Finite Group Databasebeta

← Group #10698565

Character table — Group #10698565

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12222222344444444666666644121212121212121288888888121224242424242424242424242424242424888888882266664444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
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
χ9222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000220000-2-200
χ10222222222222-2-2-22-22222222-2-2222-2-2-22-200000000-2-2000000000000000000000000000000-2-200002200
χ11222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-20000000000000000000000000000000022-2-20000
χ12222222222-2-2-2222-222222222-2-2-2-2-2222-2200000000-2-200000000000000000000000000000000-2-2220000
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
χ23222-2-22-2-220002-2-20222-2-22-2-2000002-2-202000022−2−2000000000022−2−222−2−2−i2−i2−i2−i2i2i2i2i200000000002i−2i0000
χ24222-2-22-2-220002-2-20222-2-22-2-2000002-2-202000022−2−2000000000022−2−222−2−2i2i2i2i2−i2−i2−i2−i20000000000−2i2i0000
χ25222-2-22-2-220002-2-20222-2-22-2-2000002-2-2020000−2−2220000000000−2−222−2−222−i2−i2−i2−i2i2i2i2i20000000000−2i2i0000
χ26222-2-22-2-220002-2-20222-2-22-2-2000002-2-2020000−2−2220000000000−2−222−2−222i2i2i2i2−i2−i2−i2−i200000000002i−2i0000
χ2722-222-2-2-222-2-2000202-22-2-22-2002-2-20002022−2−200000022−2−222−2−200000000−i2−i2i2i2−i2−i2i2i20000000000002i−2i00
χ2822-222-2-2-222-2-2000202-22-2-22-2002-2-20002022−2−200000022−2−222−2−200000000i2i2−i2−i2i2i2−i2−i2000000000000−2i2i00
χ2922-222-2-2-222-2-2000202-22-2-22-2002-2-200020−2−222000000−2−222−2−22200000000−i2−i2i2i2−i2−i2i2i2000000000000−2i2i00
χ3022-222-2-2-222-2-2000202-22-2-22-2002-2-200020−2−222000000−2−222−2−22200000000i2i2−i2−i2i2i2−i2−i20000000000002i−2i00
χ312-222-2-2-22222-2000-20-22-22-22-20022-2000-20−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−20000002i−2i00000000
χ322-222-2-2-22222-2000-20-22-22-22-20022-2000-20−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i200000000−22−22−22−22000000−2i2i00000000
χ332-222-2-2-22222-2000-20-22-22-22-20022-2000-20i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−2000000−2i2i00000000
χ342-222-2-2-22222-2000-20-22-22-22-20022-2000-20i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i200000000−22−22−22−220000002i−2i00000000
χ352-2-22-222-222-2222-2-2-2-2-2-2-2222-222-2222-2-2-22i−2i−2i2i00002-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ362-2-22-222-222-2222-2-2-2-2-2-2-2222-222-2222-2-2-2−2i2i2i−2i00002-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ372-2-22-222-222-22-2-22-22-2-2-2-22222-22-22-2-22-2200000000-2200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ382-2-22-222-222-22-2-22-22-2-2-2-22222-22-22-2-22-2200000000-220000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ392-2-22-222-22-22-222-22-2-2-2-2-22222-2-22-222-22-200000000-22000000000000000000000000000000000000002i−2i
χ402-2-22-222-22-22-222-22-2-2-2-2-22222-2-22-222-22-200000000-2200000000000000000000000000000000000000−2i2i
χ412-2-22-222-22-22-2-2-2222-2-2-2-2222-22-22-2-2-222200002-22-22-2000000002-22-22-22-2000000000000000000000000
χ422-2-22-222-22-22-2-2-2222-2-2-2-2222-22-22-2-2-22220000-22-222-200000000-22-22-22-22000000000000000000000000
χ432-2-22-222-2-12-2222-2-2-21111-1-1-1-22-11-1-1-11112i−2i−2i2i0000-11−iii−i−iii−i3−33−3−33−330000000000−i3i3−i3i30000000000
χ442-2-22-222-2-12-2222-2-2-21111-1-1-1-22-11-1-1-11112i−2i−2i2i0000-11−iii−i−iii−i−33−333−33−30000000000i3−i3i3−i30000000000
χ452-2-22-222-2-12-2222-2-2-21111-1-1-1-22-11-1-1-1111−2i2i2i−2i0000-11i−i−iii−i−ii3−33−3−33−330000000000i3−i3i3−i30000000000
χ462-2-22-222-2-12-2222-2-2-21111-1-1-1-22-11-1-1-1111−2i2i2i−2i0000-11i−i−iii−i−ii−33−333−33−30000000000−i3i3−i3i30000000000
