Finite Group Databasebeta

← Group #10772479

Character table — Group #10772479

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666121212124466888888881212121212121212121224242424242424242424242424242424224444446688121224242424244444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1
χ91111-1-111-1-1-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-11-111-1-11-111-1-111-1-11-1
χ101111-1-111-1-1-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-11-111-1-1-11-1-111-1-111-11
χ111111-1-111-1-1-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-11-11-1-1111-1-1-11111-1-1-11
χ121111-1-111-1-1-1-11111111111-11-1-11111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11-11-1-111-1111-1-1-1-1111-1
χ131111-1-111-1-1-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-11-1-111-1-1-1111-111-1-1-1-111-11
χ141111-1-111-1-1-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1-1-1111-1-111-1-1-111-11-1-11111-1-11-1
χ151111-1-111-1-1-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1-1111-1-11-1-1-111-1-1111-1
χ161111-1-111-1-1-1-11111111111-11-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-111-1-1111-1-1-1111-1-111-1-1-11
χ172222222222-2-22-2-22222222-2-22200000000-2-2-2-2-2-222-2-20000000000000000000022220000000000-2-20000000000
χ182222222222-2-22-2-22222222-2-22200000000-2-2-2-2-2-222-2-200000000000000000000-2-2-2-20000000000220000000000
χ192222222-2-2-222-2-2-2222-2-2-2-2-222200000000-2-222-2-2-2-2220000000000000000000000000000000000002-22-2000000
χ202222222-2-2-222-2-2-2222-2-2-2-2-222200000000-2-222-2-2-2-222000000000000000000000000000000000000-22-22000000
χ212222222-2-2-2-2-2-222222-2-2-2-22-2220000000022-2-222-2-2-2-200000000000000002-2-2200002-200-220000000000000000
χ222222222-2-2-2-2-2-222222-2-2-2-22-2220000000022-2-222-2-2-2-20000000000000000-222-20000-22002-20000000000000000
χ23222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-122-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011-2-2111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122220000-1-1-2-2-1-11111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-20000112211-1-1-1-1000000000000
χ27222222-1-2-2-2-2-2-222-1-1-111112-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−32-2-220000-11001-13−33−3000000000000
χ28222222-1-2-2-2-2-2-222-1-1-111112-2-1-100000000-1-111-1-111113333−3−3−3−33333−3−3−3−3-222-200001-100-11−33−33000000000000
χ29222222-1-2-2-2-2-2-222-1-1-111112-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−333332-2-220000-11001-1−33−33000000000000
χ30222222-1-2-2-2-2-2-222-1-1-111112-2-1-100000000-1-111-1-11111−3−3−3−33333−3−3−3−33333-222-200001-100-113−33−3000000000000
χ312222-2-222-2-2222-2-222222222-2-2-200000000-2-22222-2-2-2-20000000000000000000022-2-20000000000-220000000000
χ322222-2-222-2-2222-2-222222222-2-2-200000000-2-22222-2-2-2-200000000000000000000-2-22200000000002-20000000000
χ332222-2-22-22222-222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000000022-2-200002200-2-20000000000000000
χ342222-2-22-22222-222222-2-2-2-2-2-2-2-2000000002222-2-222-2-20000000000000000-2-2220000-2-200220000000000000000
χ352222-2-22-222-2-2-2-2-2222-2-2-2-222-2-200000000-2-2-2-22222220000000000000000000000000000000000002-2-22000000
χ362222-2-22-222-2-2-2-2-2222-2-2-2-222-2-200000000-2-2-2-2222222000000000000000000000000000000000000-222-2000000
χ372222-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111112-22-20000-112-2-11-1-111000000000000
χ382222-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-22112222-2-2-2-2-1-1111111-1-1-1-1-1-1-1-1-1-111111111-22-2200001-1-221-111-1-1000000000000
χ392222-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-12-22-20000-11-22-1111-1-1000000000000
χ402222-2-2-12-2-2-2-2222-1-1-1-1-1-1-1-2211-2-2-2-22222-1-1111111-1-111111111-1-1-1-1-1-1-1-1-22-2200001-12-21-1-1-111000000000000
χ412222-2-2-1-22222-222-1-1-11111-2-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−3333322-2-20000-1-100113−3−33000000000000
χ422222-2-2-1-22222-222-1-1-11111-2-21100000000-1-1-1-111-1-1113333−3−3−3−3−3−3−3−33333-2-22200001100-1-1−333−3000000000000
χ432222-2-2-1-22222-222-1-1-11111-2-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−322-2-20000-1-10011−333−3000000000000
χ442222-2-2-1-22222-222-1-1-11111-2-21100000000-1-1-1-111-1-111−3−3−3−333333333−3−3−3−3-2-22200001100-1-13−3−33000000000000
χ4522-2-22-22-22-200200-2-22-2-222002-222−2−222−2−20000002-20022−2−222−2−222−2−222−2−200002i−2i2i−2i0000000000000000−i2i2−i2i200
χ4622-2-22-22-22-200200-2-22-2-222002-222−2−222−2−20000002-20022−2−222−2−222−2−222−2−20000−2i2i−2i2i0000000000000000i2−i2i2−i200
