Finite Group Databasebeta

← Group #11792417

Character table — Group #11792417

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order124422233444666612121212121236666666612121212121212121244661212121212121212121212121212121212122244666612121212224466668812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-1111-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111111111-1-1
χ922222222-1222-1-12-1-1-1-1-122-122-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1202000-1-10000-1-100000000
χ1022222222-1222-1-12-1-1-1-1-122-122-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-20-20001100001100000000
χ1122222222-1222-1-12-1-1-1-1-122-122-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-20-20001100001100000000
χ1222222222-1222-1-12-1-1-1-1-122-122-1-12-1-1-1222-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-211111111-2-2-2-211111111202000-1-10000-1-100000000
χ132222222-1222222-122222-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000202-1-10022-1-100-1-1-1-10000
χ142222222-1222222-122222-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-20-21100-2-2110011110000
χ152222222-1222222-122222-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1-2-2-1-1-2-2-2-2-1-11111111111110000000000000202-1-100-2-2-1-10011110000
χ162222222-1222222-122222-1-1-1-1-122-1-1-1-1-1-1-122-1-1-1-1-2-2-1-1-2-2-2-2-1-11111111111110000000000000-20-21100221100-1-1-1-10000
χ1722222-2-222-2-22-2-22222-2-22222-22-2-22-2-22-2-22-222-2-2002-200002-2000000000000000000000000000000000000000000002-2
χ1822222-2-222-2-22-2-22222-2-22222-22-2-22-2-22-2-22-222-2-2002-200002-200000000000000000000000000000000000000000000-22
χ192222-22-2222-2-222222222222-2-2-2-22222-22-2-2-222222-2-2-222-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000
χ202222-22-2222-2-222222222222-2-2-2-22222-22-2-2-22222-22-2-2-2-222-2-2-2-222-2-2-2-222220000000000000000000000000000000000
χ212222-22-22-12-2-2-1-12-1-1-1-1-122-1-2-2112-1-1-1-22-211-1-1-1-12-211-1-1111122-2-2-1-1-1-111110000−i3−i3i3i3−i3−i3i3i3000000−i3i30000−i3i300000000
χ222222-22-22-12-2-2-1-12-1-1-1-1-122-1-2-2112-1-1-1-22-211-1-1-1-12-211-1-1111122-2-2-1-1-1-111110000i3i3−i3−i3i3i3−i3−i3000000i3−i30000i3−i300000000
χ232222-22-22-12-2-2-1-12-1-1-1-1-122-1-2-2112-1-1-1-22-211-1-1-1-1-221111-1-111-2-2221111-1-1-1-10000−i3−i3i3i3−i3−i3i3i3000000i3−i30000i3−i300000000
χ242222-22-22-12-2-2-1-12-1-1-1-1-122-1-2-2112-1-1-1-22-211-1-1-1-1-221111-1-111-2-2221111-1-1-1-10000i3i3−i3−i3i3i3−i3−i3000000−i3i30000−i3i300000000
χ252222-22-2-122-2-222-122222-1-1-111-2-2-1-1-1-11-11-2-2-1-1-1-12-21122-2-211-1-111-1-1-1-111110000000000000000−i3i30000−i3i300−i3−i3i3i30000
χ262222-22-2-122-2-222-122222-1-1-111-2-2-1-1-1-11-11-2-2-1-1-1-12-21122-2-211-1-111-1-1-1-111110000000000000000i3−i30000i3−i300i3i3−i3−i30000
χ272222-22-2-122-2-222-122222-1-1-111-2-2-1-1-1-11-11-2-2-1-1-1-1-2211-2-2221111-1-11111-1-1-1-10000000000000000−i3i30000−i3i300i3i3−i3−i30000
χ282222-22-2-122-2-222-122222-1-1-111-2-2-1-1-1-11-11-2-2-1-1-1-1-2211-2-2221111-1-11111-1-1-1-10000000000000000i3−i30000i3−i300−i3−i3i3i30000
