Finite Group Databasebeta

← Group #10690886

Character table — Group #10690886

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424242244444444121212128888888844
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
χ29222-2-2-2-222002-2020-222-22-2-2-2000002-2-202−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i200000000002i−2i2i−2i000000002−22−2000000
χ30222-2-2-2-222002-2020-222-22-2-2-2000002-2-202−i2i2−i2i2000000−i2−i2i2i2−i2−i2i2i20000000000−2i2i−2i2i00000000−22−22000000
χ31222-2-2-2-222002-2020-222-22-2-2-2000002-2-202i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i200000000002i−2i2i−2i00000000−22−22000000
χ32222-2-2-2-222002-2020-222-22-2-2-2000002-2-202i2−i2i2−i2000000i2i2−i2−i2i2i2−i2−i20000000000−2i2i−2i2i000000002−22−2000000
χ33222-2-2-2-22200-220-20222-22-2-2-200000-2220-22−2−2200000022−2−2−2−22200000000002i−2i−2i2i00000000i2−i2−i2i2000000
χ34222-2-2-2-22200-220-20222-22-2-2-200000-2220-22−2−2200000022−2−2−2−2220000000000−2i2i2i−2i00000000−i2i2i2−i2000000
χ35222-2-2-2-22200-220-20222-22-2-2-200000-2220-2−222−2000000−2−22222−2−200000000002i−2i−2i2i00000000−i2i2i2−i2000000
χ36222-2-2-2-22200-220-20222-22-2-2-200000-2220-2−222−2000000−2−22222−2−20000000000−2i2i2i−2i00000000i2−i2−i2i2000000
χ372-2-2-222-2222-2222-2-2-2-2-2-2222-22-22-2-222-22-200002i−2i2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-2-222-2222-2222-2-2-2-2-2-2222-22-22-2-222-22-20000−2i2i−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-2-222-2222-2-2-222-22-2-2-2222-2-222-2-2-2-222200000000-2200000000000000000000000000000000002-22-200
χ402-2-2-222-2222-2-2-222-22-2-2-2222-2-222-2-2-2-222200000000-220000000000000000000000000000000000-22-2200
χ412-2-2-222-222-2222-2-22-2-2-2-2222-2-22-22222-2-2-200000000-2200000000000000000000000000000000002i−2i−2i2i00
χ422-2-2-222-222-2222-2-22-2-2-2-2222-2-22-22222-2-2-200000000-220000000000000000000000000000000000−2i2i2i−2i00
χ432-2-2-222-222-22-2-2-2222-2-2-2222-22-2-222-2-22-2200002-2-222-20000000022-2-2-2-222000000000000000000000000
χ442-2-2-222-222-22-2-2-2222-2-2-2222-22-2-222-2-22-220000-222-22-200000000-2-22222-2-2000000000000000000000000
χ452-2-2-222-22-12-2222-2-2-2111-1-1-112-2-111-1-11-1100002i−2i2i−2i-11−i3i3−i3i3−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ462-2-2-222-22-12-2222-2-2-2111-1-1-112-2-111-1-11-1100002i−2i2i−2i-11i3−i3i3−i3i3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ472-2-2-222-22-12-2222-2-2-2111-1-1-112-2-111-1-11-110000−2i2i−2i2i-11−i3i3−i3i3−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ482-2-2-222-22-12-2222-2-2-2111-1-1-112-2-111-1-11-110000−2i2i−2i2i-11i3−i3i3−i3i3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ492-2-2-222-22-1-22-2-2-2222111-1-1-112-21-1-111-11-100002-2-22-113−33−3−33−33-1-11111-1-10000000000−333−30000000000
χ502-2-2-222-22-1-22-2-2-2222111-1-1-112-21-1-111-11-100002-2-22-11−33−333−33−3-1-11111-1-100000000003−3−330000000000
χ512-2-2-222-22-1-22-2-2-2222111-1-1-112-21-1-111-11-10000-222-2-113−33−3−33−3311-1-1-1-11100000000003−3−330000000000
χ522-2-2-222-22-1-22-2-2-2222111-1-1-112-21-1-111-11-10000-222-2-11−33−333−33−311-1-1-1-1110000000000−333−30000000000
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
χ55444-4-4-4-44-2004-4040-4-2-22-222200000-2220-2−2i22i2−2i22i2000000i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ56444-4-4-4-44-2004-4040-4-2-22-222200000-2220-22i2−2i22i2−2i2000000−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ57444-4-4-4-44-200-440-404-2-22-2222000002-2-20222−22−2222000000−2−22222−2−200000000000000000000000000000000
χ58444-4-4-4-44-200-440-404-2-22-2222000002-2-202−222222−2200000022−2−2−2−22200000000000000000000000000000000
χ5944-444-4-4-44000000004-44-44-4-40000000000000000000000000000000000004-40000000000000000000000
χ6044-444-4-4-44000000004-44-44-4-4000000000000000000000000000000000000-440000000000000000000000
χ6144-4-4-444-444400-40-404-4-4-4-4440044-4000-4000000000000000000000000000000000000000000000000000
χ6244-4-4-444-44-4-40040404-4-4-4-44400-4-440004000000000000000000000000000000000000000000000000000
χ6344-4-4-444-4-24400-40-40-22222-2-200-2-22000200000000000000000006−66−66−66−6000000000000000000000000
χ6444-4-4-444-4-24400-40-40-22222-2-200-2-2200020000000000000000000−66−66−66−66000000000000000000000000
χ6544-4-4-444-4-2-4-4004040-22222-2-20022-2000-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ6644-4-4-444-4-2-4-4004040-22222-2-20022-2000-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ674-444-44-4-444-400-4040-444-4-44-4004-44000-4000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-440040-40-444-4-44-400-44-40004000000000000000000000000000000000000000000000000000
χ694-444-44-4-4-24-400-40402-2-222-2200-22-200020000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ704-444-44-4-4-24-400-40402-2-222-2200-22-200020000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ714-444-44-4-4-2-440040-402-2-222-22002-22000-200000000000000000006−6−66−666−6000000000000000000000000
χ724-444-44-4-4-2-440040-402-2-222-22002-22000-20000000000000000000−666−66−6−66000000000000000000000000
χ734-44-44-44-4400000000-44-4-44-440000000000000000000000000000000000000000004i−4i0000000000000000
χ744-44-44-44-4400000000-44-4-44-44000000000000000000000000000000000000000000−4i4i0000000000000000
χ754-4-44-4-4444004-40-404-4-444-4-44000004-440-400000000000000000000000000000000000000000000000000
χ764-4-44-4-444400-44040-4-4-444-4-4400000-44-40400000000000000000000000000000000000000000000000000
χ774-4-44-4-444-2004-40-40422-2-222-200000-22-20200000000006−6−666−6−6600000000000000000000000000000000
χ784-4-44-4-444-2004-40-40422-2-222-200000-22-2020000000000−666−6−666−600000000000000000000000000000000
χ794-4-44-4-444-200-44040-422-2-222-2000002-220-20000000000i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ804-4-44-4-444-200-44040-422-2-222-2000002-220-20000000000−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ814-4-4-444-44-24-4-4-444-44222-2-2-22-44-22222-2-2-2000000002-20000000000000000000000000000000000000000
χ824-4-4-444-44-2-4444-4-44-4222-2-2-22-442-2-2-2-2222000000002-20000000000000000000000000000000000000000
χ8388-888-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000

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