Finite Group Databasebeta

← Group #13049536

Character table — Group #13049536

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222222244444444444444446668888888888991212121212121212121212121818181818181818181836363636363636365454545454108108
order1233336666333333336666666641212333336666622121212121212121212121212446666121212126612121212121244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-11-1-111-1-1
χ3111111111111111111111111111111111111111-1-11111111111111-1-1-1-1-111-1-1-1-11-111-1-1-11-1-1-11-1
χ4111111111111111111111111111111111111111-1-1111111111111-11-1-1-1-1-1-111-1-1-11-1-111-1-11-1-1-11
χ511111111111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-11-111-1-11-1111-11
χ811111111111111111111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-11-1-11111-1111-1
χ922222-12-122222-1-1-1-1-1-12-1-1-1-1222-1-12-1-1-1-12-1-1-1-1222222-1-1-1-1-1-1-1-10022-1-10000-1-1000000200-1-100
χ1022222-12-122222-1-1-1-1-1-12-1-1-1-1222-1-12-1-1-1-12-1-1-1-1-2-22222-1-1-1-1-1-1-1-100-2-211000011000000-2001100
χ1122222-12-122222-1-1-1-1-1-12-1-1-1-122-2112-1-1-1-12-1-1-1-122-2-2-2-2111111110022-1-10000-1-1000000-2001100
χ1222222-12-122222-1-1-1-1-1-12-1-1-1-122-2112-1-1-1-12-1-1-1-1-2-2-2-2-2-21111111100-2-211000011000000200-1-100
χ132222-12-12222-1-12222-1-122222-1-1000-1-1-1-1-1-1-1-1-1-12200000000000022-1-122-1-1-1-1-1-122-1-1-1-10000000
χ142222-12-12222-1-12222-1-122222-1-1000-1-1-1-1-1-1-1-1-1-122000000000000-2-2-1-1221111-1-1-2-211110000000
χ152222-12-12222-1-12222-1-122222-1-1000-1-1-1-1-1-1-1-1-1-1-2-20000000000002-211-2-2-1-111112-2-1-1110000000
χ162222-12-12222-1-12222-1-122222-1-1000-1-1-1-1-1-1-1-1-1-1-2-2000000000000-2211-2-211-1-111-2211-1-10000000
χ17222-122222-1-12-12-1-1-122-12-1-1-12-1222-12-1-1-1-12-1-1-1002-1-1-122-1-1-1-1-1-10200000022000-100-1-1002000-1
χ18222-122222-1-12-12-1-1-122-12-1-1-12-1222-12-1-1-1-12-1-1-1002-1-1-122-1-1-1-1-1-10-2000000-2-20001001100-20001
χ19222-122222-1-12-12-1-1-122-12-1-1-12-1-2-2-2-12-1-1-1-12-1-1-100-2111-2-21111110200000022000-100-1-100-20001
χ20222-122222-1-12-12-1-1-122-12-1-1-12-1-2-2-2-12-1-1-1-12-1-1-100-2111-2-21111110-2000000-2-200010011002000-1
χ2122-122222-12-1-12-12-1-122-1-12-1-1-12222-1-12-1-1-1-12-1-100-12-1-1-1-122-1-1-1-1200000220000-10-1-10002000-10
χ2222-122222-12-1-12-12-1-122-1-12-1-1-12222-1-12-1-1-1-12-1-100-12-1-1-1-122-1-1-1-1-200000-2-200001011000-200010
χ2322-122222-12-1-12-12-1-122-1-12-1-1-12-2-2-2-1-12-1-1-1-12-1-1001-21111-2-21111200000220000-10-1-1000-200010
χ2422-122222-12-1-12-12-1-122-1-12-1-1-12-2-2-2-1-12-1-1-1-12-1-1001-21111-2-21111-200000-2-2000010110002000-10
χ252-22222-2-2-2-222222222-2-2-2-2-2-2-2-200022222-2-2-2-2-22-2000000000000002-22-200002-20000000000000
χ262-22222-2-2-2-222222222-2-2-2-2-2-2-2-200022222-2-2-2-2-2-2200000000000000-22-220000-220000000000000
