Finite Group Databasebeta

← Group #10694266

Character table — Group #10694266

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424244444444444121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-111-1-1−i−iii−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-111ii−i−i−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−i−iiiii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-1-111ii−i−i−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111-1-1−i−iii−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-111-1-1ii−i−iii−i−i-11
χ1722222222222-2-22-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-22-22-22222222-2-2222-2-2-22-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-222-22-222222222-2-2-2-2-2222-2200000000-2-2000000000000000022-2-2-2-2220000000000000000
χ20222222222-2-222-22-222222222-2-2-2-2-2222-2200000000-2-20000000000000000-2-22222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122111111112i2i−2i−2i−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i2i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-12211111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ29222-2-2-2-222222-2-22-2-2-2-2-2-22222-222-22-2-2-22000000002-200000000000000000000000000000000002i−2i2i−2i00
χ30222-2-2-2-222222-2-22-2-2-2-2-2-22222-222-22-2-2-22000000002-20000000000000000000000000000000000−2i2i−2i2i00
χ31222-2-2-2-22222-22-2-2-22-2-2-2-2222-2222-2-222-2-200002i−2i2i−2i-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ32222-2-2-2-22222-22-2-2-22-2-2-2-2222-2222-2-222-2-20000−2i2i−2i2i-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ33222-2-2-2-222-2-22-2222-2-2-2-2-2222-22-2-222-2-22200002-2-22-220000000022-2-2-2-222000000000000000000000000
χ34222-2-2-2-222-2-22-2222-2-2-2-2-2222-22-2-222-2-2220000-222-2-2200000000-2-22222-2-2000000000000000000000000
χ35222-2-2-2-222-2-2-222-222-2-2-2-22222-2-2-22-2222-2000000002-200000000000000000000000000000000002-2-2200
χ36222-2-2-2-222-2-2-222-222-2-2-2-22222-2-2-22-2222-2000000002-20000000000000000000000000000000000-222-200
χ37222-2-2-2-22-122-22-2-2-221111-1-1-1-22-1-111-1-11100002i−2i2i−2i1-133−3−333−3−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ38222-2-2-2-22-122-22-2-2-221111-1-1-1-22-1-111-1-11100002i−2i2i−2i1-1−3−333−3−333−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ39222-2-2-2-22-122-22-2-2-221111-1-1-1-22-1-111-1-1110000−2i2i−2i2i1-133−3−333−3−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ40222-2-2-2-22-122-22-2-2-221111-1-1-1-22-1-111-1-1110000−2i2i−2i2i1-1−3−333−3−333ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ41222-2-2-2-22-1-2-22-2222-21111-1-1-1-2211-1-111-1-100002-2-221-1−i3−i3i3i3i3i3−i3−i3-1-11111-1-10000000000−i3i3i3−i30000000000
χ42222-2-2-2-22-1-2-22-2222-21111-1-1-1-2211-1-111-1-100002-2-221-1i3i3−i3−i3−i3−i3i3i3-1-11111-1-10000000000i3−i3−i3i30000000000
χ43222-2-2-2-22-1-2-22-2222-21111-1-1-1-2211-1-111-1-10000-222-21-1−i3−i3i3i3i3i3−i3−i311-1-1-1-1110000000000i3−i3−i3i30000000000
χ44222-2-2-2-22-1-2-22-2222-21111-1-1-1-2211-1-111-1-10000-222-21-1i3i3−i3−i3−i3−i3i3i311-1-1-1-1110000000000−i3i3i3−i30000000000
χ4522-222-2-2-2200220-20-222-2-22-2-20000022-20-22−22−20000002−22−22−22−200000000002-22-2000000002−22−2000000
χ4622-222-2-2-2200220-20-222-2-22-2-20000022-20-22−22−20000002−22−22−22−20000000000-22-2200000000−22−22000000
χ4722-222-2-2-2200220-20-222-2-22-2-20000022-20-2−22−22000000−22−22−22−2200000000002-22-200000000−22−22000000
χ4822-222-2-2-2200220-20-222-2-22-2-20000022-20-2−22−22000000−22−22−22−220000000000-22-22000000002−22−2000000
χ4922-222-2-2-2200-2-2020222-2-22-2-200000-2-2202−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i200000000002-2-2200000000−i2i2i2−i2000000
