Finite Group Databasebeta

← Group #10699708

Character table — Group #10699708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ922222222222-2-22-22-22222222-2-2222-2-2-2-2222-2-20000-2-22222-2-2-2-200000000000000000000000000000000
χ1022222222222-2-22-22-22222222-2-2222-2-2-2-22-2-2220000-2-2-2-2-2-2222200000000000000000000000000000000
χ11222222222-2-222-22-222222222-2-2-2-2-22222-200000000-2-200000000000000002222-2-2-2-20000000000000000
χ12222222222-2-222-22-222222222-2-2-2-2-22222-200000000-2-20000000000000000-2-2-2-222220000000000000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000002i2i−2i−2i00
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000000000−2i−2i2i2i00
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
χ1922222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ23222-2-2-2-222002-20-202222-2-2-2-20000022-2-20000022−2−2000000000022−2−222−2−22i2i−2i−2i0000000000−i2−i2i2i2000000
χ24222-2-2-2-222002-20-202222-2-2-2-20000022-2-20000022−2−2000000000022−2−222−2−2−2i−2i2i2i0000000000i2i2−i2−i2000000
χ25222-2-2-2-222002-20-202222-2-2-2-20000022-2-200000−2−2220000000000−2−222−2−2222i2i−2i−2i0000000000i2i2−i2−i2000000
χ26222-2-2-2-222002-20-202222-2-2-2-20000022-2-200000−2−2220000000000−2−222−2−222−2i−2i2i2i0000000000−i2−i2i2i2000000
χ2722-22-2-22-222-20020-202-2-22-2-22002-2-200002002-2000000000022-2-200000000−i2i2−i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ2822-22-2-22-222-20020-202-2-22-2-22002-2-200002002-2000000000022-2-200000000i2−i2i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ2922-22-2-22-222-20020-202-2-22-2-22002-2-20000200-220000000000-2-22200000000−i2i2−i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ3022-22-2-22-222-20020-202-2-22-2-22002-2-20000200-220000000000-2-22200000000i2−i2i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ3122-22-2-22-22-2200-20202-2-22-2-2200-2220000-22i−2i000000002i2i−2i−2i000000000000−i2i2−i2i2i2i2−i2−i200000000002−2−2200
χ3222-22-2-22-22-2200-20202-2-22-2-2200-2220000-22i−2i000000002i2i−2i−2i000000000000i2−i2i2−i2−i2−i2i2i20000000000−222−200
χ3322-22-2-22-22-2200-20202-2-22-2-2200-2220000-2−2i2i00000000−2i−2i2i2i000000000000−i2i2−i2i2i2i2−i2−i20000000000−222−200
χ3422-22-2-22-22-2200-20202-2-22-2-2200-2220000-2−2i2i00000000−2i−2i2i2i000000000000i2−i2i2−i2−i2−i2i2i200000000002−2−2200
χ352-2-222-2-2222222-2-2-2-2-2-2222-2-22-222-22-22-2-2000000002-2000000000000000000000000000000000000002-2
χ362-2-222-2-2222222-2-2-2-2-2-2222-2-22-222-22-22-2-2000000002-200000000000000000000000000000000000000-22
χ372-2-222-2-22222-2-2-22-22-2-2222-2-2-2222-2-22-22-200000000-220000000000000000000000000000002i−2i2i−2i000000
χ382-2-222-2-22222-2-2-22-22-2-2222-2-2-2222-2-22-22-200000000-22000000000000000000000000000000−2i2i−2i2i000000
χ392-2-222-2-222-2-2222-22-2-2-2222-2-2-22-2-222-22-2200000000-220000000000000000000000002i−2i2i−2i2i−2i0000000000
χ402-2-222-2-222-2-2222-22-2-2-2222-2-2-22-2-222-22-2200000000-22000000000000000000000000−2i2i−2i2i−2i2i0000000000
χ412-2-222-2-222-2-2-2-22222-2-2222-2-22-2-2-22-22-22200002-22-22-2000000002-22-22-22-2000000000000000000000000
χ422-2-222-2-222-2-2-2-22222-2-2222-2-22-2-2-22-22-2220000-22-222-200000000-22-22-22-22000000000000000000000000
χ432-2-222-2-22-1-2-2222-22-211-1-1-111-2211-1-11-11-1000000001-13−33−33−33−3−i3i3−i3i3i3−i3i3−i3000000002i−2i−ii−ii0000000000
χ442-2-222-2-22-1-2-2222-22-211-1-1-111-2211-1-11-11-1000000001-13−33−33−33−3i3−i3i3−i3−i3i3−i3i300000000−2i2ii−ii−i0000000000
χ452-2-222-2-22-1-2-2222-22-211-1-1-111-2211-1-11-11-1000000001-1−33−33−33−33−i3i3−i3i3i3−i3i3−i300000000−2i2ii−ii−i0000000000
χ462-2-222-2-22-1-2-2222-22-211-1-1-111-2211-1-11-11-1000000001-1−33−33−33−33i3−i3i3−i3−i3i3−i3i3000000002i−2i−ii−ii0000000000
χ472-2-222-2-22-1-2-2-2-2222211-1-1-1112-211-11-11-1-100002-22-2-113−33−3−33−33-11-11-11-1100000000003−3−330000000000
