Finite Group Databasebeta

← Group #10591083

Character table — Group #10591083

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order12224444223344666666121212121212121236666666666612121212121212121212121222444444666612121212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91-1-1111-1-11-1111-1-1-11-1-1111-1-111-1-111-11-1-1-111-1-111-11-111-1-111-1-11-1i−ii−i1-111-1-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ101-1-1111-1-11-1111-1-1-11-1-1111-1-111-1-111-11-1-1-111-1-111-11-111-1-111-1-11-1−ii−ii1-111-1-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ111-1-1111-1-11-1111-1-1-11-1-1111-1-111-1-111-11-1-1-111-1-111-11-111-1-111-1-1-11i−ii−i-11-1-111ii−i−iii−i−i-1-111−i−iii−i−iii
χ121-1-1111-1-11-1111-1-1-11-1-1111-1-111-1-111-11-1-1-111-1-111-11-111-1-111-1-1-11−ii−ii-11-1-111−i−iii−i−iii-1-111ii−i−iii−i−i
χ131-1-11-1-111-11111-1-1-11-1-11-1-111-1-1111-11-11-1-1-1-11111-11-111-1-1-1-1111-1i−i−ii-1111-1-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ141-1-11-1-111-11111-1-1-11-1-11-1-111-1-1111-11-11-1-1-1-11111-11-111-1-1-1-1111-1−iii−i-1111-1-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ151-1-11-1-111-11111-1-1-11-1-11-1-111-1-1111-11-11-1-1-1-11111-11-111-1-1-1-111-11i−i−ii1-1-1-111ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ161-1-11-1-111-11111-1-1-11-1-11-1-111-1-1111-11-11-1-1-1-11111-11-111-1-1-1-111-11−iii−i1-1-1-111−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ1722222222222-122-1-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122000022-1-1-1-100000000-1-1-1-100000000
χ1822222222222-122-1-1222-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-20000-2-2111100000000111100000000
χ192222222222-122222-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1002222000000-1-1-1-1-1-1-1-1000000000000
χ202222222222-122222-1-1-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100-2-2-2-200000011111111000000000000
χ2122222222-2-222-2-2222222222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2222222222-2-22-1-2-2-1-1222-12222-1-1-1-1-1-2-211-1-11111-1-2-2111111-1-1-1-100000000−i3i3−i3i300000000−i3i3−i3i300000000
χ2322222222-2-22-1-2-2-1-1222-12222-1-1-1-1-1-2-211-1-11111-1-2-2111111-1-1-1-100000000i3−i3i3−i300000000i3−i3i3−i300000000
χ2422222222-2-2-12-2-222-1-1-12-1-1-1-12222-111-2-2-1-11111-111-2-21111-1-1-1-1000000000000−i3i3−i3i3−i3i3−i3i3000000000000
χ2522222222-2-2-12-2-222-1-1-12-1-1-1-12222-111-2-2-1-11111-111-2-21111-1-1-1-1000000000000i3−i3i3−i3i3−i3i3−i3000000000000
χ262222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ272222-2-2-2-2222-1-2-2-1-1222-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-2111111111100000000−i3i3−i3i300000000i3−i3i3−i300000000
χ282222-2-2-2-2222-1-2-2-1-1222-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-1-2-2111111111100000000i3−i3i3−i300000000−i3i3−i3i300000000
χ292222-2-2-2-222-12-2-222-1-1-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111000000000000−i3i3−i3i3i3−i3i3−i3000000000000
χ302222-2-2-2-222-12-2-222-1-1-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-111-2-211111111000000000000i3−i3i3−i3−i3i3−i3i3000000000000
χ312222-2-2-2-2-2-22-122-1-1222-1-2-2-2-21111-1-2-211-1-11111-122-1-1-1-1-1-11111220000-2-2-1-1-1-100000000111100000000
