Finite Group Databasebeta

← Group #13155078

Character table — Group #13155078

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222244444444444444888888888888888888181818181818363636363636363636363636363636363636363636363636363636727272727272
order12223446663366666612121212121233666666121212121212121212122266664444488881212121212121212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i−i−iii11iiii−i−i−i−i−i−i−i−iiiii-11-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iiiii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-11-1-111
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1-111-1-1
χ9222222222222222222222222222222222222222222-2-2-2-2-2-2-200000000-2-20000000000000000000000
χ1022222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2222222-200000000-2-20000000000000000000000
χ112222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1222220000-1-1-1-1-1-1-1-1-1-100000000000000
χ122222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12-2-2-2-20000-1-11111111100000000000000
χ132222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2000000001133−3−333−3−300000000000000
χ142222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-20000000011−3−333−3−33300000000000000
χ152222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-20000000011−i3−i3i3i3i3i3−i3−i300000000000000
χ162222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-1-1-20000000011i3i3−i3−i3−i3−i3i3i300000000000000
χ172222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2111122i2i−2i−2i0000-1-1−i−i−i−iiiii00000000000000
χ182222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-211112−2i−2i2i2i0000-1-1iiii−i−i−i−i00000000000000
χ1922-2-22002-2-22222-2-2-2-20000002222-2-2-2-200000000002-222-2-2000002−22−2000000000022−2−222−2−2000000
χ2022-2-22002-2-22222-2-2-2-20000002222-2-2-2-200000000002-222-2-200000−22−220000000000−2−222−2−222000000
χ2122-2-22002-2-22222-2-2-2-20000002222-2-2-2-20000000000-22-2-22200000−i2i2i2−i20000000000−i2−i2i2i2i2i2−i2−i2000000
χ2222-2-22002-2-22222-2-2-2-20000002222-2-2-2-20000000000-22-2-22200000i2−i2−i2i20000000000i2i2−i2−i2−i2−i2i2i2000000
χ232-22-222i−2i-22-222-2-22-22-22i−2i2i−2i2i−2i22-2-222-2-22i−2i2i2i2i2i−2i−2i−2i−2i00000001+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ242-22-222i−2i-22-222-2-22-22-22i−2i2i−2i2i−2i22-2-222-2-22i−2i2i2i2i2i−2i−2i−2i−2i0000000−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ252-22-22−2i2i-22-222-2-22-22-2−2i2i−2i2i−2i2i22-2-222-2-2−2i2i−2i−2i−2i−2i2i2i2i2i00000001−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ262-22-22−2i2i-22-222-2-22-22-2−2i2i−2i2i−2i2i22-2-222-2-2−2i2i−2i−2i−2i−2i2i2i2i2i0000000−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ272-22-2-12i−2i1-1122-2-22-22-2−ii2i−2i2i−2i-1-111-1-1112i−2i−i−i−i−iiiii00−i3i3−i3i301+i−1−i1−i−1+i00003−3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ1400000000000000
χ282-22-2-12i−2i1-1122-2-22-22-2−ii2i−2i2i−2i-1-111-1-1112i−2i−i−i−i−iiiii00−i3i3−i3i30−1−i1+i−1+i1−i00003−3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ1400000000000000
χ292-22-2-12i−2i1-1122-2-22-22-2−ii2i−2i2i−2i-1-111-1-1112i−2i−i−i−i−iiiii00i3−i3i3−i301+i−1−i1−i−1+i0000−33−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ2200000000000000
