Finite Group Databasebeta

← Group #10868464

Character table — Group #10868464

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order1222222234444666666644444488881212121212121212444444444881212121212121212121224242424242424244444888826612122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1
χ911111111111111111111-1-111111111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11111-1-1-111-1-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-1-111-1-1-1-1-1111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-1-1-111111-1-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-1111-1-11111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-111-1-1-1111111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-111111-1-1-1-1-1-11
χ17222222222-2-2-2-2222222222000000002222-2-2-2-222220000-200-2-2000000000000000022-2-200000000000-20000000
χ18222222222-2-2-2-2222222222000000002222-2-2-2-2-2-2-2-20000-200-2-20000000000000000-2-2220000000000020000000
χ19222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-222220000200220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000200220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1000022-2-22-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-10000-2-2-2-2222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000-2-2222-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222222221111-1-1-1-10000-2-222-2-2-211-1-1-1-11111-1-1-1-1111100000000-211-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-1000000002-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000022-2-2-2-2-2111111-1-1-1-1-1-1-1-11111000000002-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-21111-1-1-1-100002222-222111111-1-1-1-11111-1-1-1-100000000-211-1-10000000000
χ29222-22-2-2-222-2-222-2-2-222-2002i2i−2i−2i0000000022-2-22i2i−2i−2i0000000002i2i−2i−2i000000000000002i−2i0000000002-200000000
χ30222-22-2-2-222-2-222-2-2-222-2002i2i−2i−2i0000000022-2-2−2i−2i2i2i0000000002i2i−2i−2i00000000000000−2i2i000000000-2200000000
χ31222-22-2-2-222-2-222-2-2-222-200−2i−2i2i2i0000000022-2-22i2i−2i−2i000000000−2i−2i2i2i000000000000002i−2i000000000-2200000000
χ32222-22-2-2-222-2-222-2-2-222-200−2i−2i2i2i0000000022-2-2−2i−2i2i2i000000000−2i−2i2i2i00000000000000−2i2i0000000002-200000000
χ33222-22-2-2-22-222-22-2-2-222-200000000000000-2-2222i2i−2i−2i2-20000000000022-2-20000000000−2i2i0000000000002i−2i00000
χ34222-22-2-2-22-222-22-2-2-222-200000000000000-2-2222i2i−2i−2i-2200000000000-2-2220000000000−2i2i000000000000−2i2i00000
χ35222-22-2-2-22-222-22-2-2-222-200000000000000-2-222−2i−2i2i2i2-20000000000022-2-200000000002i−2i000000000000−2i2i00000
χ36222-22-2-2-22-222-22-2-2-222-200000000000000-2-222−2i−2i2i2i-2200000000000-2-22200000000002i−2i0000000000002i−2i00000
χ3722-22-22-2-2222-2-2-2-2-22-222002-22-2000000002-22-200000000000002-22-200000000000000002i2i−2i−2i00000000002i−2i000
χ3822-22-22-2-2222-2-2-2-2-22-222002-22-2000000002-22-200000000000002-22-20000000000000000−2i−2i2i2i0000000000−2i2i000
χ3922-22-22-2-2222-2-2-2-2-22-22200-22-22000000002-22-20000000000000-22-2200000000000000002i2i−2i−2i0000000000−2i2i000
χ4022-22-22-2-2222-2-2-2-2-22-22200-22-22000000002-22-20000000000000-22-220000000000000000−2i−2i2i2i00000000002i−2i000
χ4122-2-2-2-22222-22-2-222-2-22-2002i−2i−2i2i22-2-200002-2-220000002i−2i000002i−2i−2i2i000022-2-20000000000000002i−2i0000000000
χ4222-2-2-2-22222-22-2-222-2-22-2002i−2i−2i2i-2-22200002-2-22000000−2i2i000002i−2i−2i2i0000-2-222000000000000000−2i2i0000000000
χ4322-2-2-2-22222-22-2-222-2-22-200−2i2i2i−2i22-2-200002-2-22000000−2i2i00000−2i2i2i−2i000022-2-2000000000000000−2i2i0000000000
χ4422-2-2-2-22222-22-2-222-2-22-200−2i2i2i−2i-2-22200002-2-220000002i−2i00000−2i2i2i−2i0000-2-2220000000000000002i−2i0000000000
χ4522-2-2-2-222-12-22-21-1-111-11002i−2i−2i2i22-2-233−3−3-111-10000002i−2i0003−3−iii−i−i3i3−i3i3-1-11133−3−3000000000−i3i3−ii0000000000
χ4622-2-2-2-222-12-22-21-1-111-11002i−2i−2i2i22-2-2−3−333-111-10000002i−2i000−33−iii−ii3−i3i3−i3-1-111−3−333000000000i3−i3−ii0000000000
χ4722-2-2-2-222-12-22-21-1-111-11002i−2i−2i2i-2-22233−3−3-111-1000000−2i2i0003−3−iii−i−i3i3−i3i311-1-1−3−333000000000i3−i3i−i0000000000
χ4822-2-2-2-222-12-22-21-1-111-11002i−2i−2i2i-2-222−3−333-111-1000000−2i2i000−33−iii−ii3−i3i3−i311-1-133−3−3000000000−i3i3i−i0000000000
χ4922-2-2-2-222-12-22-21-1-111-1100−2i2i2i−2i22-2-233−3−3-111-1000000−2i2i0003−3i−i−iii3−i3i3−i3-1-11133−3−3000000000i3−i3i−i0000000000
χ5022-2-2-2-222-12-22-21-1-111-1100−2i2i2i−2i22-2-2−3−333-111-1000000−2i2i000−33i−i−ii−i3i3−i3i3-1-111−3−333000000000−i3i3i−i0000000000
χ5122-2-2-2-222-12-22-21-1-111-1100−2i2i2i−2i-2-22233−3−3-111-10000002i−2i0003−3i−i−iii3−i3i3−i311-1-1−3−333000000000−i3i3−ii0000000000