χ322222-2-2-2-2-2-22-122-1-1222-1-2-2-2-21111-1-2-211-1-11111-122-1-1-1-1-1-11111-2-2000022111100000000-1-1-1-100000000
χ332222-2-2-2-2-2-2-122222-1-1-121111-2-2-2-2-111-2-2-1-11111-1-1-122-1-1-1-111110022-2-2000000-1-1-1-11111000000000000
χ342222-2-2-2-2-2-2-122222-1-1-121111-2-2-2-2-111-2-2-1-11111-1-1-122-1-1-1-1111100-2-2220000001111-1-1-1-1000000000000
χ3522-2-22i−2i2i−2i0022002-2-22-2-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i0000000000000000000000002−22−2−i2i2−i2i2
χ3622-2-22i−2i2i−2i0022002-2-22-2-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i000000000000000000000000−22−22i2−i2i2−i2
χ3722-2-2−2i2i−2i2i0022002-2-22-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i0000000000000000000000002−22−2i2−i2i2−i2
χ3822-2-2−2i2i−2i2i0022002-2-22-2-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i000000000000000000000000−22−22−i2i2−i2i2
χ392-22-22i−2i−2i2i002200-22-2-22-22i−2i−2i2i2i−2i−2i2i20000-220000-2000000002i−2i−2i2i000000000000000000000000−i2i2i2−i2−222−2
χ402-22-22i−2i−2i2i002200-22-2-22-22i−2i−2i2i2i−2i−2i2i20000-220000-2000000002i−2i−2i2i000000000000000000000000i2−i2−i2i22−2−22
χ412-22-2−2i2i2i−2i002200-22-2-22-2−2i2i2i−2i−2i2i2i−2i20000-220000-200000000−2i2i2i−2i000000000000000000000000−i2i2i2−i22−2−22
χ422-22-2−2i2i2i−2i002200-22-2-22-2−2i2i2i−2i−2i2i2i−2i20000-220000-200000000−2i2i2i−2i000000000000000000000000i2−i2−i2i2−222−2
χ432-2-2222-2-22-22-12-2112-2-2-122-2-2-1-111-12-2-1111-1-111-12-2-11-1-111-1-1112-200002-2-1-11100000000-1-11100000000
χ442-2-2222-2-22-22-12-2112-2-2-122-2-2-1-111-12-2-1111-1-111-12-2-11-1-111-1-111-220000-2211-1-10000000011-1-100000000
χ452-2-2222-2-22-2-122-2-2-2-1112-1-11122-2-2-1-112-211-1-111-1-112-2-1-111-1-111002i−2i2i−2i000000−i−iii−i−iii000000000000
χ462-2-2222-2-22-2-122-2-2-2-1112-1-11122-2-2-1-112-211-1-111-1-112-2-1-111-1-11100−2i2i−2i2i000000ii−i−iii−i−i000000000000
χ472-2-2222-2-2-2222-22-2-22-2-2222-2-222-2-22-22-22-2-2-2-2222-22-22-2-22222-2-200000000000000000000000000000000
χ482-2-2222-2-2-222-1-22112-2-2-122-2-2-1-111-1-221-11111-1-1-1-221-111-1-1-1-11100000000−i3i3i3−i300000000−i3i3i3−i300000000
χ492-2-2222-2-2-222-1-22112-2-2-122-2-2-1-111-1-221-11111-1-1-1-221-111-1-1-1-11100000000i3−i3−i3i300000000i3−i3−i3i300000000
χ502-2-2222-2-2-22-12-22-2-2-1112-1-11122-2-2-11-1-221111-1-1-11-1-2211-1-1-1-1110000000000003−3−333−3−33000000000000
χ512-2-2222-2-2-22-12-22-2-2-1112-1-11122-2-2-11-1-221111-1-1-11-1-2211-1-1-1-111000000000000−333−3−333−3000000000000
χ522-2-22-2-2222-222-22-2-22-2-22-2-222-2-22222-22-2-2-222-2-22-22-22-2-222-2-22200000000000000000000000000000000
χ532-2-22-2-2222-22-1-22112-2-2-1-2-22211-1-1-12-2-1111-1-111-1-221-111-1-111-1-100000000−i3i3i3−i300000000i3−i3−i3i300000000
χ542-2-22-2-2222-22-1-22112-2-2-1-2-22211-1-1-12-2-1111-1-111-1-221-111-1-111-1-100000000i3−i3−i3i300000000−i3i3i3−i300000000
χ552-2-22-2-2222-2-12-22-2-2-111211-1-1-2-222-1-112-211-1-111-11-1-2211-1-111-1-10000000000003−3−33−333−3000000000000
χ562-2-22-2-2222-2-12-22-2-2-111211-1-1-2-222-1-112-211-1-111-11-1-2211-1-111-1-1000000000000−333−33−3−33000000000000
χ572-2-22-2-222-222-12-2112-2-2-1-2-22211-1-1-1-221-11111-1-1-12-2-11-1-11111-1-12-20000-22-1-1110000000011-1-100000000
