Finite Group Databasebeta

← Group #10883536

Character table — Group #10883536

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order12442223444688881212666888888121212242424242424242424242424224444666688881212121212121212242424242424242424242244888824884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1111111111-1-111111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-11-1
χ10111111111111-1-1-1-1111111111-1-111111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11
χ11111111111111-1-1-1-1111111111-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-11-11
χ12111111111111-1-1-1-1111111111-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-11-1
χ13111111111111-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-11-1-11
χ14111111111111-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-111-1
χ15111111111111-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-111-1
χ16111111111111-1-1-1-111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11
χ172222222-1222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-21111-1-1-1-111111111-1-10000000000000000
χ192222222-1222-12222-1-1-1-1-1-2-2-2-222-1-1-111111111-1-1-1-12222-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111-1-10000000000000000
χ202222222-1222-12222-1-1-1-1-1-2-2-2-222-1-1-111111111-1-1-1-1-2-2-2-2-2-21111222211111111-1-1-1-1-1-1-1-1-1-10000000000000000
χ212222222-1222-1-2-2-2-2-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-111112-22-2-2-2-1-11122-2-2-1-1111111-1-1-1-11111110000000000000000
χ222222222-1222-1-2-2-2-2-1-1-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-11111-22-22-2-211-1-1-2-22211-1-111111111-1-1-1-1110000000000000000
χ232222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-2-2-2-2-1-1-11111111111112-22-222-1-111-2-222-1-111-1-1-1-11111-1-1-1-1110000000000000000
χ242222222-1222-1-2-2-2-2-1-1-1-1-1-2-2-2-2-2-2-1-1-1111111111111-22-222211-1-122-2-211-1-1-1-1-1-1-1-1-1-11111110000000000000000
χ252222-22-22-2-222222222-2-2222-2-2-2-2-2-222222-2-2-2-2222200002-200000000000022-2-200000000-2-20000000000000000
χ262222-22-22-2-222222222-2-22-2-222-2-2-2-22-2-2-2-2222222220000-22000000000000-2-22200000000-2-20000000000000000
χ272222-22-22-2-222-2-2-2-222-2-2222-2-222-2-222222-2-2-2-2-2-2-2-20000-22000000000000-2-22200000000220000000000000000
χ282222-22-22-2-222-2-2-2-222-2-22-2-22222-2-22-2-2-2-22222-2-2-2-200002-200000000000022-2-200000000220000000000000000
χ292222-22-2-1-2-22-12222-1-111-122-2-2-2-211-1-1-1-1-11111-1-1-1-100002-2−i3i3−i3i30000−i3i3−i3i3-1-111−i3−i3i3i3−i3−i3i3i3110000000000000000
χ302222-22-2-1-2-22-12222-1-111-122-2-2-2-211-1-1-1-1-11111-1-1-1-100002-2i3−i3i3−i30000i3−i3i3−i3-1-111i3i3−i3−i3i3i3−i3−i3110000000000000000
χ312222-22-2-1-2-22-12222-1-111-1-2-222-2-211-11111-1-1-1-1-1-1-1-10000-22−i3i3−i3i30000−i3i3−i3i311-1-1i3i3−i3−i3i3i3−i3−i3110000000000000000
χ322222-22-2-1-2-22-12222-1-111-1-2-222-2-211-11111-1-1-1-1-1-1-1-10000-22i3−i3i3−i30000i3−i3i3−i311-1-1−i3−i3i3i3−i3−i3i3i3110000000000000000
χ332222-22-2-1-2-22-1-2-2-2-2-1-111-122-2-22211-1-1-1-1-1111111110000-22−i3i3i3−i30000−i3i3i3−i311-1-1−i3−i3i3i3i3i3−i3−i3-1-10000000000000000
χ342222-22-2-1-2-22-1-2-2-2-2-1-111-122-2-22211-1-1-1-1-1111111110000-22i3−i3−i3i30000i3−i3−i3i311-1-1i3i3−i3−i3−i3−i3i3i3-1-10000000000000000
χ352222-22-2-1-2-22-1-2-2-2-2-1-111-1-2-2222211-11111-1-1-1-1111100002-2−i3i3i3−i30000−i3i3i3−i3-1-111i3i3−i3−i3−i3−i3i3i3-1-10000000000000000