χ302-22-2-12i−2i1-1122-2-22-22-2−ii2i−2i2i−2i-1-111-1-1112i−2i−i−i−i−iiiii00i3−i3i3−i30−1−i1+i−1+i1−i0000−33ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ2200000000000000
χ312-22-2-1−2i2i1-1122-2-22-22-2i−i−2i2i−2i2i-1-111-1-111−2i2iiiii−i−i−i−i00−i3i3−i3i301−i−1+i1+i−1−i0000−33−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ1400000000000000
χ322-22-2-1−2i2i1-1122-2-22-22-2i−i−2i2i−2i2i-1-111-1-111−2i2iiiii−i−i−i−i00−i3i3−i3i30−1+i1−i−1−i1+i0000−33ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ1400000000000000
χ332-22-2-1−2i2i1-1122-2-22-22-2i−i−2i2i−2i2i-1-111-1-111−2i2iiiii−i−i−i−i00i3−i3i3−i301−i−1+i1+i−1−i00003−3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ2200000000000000
χ342-22-2-1−2i2i1-1122-2-22-22-2i−i−2i2i−2i2i-1-111-1-111−2i2iiiii−i−i−i−i00i3−i3i3−i30−1+i1−i−1−i1+i00003−3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ2200000000000000
χ3544444444441-21-211-2-24411111-21-21-21-2-2-211-2-211-2-20000000000022220000000000-1-1-1-1-1-1-1-1000000
χ3644444444441-21-211-2-24411111-21-21-21-2-2-211-2-211-2-200000000000-2-2-2-2000000000011111111000000
χ374444444444-21-21-2-21144-2-2-2-2-21-21-21-2111-2-211-2-21100000000000000000000000000000000022-1-1-1-1
χ384444444444-21-21-2-21144-2-2-2-2-21-21-21-2111-2-211-2-211000000000000000000000000000000000-2-21111
χ3944444-4-44441-21-211-2-2-4-4-1-1-1-11-21-21-21-222-1-122-1-122000000000002i2i−2i−2i0000000000−i−i−i−iiiii000000
χ4044444-4-44441-21-211-2-2-4-4-1-1-1-11-21-21-21-222-1-122-1-12200000000000−2i−2i2i2i0000000000iiii−i−i−i−i000000
χ4144444-4-4444-21-21-2-211-4-42222-21-21-21-21-1-122-1-122-1-10000000000000000000000000000000002-2-1-111
χ4244444-4-4444-21-21-2-211-4-42222-21-21-21-21-1-122-1-122-1-1000000000000000000000000000000000-2211-1-1
χ4344-4-44004-4-41-21-2-1-122003i−3i−3i3i1-21-2-12-12003i−3i003i−3i00000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000
χ4444-4-44004-4-41-21-2-1-122003i−3i−3i3i1-21-2-12-12003i−3i003i−3i0000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000
χ4544-4-44004-4-41-21-2-1-12200−3i3i3i−3i1-21-2-12-1200−3i3i00−3i3i0000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000
χ4644-4-44004-4-41-21-2-1-12200−3i3i3i−3i1-21-2-12-1200−3i3i00−3i3i00000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000
χ4744-4-4-200-2224444-4-4-4-4000000-2-2-2-2222200000000004-4-2-222000000000000000000000000000000000
χ4844-4-4-200-2224444-4-4-4-4000000-2-2-2-222220000000000-4422-2-2000000000000000000000000000000000
χ494-44-444i−4i-44-41-2-121-1-224i−4ii−ii−i1-2-121-2-12−2i2iii−2i−2i−i−i2i2i0000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000
χ504-44-444i−4i-44-41-2-121-1-224i−4ii−ii−i1-2-121-2-12−2i2iii−2i−2i−i−i2i2i0000000000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000
χ514-44-444i−4i-44-4-212-1-221-14i−4i−2i2i−2i2i-212-1-212-1i−i−2i−2iii2i2i−i−i00000000000000000000000000000000000−i3i33−3
χ524-44-444i−4i-44-4-212-1-221-14i−4i−2i2i−2i2i-212-1-212-1i−i−2i−2iii2i2i−i−i00000000000000000000000000000000000i3−i3−33
χ534-44-44−4i4i-44-41-2-121-1-22−4i4i−ii−ii1-2-121-2-122i−2i−i−i2i2iii−2i−2i0000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000
