Finite Group Databasebeta

← Group #10828479

Character table — Group #10828479

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212222244444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
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
χ9111111111-1-1-1-111111111111-1-111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-111-1-111
χ11111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ12111111111-1-1-1-111111111111-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11111-1-1
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-22222000000000000-2-20000000000000000-2-222-2-20000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2-2-2-2-2000000000000-2-2000000000000000022-2-2220000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-2-2-2-2-1-11111111111111111000000-1-1-1-1000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
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
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-222-2-222-2-211-1-1-1-11111-1-1-1-11111000000-1-111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1000022-2-2-2-222-2-222111111-1-1-1-11111-1-1-1-1000000-1-111000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-22222-2-2-2-22211-1-1-1-111111111-1-1-1-100000011-1-1000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-10000-2-222-2-22222-2-2111111-1-1-1-1-1-1-1-1111100000011-1-1000000000000
χ2922-2-222-2-2222-2-200002-2-222-2-2000022-2-20022-2-200000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2002-200000000000000−i2i2−i2i2
χ3022-2-222-2-2222-2-200002-2-222-2-2000022-2-20022-2-200000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2002-200000000000000i2−i2i2−i2
χ3122-2-222-2-2222-2-200002-2-222-2-2000022-2-200-2-22200000000−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i200-2200000000000000i2−i2i2−i2
χ3222-2-222-2-2222-2-200002-2-222-2-2000022-2-200-2-22200000000i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i200-2200000000000000−i2i2−i2i2
χ3322-2-222-2-22-2-22200002-2-222-2-20000-2-2220022-2-200000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i200-2200000000000000−i2i2i2−i2
χ3422-2-222-2-22-2-22200002-2-222-2-20000-2-2220022-2-200000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i200-2200000000000000i2−i2−i2i2
χ3522-2-222-2-22-2-22200002-2-222-2-20000-2-22200-2-22200000000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2002-200000000000000i2−i2−i2i2
χ3622-2-222-2-22-2-22200002-2-222-2-20000-2-22200-2-22200000000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2002-200000000000000−i2i2i2−i2
χ372-22-22-22-222i−2i2i−2i2-22-2-22-22-22-22i−2i2-22i−2i2i−2i2-200000000000000002i−2i000000000000000000000000002-22i−2i00000000
χ382-22-22-22-222i−2i2i−2i2-22-2-22-22-22-22i−2i2-22i−2i2i−2i2-200000000000000002i−2i00000000000000000000000000-22−2i2i00000000
χ392-22-22-22-222i−2i2i−2i-22-22-22-22-22-2−2i2i-222i−2i2i−2i-2200002-22i−2i00000000−2i2i00000000000000000000002-22i−2i000000000000
χ402-22-22-22-222i−2i2i−2i-22-22-22-22-22-2−2i2i-222i−2i2i−2i-220000-22−2i2i00000000−2i2i0000000000000000000000-22−2i2i000000000000
χ412-22-22-22-22−2i2i−2i2i2-22-2-22-22-22-2−2i2i2-2−2i2i−2i2i2-20000000000000000−2i2i000000000000000000000000002-2−2i2i00000000
χ422-22-22-22-22−2i2i−2i2i2-22-2-22-22-22-2−2i2i2-2−2i2i−2i2i2-20000000000000000−2i2i00000000000000000000000000-222i−2i00000000
χ432-22-22-22-22−2i2i−2i2i-22-22-22-22-22-22i−2i-22−2i2i−2i2i-2200002-2−2i2i000000002i−2i00000000000000000000002-2−2i2i000000000000
χ442-22-22-22-22−2i2i−2i2i-22-22-22-22-22-22i−2i-22−2i2i−2i2i-220000-222i−2i000000002i−2i0000000000000000000000-222i−2i000000000000
χ452-22-22-22-2-12i−2i2i−2i-22-221-11-11-11−2i2i1-1−ii−ii1-100002-22i−2i00000000i−i−i3−i3i3i333−3−3−i3i3−i3i33−33−3000000-11−ii000000000000
χ462-22-22-22-2-12i−2i2i−2i-22-221-11-11-11−2i2i1-1−ii−ii1-100002-22i−2i00000000i−ii3i3−i3−i3−3−333i3−i3i3−i3−33−33000000-11−ii000000000000
χ472-22-22-22-2-12i−2i2i−2i-22-221-11-11-11−2i2i1-1−ii−ii1-10000-22−2i2i00000000i−i−i3−i3i3i333−3−3i3−i3i3−i3−33−330000001-1i−i000000000000
χ482-22-22-22-2-12i−2i2i−2i-22-221-11-11-11−2i2i1-1−ii−ii1-10000-22−2i2i00000000i−ii3i3−i3−i3−3−333−i3i3−i3i33−33−30000001-1i−i000000000000
χ492-22-22-22-2-1−2i2i−2i2i-22-221-11-11-112i−2i1-1i−ii−i1-100002-2−2i2i00000000−ii−i3−i3i3i3−3−333−i3i3−i3i3−33−33000000-11i−i000000000000
χ502-22-22-22-2-1−2i2i−2i2i-22-221-11-11-112i−2i1-1i−ii−i1-100002-2−2i2i00000000−iii3i3−i3−i333−3−3i3−i3i3−i33−33−3000000-11i−i000000000000
