Finite Group Databasebeta

← Group #10876127

Character table — Group #10876127

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order12222222222234444666666644666612121212444444444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-22222000000000000-2-20000000000000000-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-2-2-2000000000000-2-2000000000000000022-2-2220000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-2-2-2-2-1-11111111111111111000000-1-1-1-1000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000001111000000000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000220000000000000000-2-2-2-2220000000000000000
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002200000000000000002222-2-20000000000000000
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-222-2-222-2-211-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ29222-2-22-2-2000022-22-22-2-2-22-220000002-22-22i2i−2i−2i002-20000000000000022-2-2000000002i−2i000000000000002i−2i0000
χ30222-2-22-2-2000022-22-22-2-2-22-220000002-22-22i2i−2i−2i00-2200000000000000-2-222000000002i−2i00000000000000−2i2i0000
χ31222-2-22-2-2000022-22-22-2-2-22-220000002-22-2−2i−2i2i2i002-20000000000000022-2-200000000−2i2i00000000000000−2i2i0000
χ32222-2-22-2-2000022-22-22-2-2-22-220000002-22-2−2i−2i2i2i00-2200000000000000-2-22200000000−2i2i000000000000002i−2i0000
χ33222-2-22-2-200002-22-222-2-2-22-22000000-22-222i2i−2i−2i2-200000000000022-2-2000000000000−2i2i0000000000002i−2i000000
χ34222-2-22-2-200002-22-222-2-2-22-22000000-22-222i2i−2i−2i-22000000000000-2-222000000000000−2i2i000000000000−2i2i000000
χ35222-2-22-2-200002-22-222-2-2-22-22000000-22-22−2i−2i2i2i2-200000000000022-2-20000000000002i−2i000000000000−2i2i000000
χ36222-2-22-2-200002-22-222-2-2-22-22000000-22-22−2i−2i2i2i-22000000000000-2-2220000000000002i−2i0000000000002i−2i000000
χ372-2222-2-2-222-2-2222-2-2-222-2-2-222-222-2-2-2-22200000000000000002-2000000000000000000000000002i−2i2i−2i00000000
χ382-2222-2-2-222-2-2222-2-2-222-2-2-222-222-2-2-2-22200000000000000002-200000000000000000000000000−2i2i−2i2i00000000
χ392-2222-2-2-222-2-22-2-222-222-2-2-22-2222-2-222-2-2000000002i−2i2i−2i0000-2200000000000000000000002i−2i2i−2i000000000000
χ402-2222-2-2-222-2-22-2-222-222-2-2-22-2222-2-222-2-200000000−2i2i−2i2i0000-220000000000000000000000−2i2i−2i2i000000000000
χ412-2222-2-2-222-2-2-1-2-2221-1-1111-1-22-1-111-1-111000000002i−2i2i−2i00001-1−i3i3−i3i3−i3i3−i3i333−3−333−3−3000000−ii−ii000000000000
χ422-2222-2-2-222-2-2-1-2-2221-1-1111-1-22-1-111-1-111000000002i−2i2i−2i00001-1i3−i3i3−i3i3−i3i3−i3−3−333−3−333000000−ii−ii000000000000
χ432-2222-2-2-222-2-2-1-2-2221-1-1111-1-22-1-111-1-11100000000−2i2i−2i2i00001-1−i3i3−i3i3−i3i3−i3i3−3−333−3−333000000i−ii−i000000000000
χ442-2222-2-2-222-2-2-1-2-2221-1-1111-1-22-1-111-1-11100000000−2i2i−2i2i00001-1i3−i3i3−i3i3−i3i3−i333−3−333−3−3000000i−ii−i000000000000
χ452-2222-2-2-2-2-222222-2-2-222-2-2-22-22-2-222-2-2220000000000000000-22000000000000000000000000002i−2i−2i2i00000000
χ462-2222-2-2-2-2-222222-2-2-222-2-2-22-22-2-222-2-2220000000000000000-2200000000000000000000000000−2i2i2i−2i00000000
χ472-2222-2-2-2-2-2222-2-222-222-2-2-222-2-2-22222-2-2000000002i−2i−2i2i00002-200000000000000000000002i−2i−2i2i000000000000
χ482-2222-2-2-2-2-2222-2-222-222-2-2-222-2-2-22222-2-200000000−2i2i2i−2i00002-20000000000000000000000−2i2i2i−2i000000000000
χ492-2222-2-2-2-2-222-1-2-2221-1-1111-12-211-1-1-1-111000000002i−2i−2i2i0000-11−i3i3−i3i3i3−i3i3−i333−3−3−3−333000000−iii−i000000000000
χ502-2222-2-2-2-2-222-1-2-2221-1-1111-12-211-1-1-1-111000000002i−2i−2i2i0000-11i3−i3i3−i3−i3i3−i3i3−3−33333−3−3000000−iii−i000000000000
χ512-2222-2-2-2-2-222-1-2-2221-1-1111-12-211-1-1-1-11100000000−2i2i2i−2i0000-11−i3i3−i3i3i3−i3i3−i3−3−33333−3−3000000i−i−ii000000000000
χ522-2222-2-2-2-2-222-1-2-2221-1-1111-12-211-1-1-1-11100000000−2i2i2i−2i0000-11i3−i3i3−i3−i3i3−i3i333−3−3−3−333000000i−i−ii000000000000
χ532-2-22-222-22-22-220000-22-2-222-2002-22-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2002-200000000000000−i2i2−i2i2
