Finite Group Databasebeta

← Group #13047428

Character table — Group #13047428

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222333333336666666666666666666666666666181818181818181818181818181818181818181818181818545454545454545454545454
order1244234666121212123366121212123336666666666612121212121212121212121212123666991212121218181818181836363636363636362244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111-11-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-11-11-111-1-111-1-1
χ41111-11-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-1-11-11-1-111-1-111
χ511-1-111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ611-1-111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ711-1-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1111-1-111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1
χ811-1-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1111-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111
χ922222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ102222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ112222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-122-1-12-122-1-122-1-1000000000000
χ122222222222222222222222-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-122-12-1-122-1-122000000000000
χ132222-22-2-2-2222-2-222222222222-2-2-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-2-111-1-1-1-1-1111111-1-1-1-1-1-11111000000000000
χ142222-22-2-2-2222-2-222222222-1-1-1-2-2111111-1-1-1-2-2-1-1-1-1-1-11111112-2-22-1-122-2-21111-1-1-1-1-1-11111000000000000
χ152222-22-2-2-2222-2-222222222-1-1-1-2-2111111-1-1-1-2-2-1-1-1-1-1-1111111-111-12-1-1-111-2-2112-122-1-1-2-211000000000000
χ162222-22-2-2-2222-2-222222222-1-1-1-2-2111111-1-1-1-2-2-1-1-1-1-1-1111111-111-1-12-1-11111-2-2-12-1-12211-2-2000000000000
χ1722-2-222-2222-2-2-2-22222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-11111-1-1-1-1-1-111111111000000000000
χ1822-2-222-2222-2-2-2-22222-2-2-2-2-1-1-122-1-1-1-1-1-1-1-1-1-2-21111111111112222-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ1922-2-222-2222-2-2-2-22222-2-2-2-2-1-1-122-1-1-1-1-1-1-1-1-1-2-2111111111111-1-1-1-12-1111122-1-12-1-2-211-2-211000000000000
χ2022-2-222-2222-2-2-2-22222-2-2-2-2-1-1-122-1-1-1-1-1-1-1-1-1-2-2111111111111-1-1-1-1-121111-1-122-1211-2-211-2-2000000000000
χ2122-2-2-222-2-22-2-2222222-2-2-2-2222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2222222-111-1-1-111-1-11111-1-11111-1-1-1-1000000000000
χ2222-2-2-222-2-22-2-2222222-2-2-2-2-1-1-1-2-2111111-1-1-122111111-1-1-1-1-1-12-2-22-1-1-2-2221111-1-11111-1-1-1-1000000000000
χ2322-2-2-222-2-22-2-2222222-2-2-2-2-1-1-1-2-2111111-1-1-122111111-1-1-1-1-1-1-111-12-111-1-1-2-2112-1-2-21122-1-1000000000000
χ2422-2-2-222-2-22-2-2222222-2-2-2-2-1-1-1-2-2111111-1-1-122111111-1-1-1-1-1-1-111-1-1211-1-111-2-2-1211-2-2-1-122000000000000
χ252-22i−2i02000-22i−2i0022-2-22i2i−2i−2i22200000000-2-2-2002i2i2i−2i−2i−2i000000200-2222i−2i000000-2-22i−2i2i−2i0000000000000000
χ262-22i−2i02000-22i−2i0022-2-22i2i−2i−2i22200000000-2-2-2002i2i2i−2i−2i−2i000000-1−i3i31-1-1−ii3−3−i3i3−i3i311−ii−ii3−33−3000000000000
χ272-22i−2i02000-22i−2i0022-2-22i2i−2i−2i22200000000-2-2-2002i2i2i−2i−2i−2i000000-1i3−i31-1-1−ii−33i3−i3i3−i311−ii−ii−33−33000000000000
χ282-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100−i3−i3−i3i3i3i311100−i−i−iiii333−3−3−3200-2-1-12i−2i00−i3i3i3−i311−ii−ii3−3−33000000000000
χ292-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100−i3−i3−i3i3i3i311100−i−i−iiii333−3−3−3-1−i3i31-12−ii3−3i3−i3001-2−ii2i−2i−3300000000000000
χ302-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100−i3−i3−i3i3i3i311100−i−i−iiii333−3−3−3-1i3−i312-1−ii−3300−i3i3-212i−2i−ii003−3000000000000
χ312-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100i3i3i3−i3−i3−i311100−i−i−iiii−3−3−3333200-2-1-12i−2i00i3−i3−i3i311−ii−ii−333−3000000000000
χ322-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100i3i3i3−i3−i3−i311100−i−i−iiii−3−3−3333-1−i3i312-1−ii3−300i3−i3-212i−2i−ii00−33000000000000
