Finite Group Databasebeta

← Group #10692293

Character table — Group #10692293

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order122234444446661212121224448888121212121212121268888881224242424242424242424242424242424224488242424244488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ911111-11-11-1-111111111-11-1ii−i−i-1-1-1-1-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1-11ii−i−i1-1i−i
χ1011111-11-11-1-111111111-11-1ii−i−i-1-1-1-1-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-11-1−i−iii-11−ii
χ1111111-11-11-1-111111111-11-1ii−i−i-1-1-1-1-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111-11ii−i−i-11−ii
χ1211111-11-11-1-111111111-11-1ii−i−i-1-1-1-1-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1111-1−i−iii1-1i−i
χ1311111-11-11-1-111111111-11-1−i−iii-1-1-1-1-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111-11−i−iii-11i−i
χ1411111-11-11-1-111111111-11-1−i−iii-1-1-1-1-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1111-1ii−i−i1-1−ii
χ1511111-11-11-1-111111111-11-1−i−iii-1-1-1-1-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1-11−i−iii1-1−ii
χ1611111-11-11-1-111111111-11-1−i−iii-1-1-1-1-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-11-1ii−i−i-11i−i
χ172222222-222-22222222-2-2-22000022-2-222-2-2-2000000-2000000000000000022-2-20000002-200000000
χ182222222-222-22222222-2-2-22000022-2-222-2-2-2000000-20000000000000000-2-222000000-2200000000
χ19222222-22-222222-2-2-2-2-2-22-2222222-2-2-2-222-2-2-20000222-2-222-2-20000000000000000000000000000
χ20222222-22-222222-2-2-2-2-2-22-2-2-2-2-222-2-2-2-222-22200002-2-222-2-2220000000000000000000000000000
χ21222222-2-2-22-2222-2-2-2-222-2-200002222-2-2-2-22000000-200000000000000000000000000002i−2i2i−2i0000
χ22222222-2-2-22-2222-2-2-2-222-2-200002222-2-2-2-22000000-20000000000000000000000000000−2i2i−2i2i0000
χ2322222-2222-222222222-22-2-20000-2-222-2-222-2000000-200000000000000002222000000-2-200000000
χ2422222-2222-222222222-22-2-20000-2-222-2-222-2000000-20000000000000000-2-2-2-20000002200000000
χ2522222-2-22-2-22222-2-2-2-22-2-220000-2-2-2-222222000000-200000000000000000000000000002-2-220000
χ2622222-2-22-2-22222-2-2-2-22-2-220000-2-2-2-222222000000-20000000000000000000000000000-222-20000
χ2722222-2-2-2-2-2-2222-2-2-2-2-22222i2i−2i−2i-2-22222-2-2-2−2i2i000022i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2822222-2-2-2-2-2-2222-2-2-2-2-2222−2i−2i2i2i-2-22222-2-2-22i−2i00002−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ292222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ302222-1222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ312222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ322222-1222222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-11111111111111111000022-1-1-1-10000000000
χ332222-12-22-222-1-1-11111-2-22-22222-1-11111-1-11-2-20000-1-1-111-1-11133−3−333−3−30000003−33−30000000000
χ342222-12-22-222-1-1-11111-2-22-22222-1-11111-1-11-2-20000-1-1-111-1-111−3−333−3−333000000−33−330000000000
χ352222-12-22-222-1-1-11111-2-22-2-2-2-2-2-1-11111-1-11220000-111-1-111-1-133−3−333−3−3000000−33−330000000000
χ362222-12-22-222-1-1-11111-2-22-2-2-2-2-2-1-11111-1-11220000-111-1-111-1-1−3−333−3−3330000003−33−30000000000
χ372222-1-22-22-2-2-1-1-1-1-1-1-12-22-22i2i−2i−2i11111111-12i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-1110000000000
χ382222-1-22-22-2-2-1-1-1-1-1-1-12-22-22i2i−2i−2i11111111-12i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-10000000000
χ392222-1-22-22-2-2-1-1-1-1-1-1-12-22-2−2i−2i2i2i11111111-1−2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-10000000000
χ402222-1-22-22-2-2-1-1-1-1-1-1-12-22-2−2i−2i2i2i11111111-1−2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-1110000000000
χ412222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i11-1-1-1-1111−2i2i0000-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−30000000000
χ422222-1-2-2-2-2-2-2-1-1-11111-22222i2i−2i−2i11-1-1-1-1111−2i2i0000-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−330000000000