χ542-2-22-222-22-22-220000-22-2-222-2002-22-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2002-200000000000000i2−i2i2−i2
χ552-2-22-222-22-22-220000-22-2-222-2002-22-20000-22-2200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200-2200000000000000i2−i2i2−i2
χ562-2-22-222-22-22-220000-22-2-222-2002-22-20000-22-2200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200-2200000000000000−i2i2−i2i2
χ572-2-22-222-2-22-2220000-22-2-222-200-22-2200002-22-200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200-2200000000000000−i2i2i2−i2
χ582-2-22-222-2-22-2220000-22-2-222-200-22-2200002-22-200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200-2200000000000000i2−i2−i2i2
χ592-2-22-222-2-22-2220000-22-2-222-200-22-220000-22-2200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2002-200000000000000i2−i2−i2i2
χ602-2-22-222-2-22-2220000-22-2-222-200-22-220000-22-2200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2002-200000000000000−i2i2i2−i2
χ61444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000002200000000000000000000000000000000000000
χ6244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-44-4-40000-24-44-4-2222-22-2000000-22-220000004-400000000000000-2-222000000000000000000000000000000
χ64444-4-44-4-40000-24-44-4-2222-22-2000000-22-22000000-440000000000000022-2-2000000000000000000000000000000
χ65444-4-44-4-40000-2-44-44-2222-22-20000002-22-200004-4000000000000-2-2220000000000000000000000000000000000
χ66444-4-44-4-40000-2-44-44-2222-22-20000002-22-20000-4400000000000022-2-20000000000000000000000000000000000
χ6744-44-4-4-444-4-444000044-44-4-4-4004-4-44000000000000000000000000000000000000000000000000000000000000
χ6844-44-4-4-444-4-44-20000-2-22-222200-222-2000000000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ6944-44-4-4-444-4-44-20000-2-22-222200-222-2000000000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ7044-44-4-4-44-444-44000044-44-4-4-400-444-4000000000000000000000000000000000000000000000000000000000000
χ7144-44-4-4-44-444-4-20000-2-22-2222002-2-22000000000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ7244-44-4-4-44-444-4-20000-2-22-2222002-2-22000000000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ7344-4-44-44-40000400004-44-4-44-40000000000000000000000000000000000000000000000004-40000000000000000
χ7444-4-44-44-40000400004-44-4-44-4000000000000000000000000000000000000000000000000-440000000000000000
χ754-4444-4-4-444-4-4-244-4-42-2-2222-24-4-2-22222-2-20000000000000000-2200000000000000000000000000000000000000
χ764-4444-4-4-4-4-444-244-4-42-2-2222-2-4422-2-222-2-200000000000000002-200000000000000000000000000000000000000
χ774-44-4-4-444000044-4-44-4-4-44-444000000-444-400000000000000000000000000000000000000000000000000000000
χ784-44-4-4-44400004-444-4-4-4-44-4440000004-4-4400000000000000000000000000000000000000000000000000000000
χ794-44-4-4-4440000-24-4-44222-22-2-20000002-2-22000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ804-44-4-4-4440000-24-4-44222-22-2-20000002-2-220000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ814-44-4-4-4440000-2-444-4222-22-2-2000000-222-20000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ824-44-4-4-4440000-2-444-4222-22-2-2000000-222-200000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ834-4-44-444-44-44-4-200002-222-2-2200-22-220000000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ844-4-44-444-44-44-4-200002-222-2-2200-22-2200000000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ854-4-44-444-4-44-44-200002-222-2-22002-22-20000000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ864-4-44-444-4-44-44-200002-222-2-22002-22-200000000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ874-4-4-444-44000040000-4-4444-4-400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ884-4-4-444-44000040000-4-4444-4-40000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ8988-8-88-88-80000-40000-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-880000-4000044-4-4-444000000000000000000000000000000000000000000000000000000000000000000

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