χ292222-2-2222-22-2-2-22222-2-2222-22-22-22-2-2-2-22-2222-2-200-220000-220000000000000000000000000000000000000000002-200
χ302222-2-2222-22-2-2-22222-2-2222-22-22-22-2-2-2-22-2222-2-200-220000-22000000000000000000000000000000000000000000-2200
χ3122-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-200000000000022-2-22222-2-2-2-20000000000000000000000
χ3222-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-200220000-2-2000000000000-2-222-2-2-2-222220000000000000000000000
χ3322-2-22222-1-2-2-2-1-12-11111-2-2-122-1-12-1-1-1-2-2-211111100-1-1−i3i3−i3i3110000−i3−i3i3i3−i3−i3i3i322-2-2-1-1-1-11111000000−i3i30000i3−i300000000
χ3422-2-22222-1-2-2-2-1-12-11111-2-2-122-1-12-1-1-1-2-2-211111100-1-1−i3i3−i3i3110000−i3−i3i3i3−i3−i3i3i3-2-2221111-1-1-1-1000000i3−i30000−i3i300000000
χ3522-2-22222-1-2-2-2-1-12-11111-2-2-122-1-12-1-1-1-2-2-211111100-1-1i3−i3i3−i3110000i3i3−i3−i3i3i3−i3−i322-2-2-1-1-1-11111000000i3−i30000−i3i300000000
χ3622-2-22222-1-2-2-2-1-12-11111-2-2-122-1-12-1-1-1-2-2-211111100-1-1i3−i3i3−i3110000i3i3−i3−i3i3i3−i3−i3-2-2221111-1-1-1-1000000−i3i30000i3−i300000000
χ3722-2-22-2-22222-2-2-222-2-222-2-222-22-2-22-2-2-222-22-2-222002-20000-22000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ3822-2-22-2-22222-2-2-222-2-222-2-222-22-2-22-2-2-222-22-2-222002-20000-2200000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ3922-2-22-2-2-1222-2-2-2-12-2-22211-1-112-21-1111-1-1-2211-1-100-1100001-13−33−33−33−33−33−30000000000000000−i3i3002i−2ii3−i300−ii−ii0000
χ4022-2-22-2-2-1222-2-2-2-12-2-22211-1-112-21-1111-1-1-2211-1-100-1100001-13−33−33−33−33−33−30000000000000000i3−i300−2i2i−i3i300i−ii−i0000
χ4122-2-22-2-2-1222-2-2-2-12-2-22211-1-112-21-1111-1-1-2211-1-100-1100001-1−33−33−33−33−33−330000000000000000−i3i300−2i2ii3−i300i−ii−i0000
χ4222-2-22-2-2-1222-2-2-2-12-2-22211-1-112-21-1111-1-1-2211-1-100-1100001-1−33−33−33−33−33−330000000000000000i3−i3002i−2i−i3i300−ii−ii0000
χ4322-2-2-22-222-2222222-2-2-2-2-2-22-2-2-2-222222-2222-2-2-2-200-2-200002200000000000000000000000020-2000220000-2-200000000
χ4422-2-2-22-222-2222222-2-2-2-2-2-22-2-2-2-222222-2222-2-2-2-200-2-2000022000000000000000000000000-202000-2-200002200000000
χ4522-2-2-22-22-1-222-1-12-11111-2-2-1-2-2112-1-1-12-22-1-111110011−i3i3i3−i3-1-10000−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i3i3i3−i3−i320-2000-1-100001100000000
χ4622-2-2-22-22-1-222-1-12-11111-2-2-1-2-2112-1-1-12-22-1-111110011−i3i3i3−i3-1-10000−i3−i3i3i3i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i3-202000110000-1-100000000
χ4722-2-2-22-22-1-222-1-12-11111-2-2-1-2-2112-1-1-12-22-1-111110011i3−i3−i3i3-1-10000i3i3−i3−i3−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3-202000110000-1-100000000
χ4822-2-2-22-22-1-222-1-12-11111-2-2-1-2-2112-1-1-12-22-1-111110011i3−i3−i3i3-1-10000i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3−i3−i3i3i320-2000-1-100001100000000
χ4922-2-2-2-22222-22-2-222-2-222-2-22-22-22-22-2-222-22-2-2-22200-2200002-2000000000000000000000000020-2220000-2-20000000000
χ5022-2-2-2-22222-22-2-222-2-222-2-22-22-22-22-2-222-22-2-2-22200-2200002-20000000000000000000000000-202-2-20000220000000000