χ512-22-22-22-2-1−2i2i−2i2i-22-221-11-11-112i−2i1-1i−ii−i1-10000-222i−2i00000000−ii−i3−i3i3i3−3−333i3−i3i3−i33−33−30000001-1−ii000000000000
χ522-22-22-22-2-1−2i2i−2i2i-22-221-11-11-112i−2i1-1i−ii−i1-10000-222i−2i00000000−iii3i3−i3−i333−3−3−i3i3−i3i3−33−330000001-1−ii000000000000
χ532-2-2-2-2222200002-2-22-2-2-2-222200-2200002-22-22-200002-2000000002-22-20000000000002-20000000000002-2000000
χ542-2-2-2-2222200002-2-22-2-2-2-222200-2200002-22-22-20000-2200000000-22-220000000000002-2000000000000-22000000
χ552-2-2-2-2222200002-2-22-2-2-2-222200-2200002-2-22-2200002-2000000002-22-2000000000000-22000000000000-22000000
χ562-2-2-2-2222200002-2-22-2-2-2-222200-2200002-2-22-220000-2200000000-22-22000000000000-220000000000002-2000000
χ572-2-2-2-222220000-222-2-2-2-2-2222002-20000-222-22-20000002-200000000002-22-200000000-22000000000000002-20000
χ582-2-2-2-222220000-222-2-2-2-2-2222002-20000-222-22-2000000-220000000000-22-2200000000-2200000000000000-220000
χ592-2-2-2-222220000-222-2-2-2-2-2222002-20000-22-22-220000002-200000000002-22-2000000002-200000000000000-220000
χ602-2-2-2-222220000-222-2-2-2-2-2222002-20000-22-22-22000000-220000000000-22-22000000002-2000000000000002-20000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-4-4-4440000000044-4-4-4-440000000000000000000000000000000000000000000000004-40000000000000000
χ64444-4-4-4-4440000000044-4-4-4-44000000000000000000000000000000000000000000000000-440000000000000000
χ6544-44-4-44-44000044-4-44-44-4-44-400-4-400004400000000000000000000000000000000000000000000000000000000
χ6644-44-4-44-440000-4-4444-44-4-44-400440000-4-400000000000000000000000000000000000000000000000000000000
χ6744-44-4-44-4-2000044-4-4-22-222-2200220000-2-2000000000000000000000023−23−2323000000000000000000000000000000
χ6844-44-4-44-4-2000044-4-4-22-222-2200220000-2-20000000000000000000000−232323−23000000000000000000000000000000
χ6944-44-4-44-4-20000-4-444-22-222-2200-2-2000022000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ7044-44-4-44-4-20000-4-444-22-222-2200-2-20000220000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ7144-4-444-4-4-244-4-40000-222-2-2220000-2-22200000000000000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000
χ7244-4-444-4-4-244-4-40000-222-2-2220000-2-222000000000000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000
χ7344-4-444-4-4-2-4-4440000-222-2-222000022-2-200000000000000−2i22i22i2−2i20000000000i2i2−i2−i2−i2−i2i2i20000000000000000000000
χ7444-4-444-4-4-2-4-4440000-222-2-222000022-2-2000000000000002i2−2i2−2i22i20000000000−i2−i2i2i2i2i2−i2−i20000000000000000000000
χ754-444-44-4-4400000000-444-44-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ764-444-44-4-4400000000-444-44-4-40000000000-444-40000000000000000000000000000000000000000000000000000
χ774-44-44-44-4-24i−4i4i−4i4-44-42-22-22-224i−4i-22−2i2i−2i2i-220000000000000000−2i2i00000000000000000000000000000000000000
χ784-44-44-44-4-2−4i4i−4i4i4-44-42-22-22-22−4i4i-222i−2i2i−2i-2200000000000000002i−2i00000000000000000000000000000000000000
χ794-4-444-4-4444i−4i−4i4i0000-4-444-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-444−4i4i4i−4i0000-4-444-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ814-4-444-4-44-24i−4i−4i4i000022-2-222-20000−2i2i2i−2i00000000000000000000000000006−6−66i6−i6−i6i60000000000000000000000
χ824-4-444-4-44-24i−4i−4i4i000022-2-222-20000−2i2i2i−2i0000000000000000000000000000−666−6−i6i6i6−i60000000000000000000000
χ834-4-444-4-44-2−4i4i4i−4i000022-2-222-200002i−2i−2i2i00000000000000000000000000006−6−66−i6i6i6−i60000000000000000000000
χ844-4-444-4-44-2−4i4i4i−4i000022-2-222-200002i−2i−2i2i0000000000000000000000000000−666−6i6−i6−i6i60000000000000000000000
χ854-4-4-4-4444-200004-4-442222-2-2-2002-20000-22000000004-400000000-22-220000000000000000000000000000000000
χ864-4-4-4-4444-200004-4-442222-2-2-2002-20000-2200000000-44000000002-22-20000000000000000000000000000000000
χ874-4-4-4-4444-20000-444-42222-2-2-200-2200002-200000000004-40000000000-22-22000000000000000000000000000000
χ884-4-4-4-4444-20000-444-42222-2-2-200-2200002-20000000000-4400000000002-22-2000000000000000000000000000000
χ89888-8-8-8-88-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000000000
χ908-888-88-8-8-4000000004-4-44-444000000000000000000000000000000000000000000000000000000000000000000

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