Finite Group Databasebeta

← Group #10826940

Character table — Group #10826940

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order1222222222223444466666664466661212121244442222224466666666888812122424242424242424222244661212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-111-1-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-2222200000000000000000000-2-200000000-2-2-2-2220000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-200000000000000000000-2-2000000002222-2-20000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000001111000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2222211111111-2-2-2-2-1-111111111000000-1-1-1-1000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-10000001111000000000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000000000002200000000-2-222-2-20000000000000000
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000220000000022-2-2220000000000000000
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-222-2-2-1-1-1-1111122-2-211-1-1-1-11111000000-1-111000000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-2-2-222-1-1-1-11111-2-222111111-1-1-1-100000011-1-1000000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-22222-2-21111-1-1-1-1-2-222111111-1-1-1-1000000-1-111000000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-222-2-2221111-1-1-1-122-2-211-1-1-1-1111100000011-1-1000000000000
χ29222-22-2-2-222-2-22000022-2-2-22-20022-2-200002i2i−2i−2i00000000000000002−22−20022−2−222−2−200002i−2i000000000000−i2i2−i2i2
χ30222-22-2-2-222-2-22000022-2-2-22-20022-2-200002i2i−2i−2i0000000000000000−22−2200−2−222−2−22200002i−2i000000000000i2−i2i2−i2
χ31222-22-2-2-222-2-22000022-2-2-22-20022-2-20000−2i−2i2i2i00000000000000002−22−20022−2−222−2−20000−2i2i000000000000i2−i2i2−i2
χ32222-22-2-2-222-2-22000022-2-2-22-20022-2-20000−2i−2i2i2i0000000000000000−22−2200−2−222−2−2220000−2i2i000000000000−i2i2−i2i2
χ33222-22-2-2-2-2-2222000022-2-2-22-200-2-22200002i2i−2i−2i00000000000000002−2−220022−2−2−2−2220000−2i2i000000000000−i2i2i2−i2
χ34222-22-2-2-2-2-2222000022-2-2-22-200-2-22200002i2i−2i−2i0000000000000000−222−200−2−22222−2−20000−2i2i000000000000i2−i2−i2i2
χ35222-22-2-2-2-2-2222000022-2-2-22-200-2-2220000−2i−2i2i2i00000000000000002−2−220022−2−2−2−22200002i−2i000000000000i2−i2−i2i2
χ36222-22-2-2-2-2-2222000022-2-2-22-200-2-2220000−2i−2i2i2i0000000000000000−222−200−2−22222−2−200002i−2i000000000000−i2i2i2−i2
χ3722-2-2-2-222000022-22-22-22-2-2-220000002-22-22-22-2002-20000000022-2-2000000000000002-20000000000002-2000000
χ3822-2-2-2-222000022-22-22-22-2-2-220000002-22-22-22-200-2200000000-2-222000000000000002-2000000000000-22000000
χ3922-2-2-2-222000022-22-22-22-2-2-220000002-22-2-22-22002-20000000022-2-200000000000000-22000000000000-22000000
χ4022-2-2-2-222000022-22-22-22-2-2-220000002-22-2-22-2200-2200000000-2-22200000000000000-220000000000002-2000000
χ4122-2-2-2-22200002-22-222-22-2-2-22000000-22-222-22-22-200000022-2-2000000000000000000-2200000000002-200000000
χ4222-2-2-2-22200002-22-222-22-2-2-22000000-22-222-22-2-22000000-2-222000000000000000000-220000000000-2200000000
χ4322-2-2-2-22200002-22-222-22-2-2-22000000-22-22-22-222-200000022-2-20000000000000000002-20000000000-2200000000
χ4422-2-2-2-22200002-22-222-22-2-2-22000000-22-22-22-22-22000000-2-2220000000000000000002-200000000002-200000000
χ452-2-2-222-222-22-2222-2-2-2-2-22-2222-22-22-2-2-222000000002-22-20000000000002-2000000000000002-22-2000000000000
χ462-2-2-222-222-22-2222-2-2-2-2-22-2222-22-22-2-2-22200000000-22-220000000000002-200000000000000-22-22000000000000
χ472-2-2-222-222-22-22-2-222-2-2-22-222-222-22-222-2-2000000000000000000000000-220000000000000000002-200002-20000
χ482-2-2-222-222-22-22-2-222-2-2-22-222-222-22-222-2-2000000000000000000000000-22000000000000000000-220000-220000
χ492-2-2-222-222-22-2-122-2-2111-11-1-12-2-11-1111-1-1000000002-22-2−i3i3−i3i3−i3i3−i3i30000-11−i3i3−i3i3−i3i3−i3i3000000-11-11000000000000
χ502-2-2-222-222-22-2-122-2-2111-11-1-12-2-11-1111-1-1000000002-22-2i3−i3i3−i3i3−i3i3−i30000-11i3−i3i3−i3i3−i3i3−i3000000-11-11000000000000
χ512-2-2-222-222-22-2-122-2-2111-11-1-12-2-11-1111-1-100000000-22-22−i3i3−i3i3−i3i3−i3i30000-11i3−i3i3−i3i3−i3i3−i30000001-11-1000000000000
χ522-2-2-222-222-22-2-122-2-2111-11-1-12-2-11-1111-1-100000000-22-22i3−i3i3−i3i3−i3i3−i30000-11−i3i3−i3i3−i3i3−i3i30000001-11-1000000000000