χ582-2-22-2-222-222-12-2112-2-2-1-2-22211-1-1-1-221-11111-1-1-12-2-11-1-11111-1-1-2200002-211-1-100000000-1-11100000000
χ592-2-22-2-222-22-122-2-2-2-111211-1-1-2-222-11-1-221111-1-1-1-112-2-1-11111-1-1002i−2i−2i2i000000−i−iiiii−i−i000000000000
χ602-2-22-2-222-22-122-2-2-2-111211-1-1-2-222-11-1-221111-1-1-1-112-2-1-11111-1-100−2i2i2i−2i000000ii−i−i−i−iii000000000000
χ614444444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-21111111100000000000000000000000000000000
χ6244444444-4-4-2-2-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-1-1-1-1111100000000000000000000000000000000
χ634444-4-4-4-444-2-2-4-4-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-244-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-21111-1-1-1-100000000000000000000000000000000
χ6544-4-44i−4i4i−4i004-200-22-44-424i−4i4i−4i−2i2i−2i2i-20000-220000200000000−2i2i−2i2i00000000000000000000000000000000
χ6644-4-44i−4i4i−4i00-24004-42-22-4−2i2i−2i2i4i−4i4i−4i-20000-220000200000000−2i2i−2i2i00000000000000000000000000000000
χ6744-4-44i−4i4i−4i00-2-200-222-222−2i2i−2i2i−2i2i−2i2i100001-13-33-3-100003i−3i3i−3ii−ii−i00000000000000000000000000000000
χ6844-4-44i−4i4i−4i00-2-200-222-222−2i2i−2i2i−2i2i−2i2i100001-1-33-33-10000−3i3i−3i3ii−ii−i00000000000000000000000000000000
χ6944-4-4−4i4i−4i4i004-200-22-44-42−4i4i−4i4i2i−2i2i−2i-20000-2200002000000002i−2i2i−2i00000000000000000000000000000000
χ7044-4-4−4i4i−4i4i00-24004-42-22-42i−2i2i−2i−4i4i−4i4i-20000-2200002000000002i−2i2i−2i00000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-2-200-222-2222i−2i2i−2i2i−2i2i−2i100001-13-33-3-10000−3i3i−3i3i−ii−ii00000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-2-200-222-2222i−2i2i−2i2i−2i2i−2i100001-1-33-33-100003i−3i3i−3i−ii−ii00000000000000000000000000000000
χ734-44-44i−4i−4i4i004-2002-2-4-4424i−4i−4i4i−2i2i2i−2i-200002-20000200000000−2i2i2i−2i00000000000000000000000000000000
χ744-44-44i−4i−4i4i00-2400-4422-2-4−2i2i2i−2i4i−4i−4i4i-200002-20000200000000−2i2i2i−2i00000000000000000000000000000000
χ754-44-44i−4i−4i4i00-2-2002-222-22−2i2i2i−2i−2i2i2i−2i10000-113-3-33-100003i−3i−3i3ii−i−ii00000000000000000000000000000000
χ764-44-44i−4i−4i4i00-2-2002-222-22−2i2i2i−2i−2i2i2i−2i10000-11-333-3-10000−3i3i3i−3ii−i−ii00000000000000000000000000000000
χ774-44-4−4i4i4i−4i004-2002-2-4-442−4i4i4i−4i2i−2i−2i2i-200002-200002000000002i−2i−2i2i00000000000000000000000000000000
χ784-44-4−4i4i4i−4i00-2400-4422-2-42i−2i−2i2i−4i4i4i−4i-200002-200002000000002i−2i−2i2i00000000000000000000000000000000
χ794-44-4−4i4i4i−4i00-2-2002-222-222i−2i−2i2i2i−2i−2i2i10000-113-3-33-10000−3i3i3i−3i−iii−i00000000000000000000000000000000
χ804-44-4−4i4i4i−4i00-2-2002-222-222i−2i−2i2i2i−2i−2i2i10000-11-333-3-100003i−3i−3i3i−iii−i00000000000000000000000000000000
χ814-4-4444-4-44-4-2-24-422-222-2-2-222-2-2221-22-22-1-111-1-11-22-2211-1-111-1-100000000000000000000000000000000
χ824-4-4444-4-4-44-2-2-4422-222-2-2-222-2-22212-22-2-1-1-1-11112-22-2-1-11111-1-100000000000000000000000000000000
χ834-4-44-4-4444-4-2-2-4422-222-222-2-222-2-21-22-22-1-111-1-112-22-2-1-111-1-11100000000000000000000000000000000
χ844-4-44-4-444-44-2-24-422-222-222-2-222-2-212-22-2-1-1-1-1111-22-2211-1-1-1-11100000000000000000000000000000000

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