χ544-44-44−4i4i-44-41-2-121-1-22−4i4i−ii−ii1-2-121-2-122i−2i−i−i2i2iii−2i−2i0000000000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000
χ554-44-44−4i4i-44-4-212-1-221-1−4i4i2i−2i2i−2i-212-1-212-1−ii2i2i−i−i−2i−2iii00000000000000000000000000000000000−i3i3−33
χ564-44-44−4i4i-44-4-212-1-221-1−4i4i2i−2i2i−2i-212-1-212-1−ii2i2i−i−i−2i−2iii00000000000000000000000000000000000i3−i33−3
χ574-4-44400-4-441-2-12-112-20033-3-31-2-12-121-2003-300-33000000000000000000000000000−i3i3i3−i3i3−i3−i3i3000000
χ584-4-44400-4-441-2-12-112-20033-3-31-2-12-121-2003-300-33000000000000000000000000000i3−i3−i3i3−i3i3i3−i3000000
χ594-4-44400-4-441-2-12-112-200-3-3331-2-12-121-200-33003-30000000000000000000000000003−3−333−3−33000000
χ604-4-44400-4-441-2-12-112-200-3-3331-2-12-121-200-33003-3000000000000000000000000000−333−3−333−3000000
χ614-4-44400-4-4444-4-4-44-4400000044-4-4-4-4440000000000000000000000000000000000000000000000000
χ624-4-44-20022-244-4-4-44-44000000-2-22222-2-2000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ634-4-44-20022-244-4-4-44-44000000-2-22222-2-20000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ648888-488-4-4-42-42-422-4-4-4-42222-12-12-12-12-4-4-1-122-1-122000000000000000000000000000000000000000
χ658888-488-4-4-4-42-42-4-422-4-4-4-4-4-42-12-12-12-12222-1-122-1-1000000000000000000000000000000000000000
χ668888-4-8-8-4-4-42-42-422-4-444-2-2-2-2-12-12-12-124411-2-211-2-2000000000000000000000000000000000000000
χ678888-4-8-8-4-4-4-42-42-4-4224444442-12-12-12-1-2-2-2-211-2-211000000000000000000000000000000000000000
χ6888-8-88008-8-8-42-4244-2-2000000-42-424-24-20000000000000000000000000000000000000000000000000
χ6988-8-8-400-4442-42-4-2-244006i−6i−6i6i-12-121-21-200−3i3i00−3i3i00000000000000000000000000000000000000000
χ7088-8-8-400-4442-42-4-2-24400−6i6i6i−6i-12-121-21-2003i−3i003i−3i00000000000000000000000000000000000000000
χ7188-8-8-400-444-42-4244-2-20000002-12-1-21-21000033−330033−33000000000000000000000000000000000000000
χ7288-8-8-400-444-42-4244-2-20000002-12-1-21-210000−333300−3333000000000000000000000000000000000000000
χ738-88-8-48i−8i4-442-4-242-2-44−4i4i2i−2i2i−2i-121-2-121-2−4i4i−i−i2i2iii−2i−2i000000000000000000000000000000000000000
χ748-88-8-48i−8i4-44-424-2-442-2−4i4i−4i4i−4i4i2-1-212-1-212i−2i2i2i−i−i−2i−2iii000000000000000000000000000000000000000
χ758-88-8-4−8i8i4-442-4-242-2-444i−4i−2i2i−2i2i-121-2-121-24i−4iii−2i−2i−i−i2i2i000000000000000000000000000000000000000
χ768-88-8-4−8i8i4-44-424-2-442-24i−4i4i−4i4i−4i2-1-212-1-21−2i2i−2i−2iii2i2i−i−i000000000000000000000000000000000000000
χ778-8-88800-8-88-424-24-4-22000000-424-24-2-420000000000000000000000000000000000000000000000000
χ788-8-88-40044-42-4-24-224-40066-6-6-121-21-2-1200-33003-300000000000000000000000000000000000000000
χ798-8-88-40044-42-4-24-224-400-6-666-121-21-2-12003-300-3300000000000000000000000000000000000000000
χ808-8-88-40044-4-424-24-4-220000002-1-21-212-10000−3i33i3003i3−3i3000000000000000000000000000000000000000
χ818-8-88-40044-4-424-24-4-220000002-1-21-212-100003i3−3i300−3i33i3000000000000000000000000000000000000000

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