χ332-22i−2i02000-22i−2i0022-2-22i2i−2i−2i-1-1-100i3i3i3−i3−i3−i311100−i−i−iiii−3−3−3333-1i3−i31-12−ii−33−i3i3001-2−ii2i−2i3−300000000000000
χ342-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i22200000000-2-2-200−2i−2i−2i2i2i2i000000200-222−2i2i000000-2-2−2i2i−2i2i0000000000000000
χ352-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i22200000000-2-2-200−2i−2i−2i2i2i2i000000-1−i3i31-1-1i−i−33−i3i3−i3i311i−ii−i−33−33000000000000
χ362-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i22200000000-2-2-200−2i−2i−2i2i2i2i000000-1i3−i31-1-1i−i3−3i3−i3i3−i311i−ii−i3−33−3000000000000
χ372-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100−i3−i3−i3i3i3i311100iii−i−i−i−3−3−3333200-2-1-1−2i2i00−i3i3i3−i311i−ii−i−333−3000000000000
χ382-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100−i3−i3−i3i3i3i311100iii−i−i−i−3−3−3333-1−i3i31-12i−i−33i3−i3001-2i−i−2i2i3−300000000000000
χ392-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100−i3−i3−i3i3i3i311100iii−i−i−i−3−3−3333-1i3−i312-1i−i3−300−i3i3-21−2i2ii−i00−33000000000000
χ402-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100i3i3i3−i3−i3−i311100iii−i−i−i333−3−3−3200-2-1-1−2i2i00i3−i3−i3i311i−ii−i3−3−33000000000000
χ412-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100i3i3i3−i3−i3−i311100iii−i−i−i333−3−3−3-1−i3i312-1i−i−3300i3−i3-21−2i2ii−i003−3000000000000
χ422-2−2i2i02000-2−2i2i0022-2-2−2i−2i2i2i-1-1-100i3i3i3−i3−i3−i311100iii−i−i−i333−3−3−3-1i3−i31-12i−i3−3−i3i3001-2i−i−2i2i−3300000000000000
χ4333333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+3i32000000000−3−3i32−3+3i320000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4433333333333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000−3−3i32−3+3i32000000000−3−3i32−3+3i32000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32
χ4533333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000−3+3i32−3−3i32000000000−3+3i32−3−3i320000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ4633333333333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000−3+3i32−3−3i32000000000−3+3i32−3−3i32000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32
χ473333-33-3-3-3333-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320003+3i323−3i320000000003+3i323−3i320000000000000000000000000000000000001-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ483333-33-3-3-3333-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320003+3i323−3i320000000003+3i323−3i32000000000000000000000000000000000000-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ493333-33-3-3-3333-3-3−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i320003−3i323+3i320000000003−3i323+3i320000000000000000000000000000000000001-11-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32
χ503333-33-3-3-3333-3-3−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i320003−3i323+3i320000000003−3i323+3i32000000000000000000000000000000000000-11-111−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32
χ5133-3-333-3333-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32000−3−3i32−3+3i320000000003+3i323−3i320000000000000000000000000000000000001-1-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ5233-3-333-3333-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32000−3−3i32−3+3i320000000003+3i323−3i32000000000000000000000000000000000000-111-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ5333-3-333-3333-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i32000−3+3i32−3−3i320000000003−3i323+3i320000000000000000000000000000000000001-1-11−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
