Finite Group Databasebeta

← Group #10868058

Character table — Group #10868058

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-11-1-11-1
χ10111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-111-11
χ11111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-11111-1
χ12111111111-1-1-1-111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1111-1-1-1-11
χ13111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-11-1-1-11
χ14111111111-1-1-1-111111111111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-11-1111-1
χ15111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1111-11
χ16111111111-1-1-1-111111111111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-1-11-1
χ172222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-2000000000000000022000022000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-2-2-22222-2-2000000000000-2-20000000000000000-2-20000-2-2000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000220000-2-20000000000002-20000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000220000000000000000-2-2000022000000000000-220000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-222-2-2-2-22211-1-1-1-11111-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-22222-2-211-1-1-1-111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-222-2-2111111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222-2-222-2-222111111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ2922-2-2-22-2222i2i−2i−2i2-2-22-22-222-2-22i−2i2-22i2i−2i−2i2-200002-22i−2i00002i−2i000000000000000000000000000000002-22i−2i000000
χ3022-2-2-22-2222i2i−2i−2i2-2-22-22-222-2-22i−2i2-22i2i−2i−2i2-20000-22−2i2i00002i−2i00000000000000000000000000000000-22−2i2i000000
χ3122-2-2-22-2222i2i−2i−2i-222-2-22-222-2-2−2i2i-222i2i−2i−2i-22000000000000−2i2i0000000000000000002i2i−2i−2i00000000000000002-200
χ3222-2-2-22-2222i2i−2i−2i-222-2-22-222-2-2−2i2i-222i2i−2i−2i-22000000000000−2i2i000000000000000000−2i−2i2i2i0000000000000000-2200
χ3322-2-2-22-222−2i−2i2i2i2-2-22-22-222-2-2−2i2i2-2−2i−2i2i2i2-200002-2−2i2i0000−2i2i000000000000000000000000000000002-2−2i2i000000
χ3422-2-2-22-222−2i−2i2i2i2-2-22-22-222-2-2−2i2i2-2−2i−2i2i2i2-20000-222i−2i0000−2i2i00000000000000000000000000000000-222i−2i000000
χ3522-2-2-22-222−2i−2i2i2i-222-2-22-222-2-22i−2i-22−2i−2i2i2i-220000000000002i−2i0000000000000000002i2i−2i−2i0000000000000000-2200
χ3622-2-2-22-222−2i−2i2i2i-222-2-22-222-2-22i−2i-22−2i−2i2i2i-220000000000002i−2i000000000000000000−2i−2i2i2i00000000000000002-200
χ3722-2-2-22-22-12i2i−2i−2i2-2-221-11-1-1112i−2i-11−i−iii-1100002-22i−2i0000−ii−i3−i3i3i333−3−3−i3−i3i3i333−3−30000000000000000-11−ii000000
χ3822-2-2-22-22-12i2i−2i−2i2-2-221-11-1-1112i−2i-11−i−iii-1100002-22i−2i0000−iii3i3−i3−i3−3−333i3i3−i3−i3−3−3330000000000000000-11−ii000000
χ3922-2-2-22-22-12i2i−2i−2i2-2-221-11-1-1112i−2i-11−i−iii-110000-22−2i2i0000−ii−i3−i3i3i333−3−3i3i3−i3−i3−3−33300000000000000001-1i−i000000
χ4022-2-2-22-22-12i2i−2i−2i2-2-221-11-1-1112i−2i-11−i−iii-110000-22−2i2i0000−iii3i3−i3−i3−3−333−i3−i3i3i333−3−300000000000000001-1i−i000000
χ4122-2-2-22-22-1−2i−2i2i2i2-2-221-11-1-111−2i2i-11ii−i−i-1100002-2−2i2i0000i−i−i3−i3i3i3−3−333−i3−i3i3i3−3−3330000000000000000-11i−i000000
χ4222-2-2-22-22-1−2i−2i2i2i2-2-221-11-1-111−2i2i-11ii−i−i-1100002-2−2i2i0000i−ii3i3−i3−i333−3−3i3i3−i3−i333−3−30000000000000000-11i−i000000
χ4322-2-2-22-22-1−2i−2i2i2i2-2-221-11-1-111−2i2i-11ii−i−i-110000-222i−2i0000i−i−i3−i3i3i3−3−333i3i3−i3−i333−3−300000000000000001-1−ii000000
χ4422-2-2-22-22-1−2i−2i2i2i2-2-221-11-1-111−2i2i-11ii−i−i-110000-222i−2i0000i−ii3i3−i3−i333−3−3−i3−i3i3i3−3−33300000000000000001-1−ii000000
χ452-222-2-2-2220000-22-2222-2-2-22-200-2-20000222i−2i0000000000002i−2i2i−2i000000000000002i−2i2i−2i00000022-2-20000000000
χ462-222-2-2-2220000-22-2222-2-2-22-200-2-20000222i−2i0000000000002i−2i2i−2i00000000000000−2i2i−2i2i000000-2-2220000000000
χ472-222-2-2-2220000-22-2222-2-2-22-200-2-2000022−2i2i000000000000−2i2i−2i2i000000000000002i−2i2i−2i000000-2-2220000000000
χ482-222-2-2-2220000-22-2222-2-2-22-200-2-2000022−2i2i000000000000−2i2i−2i2i00000000000000−2i2i−2i2i00000022-2-20000000000
χ492-22-2-222-222-22-200002-2-22-2-2200002-22-20000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22i−2i00002i−2i22−2−22−22−20000000000
χ502-22-2-222-222-22-200002-2-22-2-2200002-22-20000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2−2i2i0000−2i2i−2−222−22−220000000000
