Finite Group Databasebeta

← Group #10696391

Character table — Group #10696391

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212888888881212242424242424242424242424242424248888888844121212124444444444
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
χ9222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-200000000000000000000000000000022-2-2000000
χ10222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000-2-222000000
χ11222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-2000000000000000000000000000000000022-2-200
χ12222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-20000000000000000000000000000000000-2-22200
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000002-222-2-20000000000
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000-22-2-2220000000000
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−33333−3−3−3−3000000002-2-1-1110000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-13333−3−3−3−3−3−3−3−3333300000000-2211-1-10000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−333333333−3−3−3−300000000-2211-1-10000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100000000-1-1−3−3−3−33333−3−3−3−33333000000002-2-1-1110000000000
χ23222-2-2-2-22200022-20-222-2-2-2-220000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i22222−2−2−2−200000000002i−2i0000
χ24222-2-2-2-22200022-20-222-2-2-2-220000022-20-20000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i2−2−2−2−222220000000000−2i2i0000
χ25222-2-2-2-22200022-20-222-2-2-2-220000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i22222−2−2−2−20000000000−2i2i0000
χ26222-2-2-2-22200022-20-222-2-2-2-220000022-20-20000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i2−2−2−2−2222200000000002i−2i0000
χ2722-222-2-2-2222-2000-202-22-22-2-20022-2000-2022−2−200000022−2−222−2−20000000022−2−222−2−2000000002-2000000
χ2822-222-2-2-2222-2000-202-22-22-2-20022-2000-2022−2−200000022−2−222−2−200000000−2−222−2−22200000000-22000000
χ2922-222-2-2-2222-2000-202-22-22-2-20022-2000-20−2−222000000−2−222−2−2220000000022−2−222−2−200000000-22000000
χ3022-222-2-2-2222-2000-202-22-22-2-20022-2000-20−2−222000000−2−222−2−22200000000−2−222−2−222000000002-2000000
χ312-222-22-2-222-22000-20-22-222-2-2002-22000-202−22−20000002−22−22−22−2000000002−22−22−22−20000002-200000000
χ322-222-22-2-222-22000-20-22-222-2-2002-22000-202−22−20000002−22−22−22−200000000−22−22−22−22000000-2200000000
χ332-222-22-2-222-22000-20-22-222-2-2002-22000-20−22−22000000−22−22−22−22000000002−22−22−22−2000000-2200000000
χ342-222-22-2-222-22000-20-22-222-2-2002-22000-20−22−22000000−22−22−22−2200000000−22−22−22−220000002-200000000
χ352-2-22-2-22222-2-22-222-2-2-2-2-2222-222-2-22-222-2000000002-200000000000000002-2-222-2-220000000000000000
χ362-2-22-2-22222-2-22-222-2-2-2-2-2222-222-2-22-222-2000000002-20000000000000000-222-2-222-20000000000000000
χ372-2-22-2-22222-2-2-22-222-2-2-2-22222-22-2-2-22-2222-2-220000-222-2-222-2-2200000000000000000000000000000000
χ382-2-22-2-22222-2-2-22-222-2-2-2-22222-22-2-2-22-222-222-20000-22-222-2-222-200000000000000000000000000000000
χ392-2-22-2-2222-2222-22-2-2-2-2-2-22222-2-2222-22-2-200002i−2i2i−2i-22000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ402-2-22-2-2222-2222-22-2-2-2-2-2-22222-2-2222-22-2-20000−2i2i−2i2i-2200000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ412-2-22-2-2222-222-22-2-22-2-2-2-2222-22-222-22-2-22000000002-2000000000000000000000000000000000000002-2
χ422-2-22-2-2222-222-22-2-22-2-2-2-2222-22-222-22-2-22000000002-200000000000000000000000000000000000000-22
χ432-2-22-2-222-12-2-2-22-2221111-1-1-12-2-1111-11-1-12-2-2200001-1-111-1-111-1−i3i3−i3i3i3−i3i3−i30000000000−i3i3−i3i30000000000
χ442-2-22-2-222-12-2-2-22-2221111-1-1-12-2-1111-11-1-12-2-2200001-1-111-1-111-1i3−i3i3−i3−i3i3−i3i30000000000i3−i3i3−i30000000000
χ452-2-22-2-222-12-2-2-22-2221111-1-1-12-2-1111-11-1-1-222-200001-11-1-111-1-11−i3i3−i3i3i3−i3i3−i30000000000i3−i3i3−i30000000000
χ462-2-22-2-222-12-2-2-22-2221111-1-1-12-2-1111-11-1-1-222-200001-11-1-111-1-11i3−i3i3−i3−i3i3−i3i30000000000−i3i3−i3i30000000000