χ272-2222-1-21-2-2222-1-1-1-1-11-21111-2-203−32-1-1-1-1-211112-200003−33−333−3−3002-2-110000-110000000003−300
χ282-2222-1-21-2-2222-1-1-1-1-11-21111-2-203−32-1-1-1-1-21111-2200003−33−333−3−300-221-100001-1000000000−3300
χ292-2222-1-21-2-2222-1-1-1-1-11-21111-2-20−332-1-1-1-1-211112-20000−33−33−3−333002-2-110000-11000000000−3300
χ302-2222-1-21-2-2222-1-1-1-1-11-21111-2-20−332-1-1-1-1-21111-220000−33−33−3−33300-221-100001-10000000003−300
χ312-222-121-2-2-22-1-12222-11-2-2-2-2-211000-1-1-1-1-1111112-200000000000000-112-23−33−3-11003−33−30000000
χ322-222-121-2-2-22-1-12222-11-2-2-2-2-211000-1-1-1-1-1111112-200000000000000-112-2−33−33-1100−33−330000000
χ332-222-121-2-2-22-1-12222-11-2-2-2-2-211000-1-1-1-1-111111-22000000000000001-1-223−3−331-1003−3−330000000
χ342-222-121-2-2-22-1-12222-11-2-2-2-2-211000-1-1-1-1-111111-22000000000000001-1-22−333−31-100−333−30000000
χ354444-2-2-2-2444-2-2-2-2-2-2114-2-2-2-2-2-2000-21111-211114400000000000000-2-2-2-20000110000000000000
χ364444-2-2-2-2444-2-2-2-2-2-2114-2-2-2-2-2-2000-21111-21111-4-40000000000000022220000-1-10000000000000
χ37444-24-24-24-2-24-2-2111-2-2-2-21114-24-2-2-2-2111-2-2111004-2-2-2-2-21111110000000000000000000000000
χ38444-24-24-24-2-24-2-2111-2-2-2-21114-2-422-2-2111-2-211100-422222-1-1-1-1-1-10000000000000000000000000
χ39444-2-24-244-2-2-214-2-2-2-2-2-24-2-2-2-210001-21111-21110000000000000004000000-2-2000-200110000000
χ40444-2-24-244-2-2-214-2-2-2-2-2-24-2-2-2-210001-21111-2111000000000000000-400000022000200-1-10000000
χ4144-244-24-2-24-2-241-211-2-2-21-211-244-2-2-21-211-21-21100-24-2-211-2-211110000000000000000000000000
χ4244-244-24-2-24-2-241-211-2-2-21-211-24-422-21-211-21-211002-422-1-122-1-1-1-10000000000000000000000000
χ4344-24-24-24-24-21-2-24-2-2-2-2-2-24-2-21-200011-21111-21100000000000000400000-2-20000-2011000000000
χ4444-24-24-24-24-21-2-24-2-2-2-2-2-24-2-21-200011-21111-21100000000000000-40000022000020-1-1000000000
χ4544-2-24444-2-21-2-2-2-211441-2-211-2-24441-2-2111-2-21100-2-211-2-2-2-211110000000000000000000000000
χ4644-2-24444-2-21-2-2-2-211441-2-211-2-2-4-4-41-2-2111-2-2110022-1-12222-1-1-1-10000000000000000000000000
χ4744-2-24-24-2-2-21-2-211−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-2-24-2-2111−1−3i32−1+3i32111−1−3i32−1+3i3200-2-2111111−1−3i32−1+3i32−1−3i32−1+3i320000000000000000000000000
χ4844-2-24-24-2-2-21-2-211−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-2-2-422111−1−3i32−1+3i32111−1−3i32−1+3i320022-1-1-1-1-1-11+3i321−3i321+3i321−3i320000000000000000000000000
χ4944-2-24-24-2-2-21-2-211−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-2-24-2-2111−1+3i32−1−3i32111−1+3i32−1−3i3200-2-2111111−1+3i32−1−3i32−1+3i32−1−3i320000000000000000000000000
χ5044-2-24-24-2-2-21-2-211−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-2-2-422111−1+3i32−1−3i32111−1+3i32−1−3i320022-1-1-1-1-1-11−3i321+3i321−3i321+3i320000000000000000000000000
