Finite Group Databasebeta

← Group #10876207

Character table — Group #10876207

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212444444444444888812121212121212121212242424242424242422444412121212224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1
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
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
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
χ9111111111-1-1-1-111111111111-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ10111111111-1-1-1-111111111111-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1-1-111
χ11111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-111
χ12111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-11111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-111-1-111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
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
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000220000000000000000-2-2-2-2220000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000002200000000000000002222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-2-2-2-2-1-11111111111111111000000-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-222-2-222-2-211-1-1-1-11111-1-1-1-1111100000011-1-1000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1000022-2-2-2-222-2-22211-1-1-1-111111111-1-1-1-1000000-1-111000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-22222-2-2-2-222111111-1-1-1-11111-1-1-1-100000011-1-1000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-10000-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-11111000000-1-111000000000000
χ2922-2-2-222-222i2i−2i−2i2-22-22-2-2-222-22i−2i2i2i−2i−2i2-22-200000000000000002i−2i000000000000000000000000002-200002i−2i0000
χ3022-2-2-222-222i2i−2i−2i2-22-22-2-2-222-22i−2i2i2i−2i−2i2-22-200000000000000002i−2i00000000000000000000000000-220000−2i2i0000
χ3122-2-2-222-222i2i−2i−2i-22-222-2-2-222-2−2i2i2i2i−2i−2i-22-22000000002i−2i2-20000−2i2i00000000000000000000002-22i−2i000000000000
χ3222-2-2-222-222i2i−2i−2i-22-222-2-2-222-2−2i2i2i2i−2i−2i-22-2200000000−2i2i-220000−2i2i0000000000000000000000-22−2i2i000000000000
χ3322-2-2-222-22−2i−2i2i2i2-22-22-2-2-222-2−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i000000000000000000000000002-20000−2i2i0000
χ3422-2-2-222-22−2i−2i2i2i2-22-22-2-2-222-2−2i2i−2i−2i2i2i2-22-20000000000000000−2i2i00000000000000000000000000-2200002i−2i0000
χ3522-2-2-222-22−2i−2i2i2i-22-222-2-2-222-22i−2i−2i−2i2i2i-22-22000000002i−2i-2200002i−2i0000000000000000000000-222i−2i000000000000
χ3622-2-2-222-22−2i−2i2i2i-22-222-2-2-222-22i−2i−2i−2i2i2i-22-2200000000−2i2i2-200002i−2i00000000000000000000002-2−2i2i000000000000
χ3722-2-2-222-2-12i2i−2i−2i-22-22-1111-1-11−2i2i−i−iii1-11-1000000002i−2i2-20000i−i−i3−i3i3i333−3−333−3−3−i3−i3i3i3000000-11−ii000000000000
χ3822-2-2-222-2-12i2i−2i−2i-22-22-1111-1-11−2i2i−i−iii1-11-1000000002i−2i2-20000i−ii3i3−i3−i3−3−333−3−333i3i3−i3−i3000000-11−ii000000000000
χ3922-2-2-222-2-12i2i−2i−2i-22-22-1111-1-11−2i2i−i−iii1-11-100000000−2i2i-220000i−i−i3−i3i3i333−3−3−3−333i3i3−i3−i30000001-1i−i000000000000
χ4022-2-2-222-2-12i2i−2i−2i-22-22-1111-1-11−2i2i−i−iii1-11-100000000−2i2i-220000i−ii3i3−i3−i3−3−33333−3−3−i3−i3i3i30000001-1i−i000000000000
χ4122-2-2-222-2-1−2i−2i2i2i-22-22-1111-1-112i−2iii−i−i1-11-1000000002i−2i-220000−ii−i3−i3i3i3−3−33333−3−3i3i3−i3−i30000001-1−ii000000000000
χ4222-2-2-222-2-1−2i−2i2i2i-22-22-1111-1-112i−2iii−i−i1-11-1000000002i−2i-220000−iii3i3−i3−i333−3−3−3−333−i3−i3i3i30000001-1−ii000000000000
χ4322-2-2-222-2-1−2i−2i2i2i-22-22-1111-1-112i−2iii−i−i1-11-100000000−2i2i2-20000−ii−i3−i3i3i3−3−333−3−333−i3−i3i3i3000000-11i−i000000000000
χ4422-2-2-222-2-1−2i−2i2i2i-22-22-1111-1-112i−2iii−i−i1-11-100000000−2i2i2-20000−iii3i3−i3−i333−3−333−3−3i3i3−i3−i3000000-11i−i000000000000
χ452-222-22-2-2200002-2-22-2-222-22-2000000-222-222-2-22i−2i0000000000002i−2i2i−2i0000000000002-20000000000002i−2i000000
χ462-222-22-2-2200002-2-22-2-222-22-2000000-222-222-2-2−2i2i000000000000−2i2i−2i2i0000000000002-2000000000000−2i2i000000
χ472-222-22-2-2200002-2-22-2-222-22-2000000-222-2-2-2222i−2i0000000000002i−2i2i−2i000000000000-22000000000000−2i2i000000
χ482-222-22-2-2200002-2-22-2-222-22-2000000-222-2-2-222−2i2i000000000000−2i2i−2i2i000000000000-220000000000002i−2i000000
χ492-222-22-2-220000-222-2-2-222-22-20000002-2-2222-2-2002i−2i000000000000002i−2i2i−2i00000000-2200000000002i−2i00000000