χ432222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i11-1-1-1-11112i−2i0000-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−330000000000
χ442222-1-2-2-2-2-2-2-1-1-11111-2222−2i−2i2i2i11-1-1-1-11112i−2i0000-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−30000000000
χ454444-244-444-4-2-2-2-2-2-2-2-4-4-440000-2-222-2-22220000002000000000000000000000000000000000000
χ464444-24-4-4-44-4-2-2-2222244-4-40000-2-2-2-22222-20000002000000000000000000000000000000000000
χ474444-2-4444-44-2-2-2-2-2-2-2-44-4-4000022-2-222-2-220000002000000000000000000000000000000000000
χ484444-2-4-44-4-44-2-2-222224-4-4400002222-2-2-2-2-20000002000000000000000000000000000000000000
χ4944-4-4400400-44-4-40000000000000000004-40002-22-20000000002-22-22-22-200000000000000000000
χ5044-4-4400400-44-4-40000000000000000004-4000-22-22000000000-22-22-22-2200000000000000000000
χ5144-4-4400-40044-4-4000000000000000000-440002i−2i−2i2i0000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ5244-4-4400-40044-4-4000000000000000000-44000−2i2i2i−2i000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ5344-4-4-200400-4-22223−2323−23000000000023−2300-220002-22-2000000000−1+31−3−1−31+3−1+31−3−1−31+300000000000000000000
χ5444-4-4-200400-4-22223−2323−23000000000023−2300-22000-22-220000000001−3−1+31+3−1−31−3−1+31+3−1−300000000000000000000
χ5544-4-4-200400-4-222−2323−23230000000000−232300-220002-22-2000000000−1−31+3−1+31−3−1−31+3−1+31−300000000000000000000
χ5644-4-4-200400-4-222−2323−23230000000000−232300-22000-22-220000000001+3−1−31−3−1+31+3−1−31−3−1+300000000000000000000
χ5744-4-4-200-4004-22223−2323−230000000000−2323002-20002i−2i−2i2i000000000ζ4+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+ζ2200000000000000000000
χ5844-4-4-200-4004-22223−2323−230000000000−2323002-2000−2i2i2i−2i000000000−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−ζ2200000000000000000000
χ5944-4-4-200-4004-222−2323−2323000000000023−23002-20002i−2i−2i2i000000000−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+ζ2200000000000000000000
χ6044-4-4-200-4004-222−2323−2323000000000023−23002-2000−2i2i2i−2i000000000ζ4−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−ζ2200000000000000000000
χ614-44-444000-40-44-40000000022−2222−224-40000000000000022−220022−22000000000000000000000000000000
χ624-44-444000-40-44-400000000−2222−22224-400000000000000−222200−2222000000000000000000000000000000
χ634-44-44-400040-44-400000000−2i22i22i2−2i2-4400000000000000−2i22i2002i2−2i2000000000000000000000000000000
χ644-44-44-400040-44-4000000002i2−2i2−2i22i2-44000000000000002i2−2i200−2i22i2000000000000000000000000000000
χ654-44-4-24000-402-2223−23−2323000022−2222−22-220023−230000000000−226−6−226−60000000000000000000000000000
χ664-44-4-24000-402-2223−23−23230000−2222−2222-220023−2300000000002−2−662−2−660000000000000000000000000000
χ674-44-4-24000-402-22−232323−23000022−2222−22-2200−23230000000000−22−66−22−660000000000000000000000000000
χ684-44-4-24000-402-22−232323−230000−2222−2222-2200−232300000000002−26−62−26−60000000000000000000000000000
χ694-44-4-2-4000402-2223−23−23230000−2i22i22i2−2i22-200−23230000000000i2−i2−i6i6−i2i2i6−i60000000000000000000000000000
χ704-44-4-2-4000402-2223−23−232300002i2−2i2−2i22i22-200−23230000000000−i2i2i6−i6i2−i2−i6i60000000000000000000000000000
χ714-44-4-2-4000402-22−232323−230000−2i22i22i2−2i22-20023−230000000000i2−i2i6−i6−i2i2−i6i60000000000000000000000000000
χ724-44-4-2-4000402-22−232323−2300002i2−2i2−2i22i22-20023−230000000000−i2i2−i6i6i2−i2i6−i60000000000000000000000000000
χ734-4-444040-400-4-4444-4-40000000000000000000000000000000000000000004i−4i0000000000000000
χ744-4-444040-400-4-4444-4-4000000000000000000000000000000000000000000−4i4i0000000000000000
χ754-4-4440-40400-4-44-4-44400000000000000000000000000000000000000004-4000000000000000000
χ764-4-4440-40400-4-44-4-4440000000000000000000000000000000000000000-44000000000000000000
χ778-8-88-4080-80044-4-4-444000000000000000000000000000000000000000000000000000000000000
χ788-8-88-40-8080044-444-4-4000000000000000000000000000000000000000000000000000000000000

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