χ512-22-2-222-222-22-200002-2-22-2-2200002-22-20000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22i−2i00002i−2i−2−222−22−220000000000
χ522-22-2-222-222-22-200002-2-22-2-2200002-22-20000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2−2i2i0000−2i2i22−2−22−22−20000000000
χ532-22-2-222-22-22-2200002-2-22-2-220000-22-220000000000−i2i2i2−i20000000000i2−i2i2−i2−i2i2−i2i22i−2i0000−2i2i22−2−2−22−220000000000
χ542-22-2-222-22-22-2200002-2-22-2-220000-22-220000000000−i2i2i2−i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i00002i−2i−2−2222−22−20000000000
χ552-22-2-222-22-22-2200002-2-22-2-220000-22-220000000000i2−i2−i2i20000000000−i2i2−i2i2i2−i2i2−i22i−2i0000−2i2i−2−2222−22−20000000000
χ562-22-2-222-22-22-2200002-2-22-2-220000-22-220000000000i2−i2−i2i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i00002i−2i22−2−2−22−220000000000
χ572-2-2-22-2222000022-2-2-222-2-2-22002-20000-22002i−2i000000000000002i−2i2i−2i00000000002-2-22002i−2i2i−2i00000000000000
χ582-2-2-22-2222000022-2-2-222-2-2-22002-20000-22002i−2i000000000000002i−2i2i−2i0000000000-222-200−2i2i−2i2i00000000000000
χ592-2-2-22-2222000022-2-2-222-2-2-22002-20000-2200−2i2i00000000000000−2i2i−2i2i00000000002-2-2200−2i2i−2i2i00000000000000
χ602-2-2-22-2222000022-2-2-222-2-2-22002-20000-2200−2i2i00000000000000−2i2i−2i2i0000000000-222-2002i−2i2i−2i00000000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000000022000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000-2-2000000000000000000000000000000000000000000
χ63444-44-4-4-44000000004-44-44-4-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ64444-44-4-4-44000000004-44-44-4-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ6544-44-4-44-4400000000-4-4-4-4444000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ6644-44-4-44-4400000000-4-4-4-44440000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ6744-4-4-44-44-24i4i−4i−4i-444-42-22-2-222−4i4i2-2−2i−2i2i2i2-20000000000002i−2i000000000000000000000000000000000000000000
χ6844-4-4-44-44-2−4i−4i4i4i-444-42-22-2-2224i−4i2-22i2i−2i−2i2-2000000000000−2i2i000000000000000000000000000000000000000000
χ694-444-4-4-44400004-44-444-4-4-44-400440000-4-400000000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-200004-44-4-2-2222-2200-2-2000022000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ714-444-4-4-44-200004-44-4-2-2222-2200-2-20000220000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ724-444-4-4-44-20000-44-44-2-2222-2200220000-2-24i−4i000000000000−2i2i−2i2i00000000000000000000000000000000000000
χ734-444-4-4-44-20000-44-44-2-2222-2200220000-2-2−4i4i0000000000002i−2i2i−2i00000000000000000000000000000000000000
χ744-44-4-444-4-24-44-40000-222-222-20000-22-220000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ754-44-4-444-4-24-44-40000-222-222-20000-22-2200000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ764-44-4-444-4-2-44-440000-222-222-200002-22-20000000000−2i22i22i2−2i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ774-44-4-444-4-2-44-440000-222-222-200002-22-200000000002i2−2i2−2i22i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ784-4-4444-4-444i−4i−4i4i0000-4-444-44-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-44−4i4i4i−4i0000-4-444-44-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-24i−4i−4i4i000022-2-22-220000−2i2i2i−2i0000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ814-4-4444-4-4-24i−4i−4i4i000022-2-22-220000−2i2i2i−2i000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ824-4-4444-4-4-2−4i4i4i−4i000022-2-22-2200002i−2i−2i2i0000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ834-4-4444-4-4-2−4i4i4i−4i000022-2-22-2200002i−2i−2i2i000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ844-4-4-44-44440000-4-444-444-4-4-4400-4400004-400000000000000000000000000000000000000000000000000000000
χ854-4-4-44-444-2000044-4-42-2-2222-200-2200002-2004i−4i00000000000000−2i2i−2i2i0000000000000000000000000000000000
χ864-4-4-44-444-2000044-4-42-2-2222-200-2200002-200−4i4i000000000000002i−2i2i−2i0000000000000000000000000000000000
χ874-4-4-44-444-20000-4-4442-2-2222-2002-20000-220000000000000023−23−232300000000000000000000000000000000000000
χ884-4-4-44-444-20000-4-4442-2-2222-2002-20000-2200000000000000−232323−2300000000000000000000000000000000000000
χ89888-88-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-8-88-8-4000000004444-4-4-4000000000000000000000000000000000000000000000000000000000000000000

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