χ472-2-22-222-2-1-22-2-2-22221111-1-1-1-221-1111-1-1-100002-22-2-11−i3i3i3−i3i3−i3−i3i3-11-11-11-110000000000−i3i3i3−i30000000000
χ482-2-22-222-2-1-22-2-2-22221111-1-1-1-221-1111-1-1-100002-22-2-11i3−i3−i3i3−i3i3i3−i3-11-11-11-110000000000i3−i3−i3i30000000000
χ492-2-22-222-2-1-22-2-2-22221111-1-1-1-221-1111-1-1-10000-22-22-11−i3i3i3−i3i3−i3−i3i31-11-11-11-10000000000i3−i3−i3i30000000000
χ502-2-22-222-2-1-22-2-2-22221111-1-1-1-221-1111-1-1-10000-22-22-11i3−i3−i3i3−i3i3i3−i31-11-11-11-10000000000−i3i3i3−i30000000000
χ512-2-2-222-222000-22-202-2-2222-2-200000-22-20200002−2−2200000000002−2−222−2−222−2−22−222−2000000002-2000000
χ522-2-2-222-222000-22-202-2-2222-2-200000-22-20200002−2−2200000000002−2−222−2−22−222−22−2−2200000000-22000000
χ532-2-2-222-222000-22-202-2-2222-2-200000-22-2020000−222−20000000000−222−2−222−22−2−22−222−200000000-22000000
χ542-2-2-222-222000-22-202-2-2222-2-200000-22-2020000−222−20000000000−222−2−222−2−222−22−2−22000000002-2000000
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
χ57444-4-44-4-44000-4440-444-4-44-4-400000-4440-400000000000000000000000000000000000000000000000000
χ58444-4-44-4-4-20004-4-404-2-222-22200000-2220-200002222−22−220000000000−2−222−2−222000000000000000000000000
χ59444-4-44-4-4-20004-4-404-2-222-22200000-2220-20000−22−222222000000000022−2−222−2−2000000000000000000000000
χ60444-4-44-4-4-2000-4440-4-2-222-222000002-2-20200000000000000000066−6−6−6−666000000000000000000000000
χ61444-4-44-4-4-2000-4440-4-2-222-222000002-2-202000000000000000000−6−66666−6−6000000000000000000000000
χ6244-444-4-4-44-444000-404-44-4-44-400-444000-4000000000000000000000000000000000000000000000000000
χ6344-444-4-4-4-24-4-400040-22-222-2200-222000-202222−22−22000000−2−222−2−22200000000000000000000000000000000
χ6444-444-4-4-4-24-4-400040-22-222-2200-222000-20−22−22222200000022−2−222−2−200000000000000000000000000000000
χ6544-444-4-4-4-2-444000-40-22-222-22002-2-200020000000000066−6−6−6−66600000000000000000000000000000000
χ6644-444-4-4-4-2-444000-40-22-222-22002-2-2000200000000000−6−66666−6−600000000000000000000000000000000
χ6744-4-4-4-4444000000004-4-44-4-4400000000000000000000000000000000000022-2-2-2-2220000000000000000
χ6844-4-4-4-4444000000004-4-44-4-44000000000000000000000000000000000000-2-22222-2-20000000000000000
χ694-444-4-4-444-4-4400040-44-44-44-400-4-440004000000000000000000000000000000000000000000000000000
χ704-444-4-4-44-244-4000-402-22-22-2200-2-2200020−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ714-444-4-4-44-244-4000-402-22-22-2200-2-22000202i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ724-444-4-4-44-2-4-44000402-22-22-220022-2000-200000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ734-444-4-4-44-2-4-44000402-22-22-220022-2000-200000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ744-44-44-44-4400000000-444-4-4-440000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ754-44-44-44-4400000000-444-4-4-44000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ764-4-44-444-4-24-44-4-44-442222-2-2-24-4-22-222-22-2000000002-20000000000000000000000000000000000000000
χ774-4-44-444-4-2-44-444-44-42222-2-2-24-42-22-2-22-22000000002-20000000000000000000000000000000000000000
χ784-4-4-444-4440004-440-4-4-4444-4-4000004-440-400000000000000000000000000000000000000000000000000
χ794-4-4-444-44-20004-440-422-2-2-22200000-22-2020000000000000000006−6−66−666−6000000000000000000000000
χ804-4-4-444-44-20004-440-422-2-2-22200000-22-202000000000000000000−666−66−6−66000000000000000000000000
χ814-4-4-444-44-2000-44-40422-2-2-222000002-220-2000022−22−22220000000000−222−2−222−2000000000000000000000000
χ824-4-4-444-44-2000-44-40422-2-2-222000002-220-20000−222222−2200000000002−2−222−2−22000000000000000000000000
χ8388-8-8-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000

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