χ4722-2-22-22-22-200200-2-22-2-222002-2−2−222−2−2220000002-200−2−222−2−222−2−222−2−22200002i−2i2i−2i0000000000000000i2−i2i2−i200
χ4822-2-22-22-22-200200-2-22-2-222002-2−2−222−2−2220000002-200−2−222−2−222−2−222−2−2220000−2i2i−2i2i0000000000000000−i2i2−i2i200
χ4922-2-2-222-2-2200200-2-22-2-22200-2222−2−2−2−222000000-220022−2−222−2−2−2−222−2−22200002i−2i−2i2i0000000000000000−i2i2i2−i200
χ5022-2-2-222-2-2200200-2-22-2-22200-2222−2−2−2−222000000-220022−2−222−2−2−2−222−2−2220000−2i2i2i−2i0000000000000000i2−i2−i2i200
χ5122-2-2-222-2-2200200-2-22-2-22200-22−2−22222−2−2000000-2200−2−222−2−22222−2−222−2−200002i−2i−2i2i0000000000000000i2−i2−i2i200
χ5222-2-2-222-2-2200200-2-22-2-22200-22−2−22222−2−2000000-2200−2−222−2−22222−2−222−2−20000−2i2i2i−2i0000000000000000−i2i2i2−i200
χ53444444-2444-4-44-4-4-2-2-2-2-2-2-2-4-4-2-200000000222222-2-2220000000000000000000000000000000000000000000000
χ54444444-2-4-4-444-4-4-4-2-2-22222-44-2-20000000022-2-22222-2-20000000000000000000000000000000000000000000000
χ554444-4-4-24-4-4444-4-4-2-2-2-2-2-2-24-4220000000022-2-2-2-222220000000000000000000000000000000000000000000000
χ564444-4-4-2-444-4-4-4-4-4-2-2-222224422000000002222-2-2-2-2-2-20000000000000000000000000000000000000000000000
χ5744-4-44-444-4400-400-4-4444-4-4004-400000000000000-44000000000000000000000000000000000000000000000000
χ5844-4-44-4-24-4400-40022-2-2-22200-22000000000000002-20066−6−6−6−66666−6−6−6−666000000000000000000000000000000
χ5944-4-44-4-24-4400-40022-2-2-22200-22000000000000002-200−6−66666−6−6−6−66666−6−6000000000000000000000000000000
χ6044-4-44-4-2-44-40040022-222-2-200-222222−22−222222−22−22000000-2200−2−222−2−222−2−222−2−222000000000000000000000000000000
χ6144-4-44-4-2-44-40040022-222-2-200-22−22−222222−22−222222000000-220022−2−222−2−222−2−222−2−2000000000000000000000000000000
χ6244-4-4-44444-400-400-4-4444-4-400-44000000000000004-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-244-400-40022-2-2-222002-200000000000000-220066−6−6−6−666−6−66666−6−6000000000000000000000000000000
χ6444-4-4-44-244-400-40022-2-2-222002-200000000000000-2200−6−66666−6−666−6−6−6−666000000000000000000000000000000
χ6544-4-4-44-2-4-440040022-222-2-2002-22222−22−22−22−2222220000002-200−2−222−2−22222−2−222−2−2000000000000000000000000000000
χ6644-4-4-44-2-4-440040022-222-2-2002-2−22−2222222222−22−220000002-20022−2−222−2−2−2−222−2−222000000000000000000000000000000
χ674-44-40040000004-44-4-4000000000000−2i22i2−2i22i24-40000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ684-44-40040000004-44-4-40000000000002i2−2i22i2−2i24-400000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ694-44-4004000000-444-4-400000000−2i22i2−2i22i20000-4400000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000
χ704-44-4004000000-444-4-4000000002i2−2i22i2−2i20000-44000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000
χ714-44-400-20000004-4-22223−2323−2300000000−2i22i2−2i22i2-2200000023−23000000002ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000
χ724-44-400-20000004-4-22223−2323−23000000002i2−2i22i2−2i2-2200000023−2300000000−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000
χ734-44-400-20000004-4-222−2323−232300000000−2i22i2−2i22i2-22000000−2323000000002ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000
χ744-44-400-20000004-4-222−2323−2323000000002i2−2i22i2−2i2-22000000−232300000000−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000
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χ784-44-400-2000000-44-222−2323−232300002i2−2i22i2−2i200002-200000023−23−2ζ13−2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ794-4-440040004-4000-44-4000000002i−2i−2i2i2i−2i−2i2i004-40000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ804-4-440040004-4000-44-400000000−2i2i2i−2i−2i2i2i−2i004-4000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ814-4-44004000-44000-44-4000000002i−2i−2i2i−2i2i2i−2i00-440000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ824-4-44004000-44000-44-400000000−2i2i2i−2i2i−2i−2i2i00-44000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
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χ884-4-4400-2000-440002-2223−23−23230000−2i2i2i−2i2i−2i−2i2i002-2−23230000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000000000
χ894-4-4400-2000-440002-22−232323−2300002i−2i−2i2i−2i2i2i−2i002-223−230000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000000000
χ904-4-4400-2000-440002-22−232323−230000−2i2i2i−2i2i−2i−2i2i002-223−230000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.