χ482-2-222-2-22-1-2-2-2-2222211-1-1-1112-211-11-11-1-100002-22-2-11−33−333−33−3-11-11-11-110000000000−333−30000000000
χ492-2-222-2-22-1-2-2-2-2222211-1-1-1112-211-11-11-1-10000-22-22-113−33−3−33−331-11-11-11-10000000000−333−30000000000
χ502-2-222-2-22-1-2-2-2-2222211-1-1-1112-211-11-11-1-10000-22-22-11−33−333−33−31-11-11-11-100000000003−3−330000000000
χ512-2-2-2-2222200-220-202-2-22-2-22200000-222-2000002−2−2200000000002−2−222−2−2200002-22-20000002−2−22000000
χ522-2-2-2-2222200-220-202-2-22-2-22200000-222-2000002−2−2200000000002−2−222−2−220000-22-22000000−222−2000000
χ532-2-2-2-2222200-220-202-2-22-2-22200000-222-200000−222−20000000000−222−2−222−200002-22-2000000−222−2000000
χ542-2-2-2-2222200-220-202-2-22-2-22200000-222-200000−222−20000000000−222−2−222−20000-22-220000002−2−22000000
χ5544444444-2-4-444-44-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ57444-4-4-4-44400-44040-4444-4-4-4-400000-4-444000000000000000000000000000000000000000000000000000
χ58444-4-4-4-44-2004-40-404-2-2-2222200000-2-222000002222−22−220000000000−2−222−2−222000000000000000000000000
χ59444-4-4-4-44-2004-40-404-2-2-2222200000-2-22200000−22−222222000000000022−2−222−2−2000000000000000000000000
χ60444-4-4-4-44-200-44040-4-2-2-222220000022-2-20000000000000000000i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ61444-4-4-4-44-200-44040-4-2-2-222220000022-2-20000000000000000000−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ6244-44-4-44-4-24-40040-40-222-222-200-2220000-2004-40000000000-2-22200000000000000000000000000000000
χ6344-44-4-44-4-24-40040-40-222-222-200-2220000-200-44000000000022-2-200000000000000000000000000000000
χ6444-44-4-44-4-2-4400-4040-222-222-2002-2-2000024i−4i00000000−2i−2i2i2i000000000000000000000000000000000000
χ6544-44-4-44-4-2-4400-4040-222-222-2002-2-200002−4i4i000000002i2i−2i−2i000000000000000000000000000000000000
χ6644-4-444-4-44000000004-4-4-444-400000000000000000000000000000000000022−22−222200000000000000000000
χ6744-4-444-4-44000000004-4-4-444-4000000000000000000000000000000000000−222222−2200000000000000000000
χ684-444-44-4-444-400-4040-44-44-44-4004-440000-400000000000000000000000000000000000000000000000000
χ694-444-44-4-44-440040-40-44-44-44-400-44-40000400000000000000000000000000000000000000000000000000
χ704-444-44-4-4-24-400-40402-22-22-2200-22-2000020000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ714-444-44-4-4-24-400-40402-22-22-2200-22-20000200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ724-444-44-4-4-2-440040-402-22-22-22002-220000-20000000000000023−23−232300000000000000000000000000000000
χ734-444-44-4-4-2-440040-402-22-22-22002-220000-200000000000000−232323−2300000000000000000000000000000000
χ744-44-44-44-4400000000-44-4-44-440000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ754-44-44-44-4400000000-44-4-44-4400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ764-4-444-4-44-24444-4-4-4-422-2-2-2224-4-2-22-22-22200000000-220000000000000000000000000000000000000000
χ774-4-444-4-44-244-4-4-44-4422-2-2-222-44-2-222-22-22000000002-20000000000000000000000000000000000000000
χ784-4-4-4-44444004-4040-4-4-44-4-444000004-4-44000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-2004-4040-422-222-2-200000-222-20000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-4-4-4444-2004-4040-422-222-2-200000-222-20000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-4-4-4444-200-440-40422-222-2-2000002-2-220000022−22−22220000000000−222−2−222−2000000000000000000000000
χ824-4-4-4-4444-200-440-40422-222-2-2000002-2-2200000−222222−2200000000002−2−222−2−22000000000000000000000000
χ8388-8-888-8-8-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000
χ848-88-88-88-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000

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