Finite Group Databasebeta

← Group #10698465

Character table — Group #10698465

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12222222222236666666444466661212121244448888121212121212121212122424242424242424441212121222444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-2000000000000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000-2-2220000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-200000000000000000000000000000000002-2
χ1622222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-20000000000000000000000000000000000-22
χ1722222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000002-222-2-200000000000000
χ1822222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000220000000000000000-22-2-22200000000000000
χ1922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−33333−3−3−3−32-2-1-11100000000000000
χ2022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-13333−3−3−3−3−3−3−3−33333-2211-1-100000000000000
χ2122222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−333333333−3−3−3−3-2211-1-100000000000000
χ2222222222-2-2-2-2-1-1-1-1-1-1-1-1-22-221111111100000000-1-1−3−3−3−33333−3−3−3−333332-2-1-11100000000000000
χ2322-2-2-22-2222-2-22222-2-2-2-2000022-2-20000000022−2−2000000000022−2−222−2−2000000002i−2i0000−i2−i2i2i200
χ2422-2-2-22-2222-2-22222-2-2-2-2000022-2-20000000022−2−2000000000022−2−222−2−200000000−2i2i0000i2i2−i2−i200
χ2522-2-2-22-2222-2-22222-2-2-2-2000022-2-200000000−2−2220000000000−2−222−2−222000000002i−2i0000i2i2−i2−i200
χ2622-2-2-22-2222-2-22222-2-2-2-2000022-2-200000000−2−2220000000000−2−222−2−22200000000−2i2i0000−i2−i2i2i200
χ272-222-22-2-22-22-222-2-2-222-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i200
χ282-222-22-2-22-22-222-2-2-222-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i200
χ292-222-22-2-22-22-222-2-2-222-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i200
χ302-222-22-2-22-22-222-2-2-222-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i200
χ312-2-2-2222-22-2-2222-2-22-2-2222-2-22-2-2222-2-200002i−2i−2i2i2-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ322-2-2-2222-22-2-2222-2-22-2-2222-2-22-2-2222-2-20000−2i2i2i−2i2-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ332-2-2-2222-22-2-2222-2-22-2-22-2-2222-2-22-2-22200000000-220000000000000000000000000000002-2-2200
χ342-2-2-2222-22-2-2222-2-22-2-22-2-2222-2-22-2-22200000000-22000000000000000000000000000000-222-200
χ352-2-2-2222-22-2-22-1-111-111-122-2-2-111-1-1-11100002i−2i−2i2i-11−i3−i3i3i3−i3−i3i3i3−iii−i−iii−i003−33−300000000000000
χ362-2-2-2222-22-2-22-1-111-111-122-2-2-111-1-1-11100002i−2i−2i2i-11i3i3−i3−i3i3i3−i3−i3−iii−i−iii−i00−33−3300000000000000
χ372-2-2-2222-22-2-22-1-111-111-122-2-2-111-1-1-1110000−2i2i2i−2i-11−i3−i3i3i3−i3−i3i3i3i−i−iii−i−ii00−33−3300000000000000
χ382-2-2-2222-22-2-22-1-111-111-122-2-2-111-1-1-1110000−2i2i2i−2i-11i3i3−i3−i3i3i3−i3−i3i−i−iii−i−ii003−33−300000000000000
χ392-2-2-2222-2-222-222-2-22-2-222-2-22-222-222-2-200000000-22000000000000000000000000002i2i−2i−2i000000
χ402-2-2-2222-2-222-222-2-22-2-222-2-22-222-222-2-200000000-2200000000000000000000000000−2i−2i2i2i000000
χ412-2-2-2222-2-222-222-2-22-2-22-222-2-222-2-2-2222i2i−2i−2i00002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422-2-2-2222-2-222-222-2-22-2-22-222-2-222-2-2-222−2i−2i2i2i00002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432-2-2-2222-2-222-2-1-111-111-1-222-21-1-1111-1-12i2i−2i−2i0000-11−i−iiiii−i−i−i3i3i3−i3i3−i3−i3i300−333−300000000000000
χ442-2-2-2222-2-222-2-1-111-111-1-222-21-1-1111-1-12i2i−2i−2i0000-11−i−iiiii−i−ii3−i3−i3i3−i3i3i3−i3003−3−3300000000000000