χ5122-2-2-2-22-122-22-2-2-12-2-22211-11-1-221-111-1-112-211-1-1001-10000-113−3−333−33−3−33−33000000000000020-2-1-1000011003−3−330000
χ5222-2-2-2-22-122-22-2-2-12-2-22211-11-1-221-111-1-112-211-1-1001-10000-113−3−333−33−3−33−330000000000000-202110000-1-100−333−30000
χ5322-2-2-2-22-122-22-2-2-12-2-22211-11-1-221-111-1-112-211-1-1001-10000-11−333−3−33−333−33−3000000000000020-2-1-100001100−333−30000
χ5422-2-2-2-22-122-22-2-2-12-2-22211-11-1-221-111-1-112-211-1-1001-10000-11−333−3−33−333−33−30000000000000-202110000-1-1003−3−330000
χ554444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-211114411-2-2-2-211-2-2-2-2111111110000000000000000000000000000000000
χ564444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-2-21111-4-4112222112222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ5744444-4-44-2-4-44224-2-2-22244-24-4-22-4-2224-4-4-22-2-22200-220000-220000000000000000000000000000000000000000000000
χ5844444-4-4-24-4-44-4-4-2444-4-4-2-2-2-224-42-222-2224-4-2-22200-220000-220000000000000000000000000000000000000000000000
χ5944444-4-4-2-2-4-4422-2-2-2-222-2-21-22-2221-1-1-222-2211-1-1001-100001-100003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000000000
χ6044444-4-4-2-2-4-4422-2-2-2-222-2-21-22-2221-1-1-222-2211-1-1001-100001-10000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000000000
χ614444-44-4-2-24-4-4-2-2-2-2-2-2-2-2-2-212222-21112-222211114-4-1-1-2-222-1-1-2-2221111-1-1-1-10000000000000000000000000000000000
χ624444-44-4-2-24-4-4-2-2-2-2-2-2-2-2-2-212222-21112-22221111-44-1-122-2-2-1-122-2-2-1-1-1-111110000000000000000000000000000000000
χ634444-4-444-2-44-4224-2-2-22244-2-442-2-4-222-4-442-2-2-222002-200002-20000000000000000000000000000000000000000000000
χ644444-4-44-24-44-4-4-4-2444-4-4-2-2-22-2-442-22222-2-44-2-222002-200002-20000000000000000000000000000000000000000000000
χ654444-4-44-2-2-44-422-2-2-2-222-2-212-22-221-1-122-22-211-1-100-110000-1100003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000000000
χ664444-4-44-2-2-44-422-2-2-2-222-2-212-22-221-1-122-22-211-1-100-110000-110000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000000000
χ6744-4-4444-24-4-4-444-24-4-4-4-422-2-2-244-2-2-2-2222-4-4222200-2-20000220000000000000000000000000000000000000000000000
χ6844-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2-211122222-1-1-1-10011−2i32i3−2i32i3-1-10000i3i3−i3−i3i3i3−i3−i30000000000000000000000000000000000
χ6944-4-4444-2-2-4-4-4-2-2-2-22222221-2-2-2-2-211122222-1-1-1-100112i3−2i32i3−2i3-1-10000−i3−i3i3i3−i3−i3i3i30000000000000000000000000000000000
χ7044-4-44-4-44-244-4224-222-2-2-4-4-24-4-22-4-222-4442-222-2-200-2200002-20000000000000000000000000000000000000000000000
χ7144-4-44-4-4-2-244-422-2-222-2-2221-22-2221-1-12-2-22-2-1-111001-10000-1123−2323−23−33−33−33−330000000000000000000000000000000000
χ7244-4-44-4-4-2-244-422-2-222-2-2221-22-2221-1-12-2-22-2-1-111001-10000-11−2323−23233−33−33−33−30000000000000000000000000000000000
χ7344-4-4-44-4-24-44444-24-4-4-4-422-222-4-4-2-2-2-2-22-244222200220000-2-20000000000000000000000000000000000000000000000
χ7444-4-4-44-4-2-2-444-2-2-2-222222212222-2111-22-2-2-2-1-1-1-100-1-1−2i32i32i3−2i3110000i3i3−i3−i3−i3−i3i3i30000000000000000000000000000000000