χ532-2-2-222-22-22-22222-2-2-2-2-22-222-22-22-22-2-222000000002-2-22000000000000-22000000000000002-2-22000000000000
χ542-2-2-222-22-22-22222-2-2-2-2-22-222-22-22-22-2-22200000000-222-2000000000000-2200000000000000-222-2000000000000
χ552-2-2-222-22-22-222-2-222-2-2-22-2222-2-22-2222-2-20000000000000000000000002-20000000000000000002-20000-220000
χ562-2-2-222-22-22-222-2-222-2-2-22-2222-2-22-2222-2-20000000000000000000000002-2000000000000000000-2200002-20000
χ572-2-2-222-22-22-22-122-2-2111-11-1-1-221-11-111-1-1000000002-2-22−i3i3−i3i3i3−i3i3−i300001-1−i3i3−i3i3i3−i3i3−i3000000-111-1000000000000
χ582-2-2-222-22-22-22-122-2-2111-11-1-1-221-11-111-1-1000000002-2-22i3−i3i3−i3−i3i3−i3i300001-1i3−i3i3−i3−i3i3−i3i3000000-111-1000000000000
χ592-2-2-222-22-22-22-122-2-2111-11-1-1-221-11-111-1-100000000-222-2−i3i3−i3i3i3−i3i3−i300001-1i3−i3i3−i3−i3i3−i3i30000001-1-11000000000000
χ602-2-2-222-22-22-22-122-2-2111-11-1-1-221-11-111-1-100000000-222-2i3−i3i3−i3−i3i3−i3i300001-1−i3i3−i3i3i3−i3i3−i30000001-1-11000000000000
χ61444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000000000000022000000000000000000000000000000
χ6244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-24422222222000000000000000000000000-2-2000000000000000000000000000000
χ63444-44-4-4-444-4-4-20000-2-2222-2200-2-22200000000000000000000000022−2222−2200−2−222−2−2220000000000000000000000
χ64444-44-4-4-444-4-4-20000-2-2222-2200-2-222000000000000000000000000−2222−22220022−2−222−2−20000000000000000000000
χ65444-44-4-4-4-4-444-20000-2-2222-220022-2-200000000000000000000000022−22−222200−2−22222−2−20000000000000000000000
χ66444-44-4-4-4-4-444-20000-2-2222-220022-2-2000000000000000000000000−222222−220022−2−2−2−2220000000000000000000000
χ6744-44-44-4-40000400004-4-444-4-400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6844-44-44-4-40000400004-4-444-4-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ6944-4-4-4-4440000-24-44-4-22-2222-2000000-22-220000004-400000000-2-222000000000000000000000000000000000000
χ7044-4-4-4-4440000-24-44-4-22-2222-2000000-22-22000000-440000000022-2-2000000000000000000000000000000000000
χ7144-4-4-4-4440000-2-44-44-22-2222-20000002-22-200004-4000000-2-2220000000000000000000000000000000000000000
χ7244-4-4-4-4440000-2-44-44-22-2222-20000002-22-20000-4400000022-2-20000000000000000000000000000000000000000
χ734-444-4-4-44000044-4-44-44-4-44-44000000-444-400000000000000000000000000000000000000000000000000000000
χ744-444-4-4-4400004-444-4-44-4-44-440000004-4-4400000000000000000000000000000000000000000000000000000000
χ754-444-4-4-440000-24-4-442-222-22-20000002-2-220000000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ764-444-4-4-440000-24-4-442-222-22-20000002-2-2200000000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ774-444-4-4-440000-2-444-42-222-22-2000000-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ784-444-4-4-440000-2-444-42-222-22-2000000-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ794-44-4-444-4000040000-4444-4-4-400000000000000000000000000000000000000000000004-4000000000000000000
χ804-44-4-444-4000040000-4444-4-4-40000000000000000000000000000000000000000000000-44000000000000000000
χ814-4-444-44-44-4-4440000-4-44-444-4004-4-44000000000000000000000000000000000000000000000000000000000000
χ824-4-444-44-44-4-44-2000022-22-2-2200-222-2000000000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ834-4-444-44-44-4-44-2000022-22-2-2200-222-2000000000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ844-4-444-44-4-444-440000-4-44-444-400-444-4000000000000000000000000000000000000000000000000000000000000
χ854-4-444-44-4-444-4-2000022-22-2-22002-2-22000000000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ864-4-444-44-4-444-4-2000022-22-2-22002-2-22000000000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ874-4-4-444-444-44-4-2-4-444222-22-2-2-44-22-22-2-2220000000000000000000000002-2000000000000000000000000000000
χ884-4-4-444-44-44-44-2-4-444222-22-2-24-42-22-2-2-222000000000000000000000000-22000000000000000000000000000000
χ8988-88-88-8-80000-40000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-80000-400004-4-4-4444000000000000000000000000000000000000000000000000000000000000000000

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