χ5222-2-2-2-222-12-22-21-1-111-1100−2i2i2i−2i-2-222−3−333-111-10000002i−2i000−33i−i−ii−i3i3−i3i311-1-133−3−3000000000i3−i3−ii0000000000
χ532-2-222-22-220000-22-222-2-22-20000−i2i2−i2i22-22-200002i−2i2i−2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i002−22−20000000000002−20
χ542-2-222-22-220000-22-222-2-22-20000−i2i2−i2i22-22-20000−2i2i−2i2i00000−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i00−22−22000000000000−220
χ552-2-222-22-220000-22-222-2-22-20000i2−i2i2−i22-22-200002i−2i2i−2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i00−22−22000000000000−220
χ562-2-222-22-220000-22-222-2-22-20000i2−i2i2−i22-22-20000−2i2i−2i2i00000i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i002−22−20000000000002−20
χ572-2-222-22-220000-22-222-2-2-220000−i2i2−i2i2-22-2200002i−2i2i−2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i002−22−2000000000000−220
χ582-2-222-22-220000-22-222-2-2-220000−i2i2−i2i2-22-220000−2i2i−2i2i00000i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i00−22−220000000000002−20
χ592-2-222-22-220000-22-222-2-2-220000i2−i2i2−i2-22-2200002i−2i2i−2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i00−22−220000000000002−20
χ602-2-222-22-220000-22-222-2-2-220000i2−i2i2−i2-22-220000−2i2i−2i2i00000−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i002−22−2000000000000−220
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-24400000000-2-2-2-2222200000000-40022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000000002222222200000000400-2-2000000000000000000000000000000000000000
χ63444-44-4-4-4-24-4-44-2222-2-22004i4i−4i−4i00000000-2-2220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ64444-44-4-4-4-24-4-44-2222-2-2200−4i−4i4i4i00000000-2-22200000000000002i2i−2i−2i00000000000000000000000000000000000
χ65444-44-4-4-4-2-444-4-2222-2-220000000000000022-2-200004-400000000000-2-2220000000000000000000000000000000
χ66444-44-4-4-4-2-444-4-2222-2-220000000000000022-2-20000-440000000000022-2-20000000000000000000000000000000
χ6744-44-44-4-44-4-444-4-4-44-44400000000000000-44-440000000000000000000000000000000000000000000000000000
χ6844-44-44-4-4-244-4-4222-22-2-2004-44-400000000-22-220000000000000-22-2200000000000000000000000000000000000
χ6944-44-44-4-4-244-4-4222-22-2-200-44-4400000000-22-2200000000000002-22-200000000000000000000000000000000000
χ7044-44-44-4-4-2-4-444222-22-2-2000000000000002-22-200000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ7144-44-44-4-4-2-4-444222-22-2-2000000000000002-22-2000000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ7244-4-4-4-4444-44-44-444-4-44-400000000000000-444-40000000000000000000000000000000000000000000000000000
χ7344-4-4-4-444-2-44-442-2-222-2200000000002323−23−232-2-2200000000000−2323000000000000000000000000000000000000000
χ7444-4-4-4-444-2-44-442-2-222-220000000000−23−2323232-2-220000000000023−23000000000000000000000000000000000000000
χ754-444-4-4-44400004-444-4-4-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ764-444-4-4-44400004-444-4-4-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ774-44-4-444-44000044-4-4-4-44000000−2i22i22i2−2i200000000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ784-44-4-444-44000044-4-4-4-440000002i2−2i2−2i22i2000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ794-44-4-444-4-20000-2-22222-2000000−2i22i22i2−2i223−23−23230000000000000000000000000i2−i2−i2i2−i6i6i6−i600000000000000000000000
χ804-44-4-444-4-20000-2-22222-2000000−2i22i22i2−2i2−232323−230000000000000000000000000i2−i2−i2i2i6−i6−i6i600000000000000000000000
χ814-44-4-444-4-20000-2-22222-20000002i2−2i2−2i22i223−23−23230000000000000000000000000−i2i2i2−i2i6−i6−i6i600000000000000000000000
χ824-44-4-444-4-20000-2-22222-20000002i2−2i2−2i22i2−232323−230000000000000000000000000−i2i2i2−i2−i6i6i6−i600000000000000000000000
χ834-4-444-44-4-200002-22-2-2224-40000−2i22i2−2i22i2-22-220000000000000−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000
χ844-4-444-44-4-200002-22-2-2224-400002i2−2i22i2−2i2-22-2200000000000002i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000
χ854-4-444-44-4-200002-22-2-222-440000−2i22i2−2i22i22-22-200000000000002i2−2i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000
χ864-4-444-44-4-200002-22-2-222-4400002i2−2i22i2−2i22-22-20000000000000−2i22i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000
χ874-4-4-444-4440000-4-44-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ884-4-4-444-4440000-4-44-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ898-888-8-8-88-40000-44-4-44440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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