χ7544-4-4-44-4-2-2-444-2-2-2-222222212222-2111-22-2-2-2-1-1-1-100-1-12i3−2i3−2i32i3110000−i3−i3i3i3i3i3−i3−i30000000000000000000000000000000000
χ7644-4-4-4-444-24-44224-222-2-2-4-4-2-442-2-4-22244-4-2222-2-2002-20000-220000000000000000000000000000000000000000000000
χ7744-4-4-4-44-2-24-4422-2-222-2-22212-22-221-1-1-2-22-22-1-11100-1100001-123−23−2323−33−333−33−30000000000000000000000000000000000
χ7844-4-4-4-44-2-24-4422-2-222-2-22212-22-221-1-1-2-22-22-1-11100-1100001-1−232323−233−33−3−33−330000000000000000000000000000000000
χ794-44i−4i0004400000-4-44i−4i004i−4i400000-400000004i−4i0000000000000000000000002-22i−2i2-22-22i−2i2i−2i0000000000000000000000
χ804-44i−4i0004400000-4-44i−4i004i−4i400000-400000004i−4i000000000000000000000000-22−2i2i-22-22−2i2i−2i2i0000000000000000000000
χ814-44i−4i0004-2000−2i32i3-42−2i2i23−234i−4i-2000002−2i32i300000−2i2i23−2300000000000000000000002-22i−2i−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ824-44i−4i0004-2000−2i32i3-42−2i2i23−234i−4i-2000002−2i32i300000−2i2i23−230000000000000000000000-22−2i2i1−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ834-44i−4i0004-20002i3−2i3-42−2i2i−23234i−4i-20000022i3−2i300000−2i2i−232300000000000000000000002-22i−2i−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ844-44i−4i0004-20002i3−2i3-42−2i2i−23234i−4i-20000022i3−2i300000−2i2i−23230000000000000000000000-22−2i2i1+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ854-4−4i4i0004400000-4-4−4i4i00−4i4i400000-40000000−4i4i0000000000000000000000002-2−2i2i2-22-2−2i2i−2i2i0000000000000000000000
χ864-4−4i4i0004400000-4-4−4i4i00−4i4i400000-40000000−4i4i000000000000000000000000-222i−2i-22-222i−2i2i−2i0000000000000000000000
χ874-4−4i4i0004-2000−2i32i3-422i−2i−2323−4i4i-2000002−2i32i3000002i−2i−232300000000000000000000002-2−2i2i−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ884-4−4i4i0004-2000−2i32i3-422i−2i−2323−4i4i-2000002−2i32i3000002i−2i−23230000000000000000000000-222i−2i1−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ894-4−4i4i0004-20002i3−2i3-422i−2i23−23−4i4i-20000022i3−2i3000002i−2i23−2300000000000000000000002-2−2i2i−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ904-4−4i4i0004-20002i3−2i3-422i−2i23−23−4i4i-20000022i3−2i3000002i−2i23−230000000000000000000000-222i−2i1+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ918-88i−8i000-48000004-88i−8i00−4i4i-40000040000000−4i4i0000000000000000000000000000000000000000000000000000000000
χ928-88i−8i000-4-4000−4i34i344−4i4i43−43−4i4i200000-22i3−2i3000002i−2i−232300000000000000000000000000000000000000000000000000000000
χ938-88i−8i000-4-40004i3−4i344−4i4i−4343−4i4i200000-2−2i32i3000002i−2i23−2300000000000000000000000000000000000000000000000000000000
χ948-8−8i8i000-48000004-8−8i8i004i−4i-400000400000004i−4i0000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i000-4-4000−4i34i3444i−4i−43434i−4i200000-22i3−2i300000−2i2i23−2300000000000000000000000000000000000000000000000000000000
χ968-8−8i8i000-4-40004i3−4i3444i−4i43−434i−4i200000-2−2i32i300000−2i2i−232300000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.