χ5433-3-333-3333-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i32000−3+3i32−3−3i320000000003−3i323+3i32000000000000000000000000000000000000-111-11−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ5533-3-3-333-3-33-3-333−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320003+3i323−3i32000000000−3−3i32−3+3i3200000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ5633-3-3-333-3-33-3-333−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320003+3i323−3i32000000000−3−3i32−3+3i32000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ5733-3-3-333-3-33-3-333−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i320003−3i323+3i32000000000−3+3i32−3−3i3200000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ5833-3-3-333-3-33-3-333−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i320003−3i323+3i32000000000−3+3i32−3−3i32000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ5966666-36-3-3-3-3-3-3-30000000003-30003-303-303-30003-303-303-303-3000000000000000000000000000000000000
χ6066666-36-3-3-3-3-3-3-3000000003-30003-303-303-30003-303-303-303-30000000000000000000000000000000000000
χ6166666-36-3-3-3-3-3-3-300000000-30300-303-303-30300-303-303-303-303000000000000000000000000000000000000
χ626666-6-3-633-3-3-3330000000003-3000-330-3303-30003-303-30-330-33000000000000000000000000000000000000
χ636666-6-3-633-3-3-333000000003-3000-330-3303-30003-303-30-330-330000000000000000000000000000000000000
χ646666-6-3-633-3-3-33300000000-3030030-330-3-30300-303-30330-330-3000000000000000000000000000000000000
χ6566-6-66-3-6-3-3-333330000000003-30003-303-303-3000-330-330-330-33000000000000000000000000000000000000
χ6666-6-66-3-6-3-3-33333000000003-30003-303-303-3000-330-330-330-330000000000000000000000000000000000000
χ6766-6-66-3-6-3-3-3333300000000-30300-303-303-3030030-330-330-330-3000000000000000000000000000000000000
χ6866-6-6-6-3633-333-3-30000000003-3000-330-3303-3000-330-3303-303-3000000000000000000000000000000000000
χ6966-6-6-6-3633-333-3-3000000003-3000-330-3303-3000-330-3303-303-30000000000000000000000000000000000000
χ7066-6-6-6-3633-333-3-300000000-3030030-330-3-3030030-330-3-303-303000000000000000000000000000000000000
χ716-66i−6i06000-66i−6i00−3−3i3−3+3i33+3i33−3i36ζ116ζ7−6ζ11−6ζ70000000000000000000000000000000000000000000000000000000000000000
χ726-66i−6i06000-66i−6i00−3+3i3−3−3i33−3i33+3i36ζ76ζ11−6ζ7−6ζ110000000000000000000000000000000000000000000000000000000000000000
χ736-66i−6i0-30−3i33i33−3i3i33−330000000003-300−2i3i3i32i3−i3−i30-330003i−3i0−3i3i23−3−3−2333000000000000000000000000000000000000
χ746-66i−6i0-30−3i33i33−3i3i33−33000000003-3000i3i3−2i3−i3−i32i3-330003i−3i0−3i3i0−3−32333−23000000000000000000000000000000000000
χ756-66i−6i0-30−3i33i33−3i3i33−3300000000-30300i3−2i3i3−i32i3−i330-300−3i03i3i0−3i−323−33−233000000000000000000000000000000000000
χ766-66i−6i0-303i3−3i33−3i3i−33330000000003-3002i3−i3−i3−2i3i3i30-330003i−3i0−3i3i−233323−3−3000000000000000000000000000000000000
χ776-66i−6i0-303i3−3i33−3i3i−3333000000003-3000−i3−i32i3i3i3−2i3-330003i−3i0−3i3i033−23−3−323000000000000000000000000000000000000
χ786-66i−6i0-303i3−3i33−3i3i−333300000000-30300−i32i3−i3i3−2i3i330-300−3i03i3i0−3i3−233−323−3000000000000000000000000000000000000
χ796-6−6i6i06000-6−6i6i00−3−3i3−3+3i33+3i33−3i3−6ζ11−6ζ76ζ116ζ70000000000000000000000000000000000000000000000000000000000000000
χ806-6−6i6i06000-6−6i6i00−3+3i3−3−3i33−3i33+3i3−6ζ7−6ζ116ζ76ζ110000000000000000000000000000000000000000000000000000000000000000
χ816-6−6i6i0-30−3i33i333i−3i−33330000000003-300−2i3i3i32i3−i3−i30-33000−3i3i03i−3i−233323−3−3000000000000000000000000000000000000
χ826-6−6i6i0-30−3i33i333i−3i−3333000000003-3000i3i3−2i3−i3−i32i3-33000−3i3i03i−3i033−23−3−323000000000000000000000000000000000000
χ836-6−6i6i0-30−3i33i333i−3i−333300000000-30300i3−2i3i3−i32i3−i330-3003i0−3i−3i03i3−233−323−3000000000000000000000000000000000000
χ846-6−6i6i0-303i3−3i333i−3i33−330000000003-3002i3−i3−i3−2i3i3i30-33000−3i3i03i−3i23−3−3−2333000000000000000000000000000000000000
χ856-6−6i6i0-303i3−3i333i−3i33−33000000003-3000−i3−i32i3i3i3−2i3-33000−3i3i03i−3i0−3−32333−23000000000000000000000000000000000000
χ866-6−6i6i0-303i3−3i333i−3i33−3300000000-30300−i32i3−i3i3−2i3i330-3003i0−3i−3i03i−323−33−233000000000000000000000000000000000000

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