χ502-222-22-2-220000-222-2-2-222-22-20000002-2-2222-2-200−2i2i00000000000000−2i2i−2i2i00000000-220000000000−2i2i00000000
χ512-222-22-2-220000-222-2-2-222-22-20000002-2-22-2-222002i−2i000000000000002i−2i2i−2i000000002-20000000000−2i2i00000000
χ522-222-22-2-220000-222-2-2-222-22-20000002-2-22-2-22200−2i2i00000000000000−2i2i−2i2i000000002-200000000002i−2i00000000
χ532-22-2-2-22222-22-20000222-2-2-2-2002-22-200002i−2i2i−2i000000002−22−200000000002−22−22−22−2002i−2i00000000000000−i2i2−i2i2
χ542-22-2-2-22222-22-20000222-2-2-2-2002-22-200002i−2i2i−2i00000000−22−220000000000−22−22−22−22002i−2i00000000000000i2−i2i2−i2
χ552-22-2-2-22222-22-20000222-2-2-2-2002-22-20000−2i2i−2i2i000000002−22−200000000002−22−22−22−200−2i2i00000000000000i2−i2i2−i2
χ562-22-2-2-22222-22-20000222-2-2-2-2002-22-20000−2i2i−2i2i00000000−22−220000000000−22−22−22−2200−2i2i00000000000000−i2i2−i2i2
χ572-22-2-2-2222-22-220000222-2-2-2-200-22-2200002i−2i2i−2i000000002−2−2200000000002−22−2−22−2200−2i2i00000000000000−i2i2i2−i2
χ582-22-2-2-2222-22-220000222-2-2-2-200-22-2200002i−2i2i−2i00000000−222−20000000000−22−222−22−200−2i2i00000000000000i2−i2−i2i2
χ592-22-2-2-2222-22-220000222-2-2-2-200-22-220000−2i2i−2i2i000000002−2−2200000000002−22−2−22−22002i−2i00000000000000i2−i2−i2i2
χ602-22-2-2-2222-22-220000222-2-2-2-200-22-220000−2i2i−2i2i00000000−222−20000000000−22−222−22−2002i−2i00000000000000−i2i2i2−i2
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-44-4-4-4400000000-4-44-44-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4400000000-4-44-44-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ6544-44-4-4-44400000000-44-444-4-40000000000000000000000000000000000000000000000004i−4i0000000000000000
χ6644-44-4-4-44400000000-44-444-4-4000000000000000000000000000000000000000000000000−4i4i0000000000000000
χ6744-4-4-444-4-24i4i−4i−4i4-44-4-2222-2-224i−4i−2i−2i2i2i-22-220000000000000000−2i2i00000000000000000000000000000000000000
χ6844-4-4-444-4-2−4i−4i4i4i4-44-4-2222-2-22−4i4i2i2i−2i−2i-22-2200000000000000002i−2i00000000000000000000000000000000000000
χ694-444-44-4-4-200004-4-4422-2-22-220000002-2-2200004i−4i000000000000−2i2i−2i2i0000000000000000000000000000000000
χ704-444-44-4-4-200004-4-4422-2-22-220000002-2-220000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000000000
χ714-444-44-4-4-20000-444-422-2-22-22000000-222-20000004i−4i00000000000000−2i2i−2i2i000000000000000000000000000000
χ724-444-44-4-4-20000-444-422-2-22-22000000-222-2000000−4i4i000000000000002i−2i2i−2i000000000000000000000000000000
χ734-44-4-4-444-24-44-40000-2-2-2222200-22-22000000000000000022−2222−220000000000−22−22−22−220000000000000000000000
χ744-44-4-4-444-24-44-40000-2-2-2222200-22-220000000000000000−2222−222200000000002−22−22−22−20000000000000000000000
χ754-44-4-4-444-2-44-440000-2-2-22222002-22-2000000000000000022−22−22220000000000−22−222−22−20000000000000000000000
χ764-44-4-4-444-2-44-440000-2-2-22222002-22-20000000000000000−222222−2200000000002−22−2−22−220000000000000000000000
χ774-4-444-44-444i−4i−4i4i00004-4-44-4-44004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ784-4-444-44-44−4i4i4i−4i00004-4-44-4-4400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ794-4-444-44-4-24i−4i−4i4i0000-222-222-200−2i2i2i−2i0000000000000000000000000000006−6−66−i6i6i6−i60000000000000000000000
χ804-4-444-44-4-24i−4i−4i4i0000-222-222-200−2i2i2i−2i000000000000000000000000000000−666−6i6−i6−i6i60000000000000000000000
χ814-4-444-44-4-2−4i4i4i−4i0000-222-222-2002i−2i−2i2i0000000000000000000000000000006−6−66i6−i6−i6i60000000000000000000000
χ824-4-444-44-4-2−4i4i4i−4i0000-222-222-2002i−2i−2i2i000000000000000000000000000000−666−6−i6i6i6−i60000000000000000000000
χ834-4-4-444-444000044-4-4-44-4-4-444000000-4-44400000000000000000000000000000000000000000000000000000000
χ844-4-4-444-4440000-4-444-44-4-4-44400000044-4-400000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-2000044-4-42-2222-2-200000022-2-20000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ864-4-4-444-44-2000044-4-42-2222-2-200000022-2-200000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ874-4-4-444-44-20000-4-4442-2222-2-2000000-2-22200000000000000000023−23−23230000000000000000000000000000000000
χ884-4-4-444-44-20000-4-4442-2222-2-2000000-2-222000000000000000000−232323−230000000000000000000000000000000000
χ89888-88-8-8-8-40000000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-8-88-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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