χ362222-22-2-1-2-22-1-2-2-2-2-1-111-1-2-2222211-11111-1-1-1-1111100002-2i3−i3−i3i30000i3−i3−i3i3-1-111−i3−i3i3i3i3i3−i3−i3-1-10000000000000000
χ3722-2-22222-2-2-220000-2-22222i−2i2i−2i00-2-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000022-2-20000002i−2i0000
χ3822-2-22222-2-2-220000-2-22222i−2i2i−2i00-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000-2-222000000−2i2i0000
χ3922-2-22222-2-2-220000-2-2222−2i2i−2i2i00-2-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000022-2-2000000−2i2i0000
χ4022-2-22222-2-2-220000-2-2222−2i2i−2i2i00-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000-2-2220000002i−2i0000
χ4122-2-22-2-222-22222-2-2-2-22-2-200002-22-220000000022-2-200000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i2-20000000000000000
χ4222-2-22-2-222-22222-2-2-2-22-2-200002-22-220000000022-2-20000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i2-20000000000000000
χ4322-2-22-2-222-222-2-222-2-22-2-20000-222-2200000000-2-22200000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i-220000000000000000
χ4422-2-22-2-222-222-2-222-2-22-2-20000-222-2200000000-2-2220000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i-220000000000000000
χ4522-2-22-2-2-12-22-122-2-211-11100002-2-11-13−33−33−33−3-1-111000000−i3i3−i3i32i−2i2i−2ii3−i3i3−i33−33−3−ii−ii−ii−ii-110000000000000000
χ4622-2-22-2-2-12-22-122-2-211-11100002-2-11-13−33−33−33−3-1-111000000i3−i3i3−i3−2i2i−2i2i−i3i3−i3i33−33−3i−ii−ii−ii−i-110000000000000000
χ4722-2-22-2-2-12-22-122-2-211-11100002-2-11-1−33−33−33−33-1-111000000−i3i3−i3i3−2i2i−2i2ii3−i3i3−i3−33−33i−ii−ii−ii−i-110000000000000000
χ4822-2-22-2-2-12-22-122-2-211-11100002-2-11-1−33−33−33−33-1-111000000i3−i3i3−i32i−2i2i−2i−i3i3−i3i3−33−33−ii−ii−ii−ii-110000000000000000
χ4922-2-22-2-2-12-22-1-2-22211-1110000-22-11-13−33−33−33−311-1-1000000−i3i3i3−i32i−2i−2i2ii3−i3−i3i3−33−33−ii−iii−ii−i1-10000000000000000
χ5022-2-22-2-2-12-22-1-2-22211-1110000-22-11-13−33−33−33−311-1-1000000i3−i3−i3i3−2i2i2i−2i−i3i3i3−i3−33−33i−ii−i−ii−ii1-10000000000000000
χ5122-2-22-2-2-12-22-1-2-22211-1110000-22-11-1−33−33−33−3311-1-1000000−i3i3i3−i3−2i2i2i−2ii3−i3−i3i33−33−3i−ii−i−ii−ii1-10000000000000000
χ5222-2-22-2-2-12-22-1-2-22211-1110000-22-11-1−33−33−33−3311-1-1000000i3−i3−i3i32i−2i−2i2i−i3i3i3−i33−33−3−ii−iii−ii−i1-10000000000000000
χ5322-2-2-22-2222-220000-2-2-2-222i−2i−2i2i0022-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000002i2i−2i−2i2-2000000
χ5422-2-2-22-2222-220000-2-2-2-222i−2i−2i2i0022-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000−2i−2i2i2i-22000000
χ5522-2-2-22-2222-220000-2-2-2-22−2i2i2i−2i0022-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000002i2i−2i−2i-22000000
χ5622-2-2-22-2222-220000-2-2-2-22−2i2i2i−2i0022-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000−2i−2i2i2i2-2000000
χ5722-2-2-2-222-222222-2-2-2-2-22-20000-22-2220000000022-2-222-2-20022220000-2-2-2-2000000000000-220000000000000000
χ5822-2-2-2-222-222222-2-2-2-2-22-20000-22-2220000000022-2-2-2-22200-2-2-2-200002222000000000000-220000000000000000
χ5922-2-2-2-222-2222-2-222-2-2-22-200002-2-22200000000-2-2222-2-220022-2-20000-2-2220000000000002-20000000000000000
χ6022-2-2-2-222-2222-2-222-2-2-22-200002-2-22200000000-2-222-222-200-2-222000022-2-20000000000002-20000000000000000
χ6122-2-2-2-22-1-222-122-2-2111-110000-221-1-13−33−3−33−33-1-11122-2-200-1-1-1-1000011113−3−333−3−333−3−331-10000000000000000