χ472-2-22-2-222-1-2222-22-2-21111-1-1-12-21-1-1-11-11100002i−2i2i−2i1-13−3−33−333−3−ii−ii−ii−ii0000000000−i3i3i3−i30000000000
χ482-2-22-2-222-1-2222-22-2-21111-1-1-12-21-1-1-11-11100002i−2i2i−2i1-1−333−33−3−33−ii−ii−ii−ii0000000000i3−i3−i3i30000000000
χ492-2-22-2-222-1-2222-22-2-21111-1-1-12-21-1-1-11-1110000−2i2i−2i2i1-13−3−33−333−3i−ii−ii−ii−i0000000000i3−i3−i3i30000000000
χ502-2-22-2-222-1-2222-22-2-21111-1-1-12-21-1-1-11-1110000−2i2i−2i2i1-1−333−33−3−33i−ii−ii−ii−i0000000000−i3i3i3−i30000000000
χ512-2-2-222-2220002-2-202-2-222-2-22000002-2-20200002−2−2200000000002−2−222−2−222−2−22−222−20000000000002-200
χ522-2-2-222-2220002-2-202-2-222-2-22000002-2-20200002−2−2200000000002−2−222−2−22−222−22−2−22000000000000-2200
χ532-2-2-222-2220002-2-202-2-222-2-22000002-2-2020000−222−20000000000−222−2−222−22−2−22−222−2000000000000-2200
χ542-2-2-222-2220002-2-202-2-222-2-22000002-2-2020000−222−20000000000−222−2−222−2−222−22−2−220000000000002-200
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-4-2-2-2222-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-22-200000000220000000000000000000000000000000000000000
χ57444-4-4-4-444000-4-440444-4-4-4-4400000-4-440400000000000000000000000000000000000000000000000000
χ58444-4-4-4-44-200044-40-4-2-22222-200000-2-22020000−2i2−2i22i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ59444-4-4-4-44-200044-40-4-2-22222-200000-2-220200002i22i2−2i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ60444-4-4-4-44-2000-4-4404-2-22222-20000022-20-2000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ61444-4-4-4-44-2000-4-4404-2-22222-20000022-20-2000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6244-444-4-4-44-4-44000404-44-44-4-400-4-440004000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4-244-4000-40-22-22-22200-2-22000202222−22−22000000−2−222−2−22200000000000000000000000000000000
χ6444-444-4-4-4-244-4000-40-22-22-22200-2-2200020−22−22222200000022−2−222−2−200000000000000000000000000000000
χ6544-444-4-4-4-2-4-4400040-22-22-2220022-2000-20000000000066−6−6−6−66600000000000000000000000000000000
χ6644-444-4-4-4-2-4-4400040-22-22-2220022-2000-200000000000−6−66666−6−600000000000000000000000000000000
χ6744-4-4-444-44000000004-4-44-44-400000000000000000000000000000000000022-2-2-2-2220000000000000000
χ6844-4-4-444-44000000004-4-44-44-4000000000000000000000000000000000000-2-22222-2-20000000000000000
χ694-444-44-4-44-44-400040-44-444-4-400-44-40004000000000000000000000000000000000000000000000000000
χ704-444-44-4-4-24-44000-402-22-2-22200-22-20002022−2222−22000000−22−22−22−2200000000000000000000000000000000
χ714-444-44-4-4-24-44000-402-22-2-22200-22-200020−2222−22220000002−22−22−22−200000000000000000000000000000000
χ724-444-44-4-4-2-44-4000402-22-2-222002-22000-2000000000006−66−6−66−6600000000000000000000000000000000
χ734-444-44-4-4-2-44-4000402-22-2-222002-22000-200000000000−66−666−66−600000000000000000000000000000000
χ744-44-44-44-4400000000-444-4-44-40000000000000000000000000000000000002-22-2-22-220000000000000000
χ754-44-44-44-4400000000-444-4-44-4000000000000000000000000000000000000-22-222-22-20000000000000000
χ764-4-44-4-444-24-4-44-444-42222-2-2-2-44-222-22-2-2200000000-220000000000000000000000000000000000000000
χ774-4-44-4-444-2-444-44-4-442222-2-2-2-442-2-22-222-200000000-220000000000000000000000000000000000000000
χ784-4-4-444-444000-4440-4-4-444-4-4400000-4440-400000000000000000000000000000000000000000000000000
χ794-4-4-444-44-20004-4-40422-2-222-200000-2220-2000022−22−22220000000000−222−2−222−2000000000000000000000000
χ804-4-4-444-44-20004-4-40422-2-222-200000-2220-20000−222222−2200000000002−2−222−2−22000000000000000000000000
χ814-4-4-444-44-2000-4440-422-2-222-2000002-2-2020000000000000000006−6−66−666−6000000000000000000000000
χ824-4-4-444-44-2000-4440-422-2-222-2000002-2-202000000000000000000−666−66−6−66000000000000000000000000
χ8388-8-8-888-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000

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