χ5022-222-2-2-2200-2-2020222-2-22-2-200000-2-2202−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i20000000000-222-200000000i2−i2−i2i2000000
χ5122-222-2-2-2200-2-2020222-2-22-2-200000-2-2202i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i200000000002-2-2200000000i2−i2−i2i2000000
χ5222-222-2-2-2200-2-2020222-2-22-2-200000-2-2202i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i20000000000-222-200000000−i2i2i2−i2000000
χ5344444444-244-4-44-44-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5444444444-2-4-444-44-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ55444-4-4-4-44-2444-4-44-4-42222-2-2-24-4-2-22-2222-200000000-220000000000000000000000000000000000000000
χ56444-4-4-4-44-2-4-4-444-4442222-2-2-24-422-22-2-2-2200000000-220000000000000000000000000000000000000000
χ5744-444-4-4-4-200440-40-4-2-222-22200000-2-220222−2222−22000000−22−22−22−2200000000000000000000000000000000
χ5844-444-4-4-4-200440-40-4-2-222-22200000-2-2202−2222−22220000002−22−22−22−200000000000000000000000000000000
χ5944-444-4-4-4-200-4-40404-2-222-2220000022-20-2−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ6044-444-4-4-4-200-4-40404-2-222-2220000022-20-22i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ6144-4-4-444-44004-40-404-4-4444-4-4000004-440-400000000000000000000000000000000000000000000000000
χ6244-4-4-444-4400-44040-4-4-4444-4-400000-44-40400000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-2004-40-40422-2-2-22200000-22-2020000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ6444-4-4-444-4-2004-40-40422-2-2-22200000-22-2020000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ6544-4-4-444-4-200-44040-422-2-2-222000002-220-200000000006−6−666−6−6600000000000000000000000000000000
χ6644-4-4-444-4-200-44040-422-2-2-222000002-220-20000000000−666−6−666−600000000000000000000000000000000
χ674-444-44-4-444-40040-404-44-4-44-4004-4-40004000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-4400-40404-44-4-44-400-444000-4000000000000000000000000000000000000000000000000000
χ694-444-44-4-4-24-40040-40-22-222-2200-222000-200000000000000000006−66−66−66−6000000000000000000000000
χ704-444-44-4-4-24-40040-40-22-222-2200-222000-20000000000000000000−66−66−66−66000000000000000000000000
χ714-444-44-4-4-2-4400-4040-22-222-22002-2-200020000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ724-444-44-4-4-2-4400-4040-22-222-22002-2-200020000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ734-44-44-44-444-400-4040-44-44-44-4004-44000-4000000000000000000000000000000000000000000000000000
χ744-44-44-44-44-440040-40-44-44-44-400-44-40004000000000000000000000000000000000000000000000000000
χ754-44-44-44-4-24-400-40402-22-22-2200-22-200020000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ764-44-44-44-4-24-400-40402-22-22-2200-22-200020000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ774-44-44-44-4-2-440040-402-22-22-22002-22000-200000000000000000006−6−66−666−6000000000000000000000000
χ784-44-44-44-4-2-440040-402-22-22-22002-22000-20000000000000000000−666−66−6−66000000000000000000000000
χ794-4-44-4-4444000000004-4-44-4-440000000000000000000000000000000000000000004-40000000000000000
χ804-4-44-4-4444000000004-4-44-4-44000000000000000000000000000000000000000000-440000000000000000
χ814-4-4-444-44400000000-444-4-4-440000000000000000000000000000000000004-40000000000000000000000
χ824-4-4-444-44400000000-444-4-4-44000000000000000000000000000000000000-440000000000000000000000
χ838-8-88-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-8-8-888-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000

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