χ6222-2-2-2-22-1-222-122-2-2111-110000-221-1-13−33−3−33−33-1-111-2-2220011110000-1-1-1-13−3−33−333−3−333−31-10000000000000000
χ6322-2-2-2-22-1-222-122-2-2111-110000-221-1-1−33−333−33−3-1-11122-2-200-1-1-1-100001111−333−3−333−3−333−31-10000000000000000
χ6422-2-2-2-22-1-222-122-2-2111-110000-221-1-1−33−333−33−3-1-111-2-2220011110000-1-1-1-1−333−33−3−333−3−331-10000000000000000
χ6522-2-2-2-22-1-222-1-2-222111-1100002-21-1-13−33−3−33−3311-1-12-2-2200-1-111000011-1-1−333−33−3−33−333−3-110000000000000000
χ6622-2-2-2-22-1-222-1-2-222111-1100002-21-1-13−33−3−33−3311-1-1-222-20011-1-10000-1-111−333−3−333−33−3−33-110000000000000000
χ6722-2-2-2-22-1-222-1-2-222111-1100002-21-1-1−33−333−33−311-1-12-2-2200-1-111000011-1-13−3−33−333−33−3−33-110000000000000000
χ6822-2-2-2-22-1-222-1-2-222111-1100002-21-1-1−33−333−33−311-1-1-222-20011-1-10000-1-1113−3−333−3−33−333−3-110000000000000000
χ6944444-4-44-44-440000444-4-4000000-44-4000000000000000000000000000000000000000000000000000000000000
χ7044444-4-4-2-44-4-20000-2-2-2220000002-22−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ7144444-4-4-2-44-4-20000-2-2-2220000002-222i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ724444-4-4444-4-44000044-44-40000004-4-4000000000000000000000000000000000000000000000000000000000000
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χ744444-4-44-24-4-4-20000-2-22-22000000-2222i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-2000022-2-2-24i−4i4i−4i00222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-2000022-2-2-2−4i4i−4i4i002222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ7744-4-4-44-4-244-4-200002222-24i−4i−4i4i00-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ7844-4-4-44-4-244-4-200002222-2−4i4i4i−4i00-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ794-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i2000000000000000000000000000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ804-44i−4i0004000-422−22−2i22i24i−4i0000000000000000000022−22−2i22i200000000000000000000000000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ814-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i2000000000000000000000000000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ824-44i−4i0004000-4−22222i2−2i24i−4i00000000000000000000−22222i2−2i200000000000000000000000000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ834-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i2000000000000000000000000000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ844-4−4i4i0004000-422−222i2−2i2−4i4i0000000000000000000022−222i2−2i200000000000000000000000000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ854-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i2000000000000000000000000000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ864-4−4i4i0004000-4−2222−2i22i2−4i4i00000000000000000000−2222−2i22i200000000000000000000000000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ878-88i−8i000-4000442−42−4i24i2−4i4i00000000000000000000−22222i2−2i2000000000000000000000000000000000000000000000000
χ888-88i−8i000-40004−42424i2−4i2−4i4i0000000000000000000022−22−2i22i2000000000000000000000000000000000000000000000000
χ898-8−8i8i000-4000442−424i2−4i24i−4i00000000000000000000−2222−2i22i2000000000000000000000000000000000000000000000000
χ908-8−8i8i000-40004−4242−4i24i24i−4i0000000000000000000022−222i2−2i2000000000000000000000000000000000000000000000000

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