χ452-2-2-2222-2-222-2-1-111-111-1-222-21-1-1111-1-1−2i−2i2i2i0000-11ii−i−i−i−iii−i3i3i3−i3i3−i3−i3i3003−3−3300000000000000
χ462-2-2-2222-2-222-2-1-111-111-1-222-21-1-1111-1-1−2i−2i2i2i0000-11ii−i−i−i−iiii3−i3−i3i3−i3i3i3−i300−333−300000000000000
χ47444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-2-2-20000000022000000000000000000000000000000000000
χ49444-44-4-4-400004-44-4-44-440000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ50444-44-4-4-400004-44-4-44-44000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ5144-44-4-44-400004-44-44-44-40000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ5244-44-4-44-400004-44-44-44-4000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ5344-44-4-44-40000-22-22-22-220000000023−2323−232i−2i2i−2i000000−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−ζ220000000000000000000000000000
χ5444-44-4-44-40000-22-22-22-220000000023−2323−23−2i2i−2i2i000000ζ4−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+ζ220000000000000000000000000000
χ5544-44-4-44-40000-22-22-22-2200000000−2323−23232i−2i2i−2i000000ζ4+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−ζ220000000000000000000000000000
χ5644-44-4-44-40000-22-22-22-2200000000−2323−2323−2i2i−2i2i000000−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+ζ220000000000000000000000000000
χ5744-4-4-44-4444-4-4-2-2-2-222220000-2-222000000002222−22−220000000000−2−222−2−22200000000000000000000
χ5844-4-4-44-4444-4-4-2-2-2-222220000-2-22200000000−22−222222000000000022−2−222−2−200000000000000000000
χ5944-4-4-44-44-4-4444444-4-4-4-40000-4-44400000000000000000000000000000000000000000000000000
χ6044-4-4-44-44-4-444-2-2-2-22222000022-2-2000000000000000000000066−6−6−6−66600000000000000000000
χ6144-4-4-44-44-4-444-2-2-2-22222000022-2-20000000000000000000000−6−66666−6−600000000000000000000
χ624-444-44-4-44-44-4-2-2222-2-220000-22-2200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000
χ634-444-44-4-44-44-4-2-2222-2-220000-22-22000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000
χ644-444-44-4-4-44-4444-4-4-444-40000-44-4400000000000000000000000000000000000000000000000000
χ654-444-44-4-4-44-44-2-2222-2-2200002-22-20000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000
χ664-444-44-4-4-44-44-2-2222-2-2200002-22-20000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000
χ674-44-4-4-44400004-4-4444-4-40000000000002-2-220000002-2-22-222-20000000000000000000000000000
χ684-44-4-4-44400004-4-4444-4-4000000000000-222-2000000-222-22-2-220000000000000000000000000000
χ694-44-4-4-4440000-222-2-2-2220000000023−23−23232-2-22000000−1+31−31−3−1+31+3−1−3−1−31+30000000000000000000000000000
χ704-44-4-4-4440000-222-2-2-2220000000023−23−2323-222-20000001−3−1+3−1+31−3−1−31+31+3−1−30000000000000000000000000000
χ714-44-4-4-4440000-222-2-2-22200000000−232323−232-2-22000000−1−31+31+3−1−31−3−1+3−1+31−30000000000000000000000000000
χ724-44-4-4-4440000-222-2-2-22200000000−232323−23-222-20000001+3−1−3−1−31+3−1+31−31−3−1+30000000000000000000000000000
χ734-4-444-4-4400004-4-44-4-4440000000000000000000000000000000000000000000000002-2-22000000
χ744-4-444-4-4400004-4-44-4-444000000000000000000000000000000000000000000000000-222-2000000
χ754-4-4-4444-44-4-44-2-222-222-2-4-444-222-222-2-2000000002-2000000000000000000000000000000000000
χ764-4-4-4444-4-444-4-2-222-222-24-4-442-2-22-2-222000000002-2000000000000000000000000000000000000
χ77888-88-8-8-80000-44-444-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-888-8-880000-444-444-4-40000000000000000000000000000000000000000000000000000000000

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