2-2-22-2222-222-2-2-2-222-22000000000000002-2-222-22-20002-2000000002-22-20000000000-220000000000002-200000
χ582-2-2-22-2222-222-2-2-2-222-22000000000000002-2-222-22-2000-2200000000-22-220000000000-22000000000000-2200000
χ592-2-2-22-2222-222-2-2-2-222-22000000000000002-2-22-22-220002-2000000002-22-200000000002-2000000000000-2200000
χ602-2-2-22-2222-222-2-2-2-222-22000000000000002-2-22-22-22000-2200000000-22-2200000000002-20000000000002-200000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-200002222000000-4000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000222200000040000-2-2000000000000000000000000000000000000000
χ63444-44-4-4-4400004-444-4-4-40000000000000000004-4-44000000000000000000000000000000000000000000000000
χ64444-44-4-4-4400004-444-4-4-4000000000000000000-444-4000000000000000000000000000000000000000000000000
χ6544-44-4-4-4444-44-44-4-4-4-4440000000000000044-4-40000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-24-44-4-22222-2-2000000−2i3−2i32i32i30000-2-222000000000002i3−2i3000000000000000000000000000000000000000
χ6744-44-4-4-44-24-44-4-22222-2-20000002i32i3−2i3−2i30000-2-22200000000000−2i32i3000000000000000000000000000000000000000
χ6844-4-4-444-44000044-4-44-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ6944-4-4-444-44000044-4-44-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ704-444-4-44-440000-4-44-444-40000000000−2i22i22i2−2i20000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ714-444-4-44-440000-4-44-444-400000000002i2−2i2−2i22i200000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ724-444-4-44-4-2000022-22-2-22000000−2i32i32i3−2i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ734-444-4-44-4-2000022-22-2-22000000−2i32i32i3−2i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ744-444-4-44-4-2000022-22-2-220000002i3−2i3−2i32i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ754-444-4-44-4-2000022-22-2-220000002i3−2i3−2i32i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ764-44-4-44-44444-4-4-444-4-4-4400000000000000-44-440000000000000000000000000000000000000000000000000000
χ774-44-4-44-44-244-4-42-2-2222-2000000000000002-22-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ784-44-4-44-44-244-4-42-2-2222-2000000000000002-22-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ794-44-4-44-44-2-4-4442-2-2222-2004-44-400000000-22-220000000000000-22-2200000000000000000000000000000000000
χ804-44-4-44-44-2-4-4442-2-2222-200-44-4400000000-22-2200000000000002-22-200000000000000000000000000000000000
χ814-4-4444-4-4-200002-22-22-224-40000-22-22−2i22i2−2i22i20000000000000−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ824-4-4444-4-4-200002-22-22-224-40000-22-222i2−2i22i2−2i200000000000002i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ834-4-4444-4-4-200002-22-22-22-4400002-22-2−2i22i2−2i22i200000000000002i2−2i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ844-4-4444-4-4-200002-22-22-22-4400002-22-22i2−2i22i2−2i20000000000000−2i22i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ854-4-4-44-444-24-4-44222-2-22-2004-4-44000000002-2-220000000000000-222-200000000000000000000000000000000000
χ864-4-4-44-444-24-4-44222-2-22-200-444-4000000002-2-2200000000000002-2-2200000000000000000000000000000000000
χ874-4-4-44-444-2-444-4222-2-22-200000000000000-222-200000004-400000000-22-220000000000000000000000000000000
χ884-4-4-44-444-2-444-4222-2-22-200000000000000-222-20000000-44000000002-22-20000000000000000000000000000000
χ89888-88-8-8-8-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-888-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000

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