χ514-444-2-222-4-44-2-2-2-2-2-21-1-4222222000-211112-1-1-1-14-400000000000000-22-2200001-10000000000000
χ524-444-2-222-4-44-2-2-2-2-2-21-1-4222222000-211112-1-1-1-1-44000000000000002-22-20000-110000000000000
χ534-44-244-4-4-42-24-24-2-2-24-42-4222-42000-24-2-2-22-4222000000000000000000000000000000000000000
χ544-44-24-2-42-42-24-2-2111-2222-1-1-1-42023−23-2-211122-1-1-100000023−23−33−3−3330000000000000000000000000
χ554-44-24-2-42-42-24-2-2111-2222-1-1-1-420−2323-2-211122-1-1-1000000−23233−333−3−30000000000000000000000000
χ564-44-2-242-4-42-2-214-2-2-2-222-42222-10001-2111-12-1-1-1000000000000000000000023−23000000−330000000
χ574-44-2-242-4-42-2-214-2-2-2-222-42222-10001-2111-12-1-1-10000000000000000000000−23230000003−30000000
χ584-4-2444-4-42-4-2-24-24-2-24-422-4222-4000-2-24-2-222-422000000000000000000000000000000000000000
χ594-4-244-2-422-4-2-241-211-222-12-1-12-4023−23-21-2112-12-1-1000000−3323−23−3−3330000000000000000000000000
χ604-4-244-2-422-4-2-241-211-222-12-1-12-40−2323-21-2112-12-1-10000003−3−232333−3−30000000000000000000000000
χ614-4-24-242-42-4-21-2-24-2-2-2222-422-1200011-211-1-12-1-10000000000000000000023−23000000−33000000000
χ624-4-24-242-42-4-21-2-24-2-2-2222-422-1200011-211-1-12-1-100000000000000000000−23230000003−3000000000
χ634-4-2-244-4-4221-2-2-2-2114-4-122-1-1220001-2-211-122-1-100003i−3i00003i−3i−3i3i0000000000000000000000000
χ644-4-2-244-4-4221-2-2-2-2114-4-122-1-1220001-2-211-122-1-10000−3i3i0000−3i3i3i−3i0000000000000000000000000
χ654-4-2-24-2-42221-2-211−1−3i32−1+3i32-22-1-1-11+3i321−3i3222023−23111−1−3i32−1+3i32-1-1-11+3i321−3i3200003i−3i−33−33ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ110000000000000000000000000
χ664-4-2-24-2-42221-2-211−1−3i32−1+3i32-22-1-1-11+3i321−3i32220−2323111−1−3i32−1+3i32-1-1-11+3i321−3i320000−3i3i3−33−3−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ110000000000000000000000000
χ674-4-2-24-2-42221-2-211−1+3i32−1−3i32-22-1-1-11−3i321+3i3222023−23111−1+3i32−1−3i32-1-1-11−3i321+3i320000−3i3i−33−33−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ110000000000000000000000000
χ684-4-2-24-2-42221-2-211−1+3i32−1−3i32-22-1-1-11−3i321+3i32220−2323111−1+3i32−1−3i32-1-1-11−3i321+3i3200003i−3i3−33−32ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ110000000000000000000000000
χ69888-4-4-4-4-48-4-4-42-422222-4-4222-4200022-1-1-122-1-1-1000000000000000000000000000000000000000
χ7088-48-4-4-4-4-48-42-42-42222-42-4222-40002-12-1-12-12-1-1000000000000000000000000000000000000000
χ7188-4-4-48-48-4-4222-4-422-4-42-4-42222000-122-1-1-122-1-1000000000000000000000000000000000000000
χ7288-4-4-4-4-4-4-4-422222−1−3i3−1+3i322222−1−3i3−1+3i322000-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000000000000000000
χ7388-4-4-4-4-4-4-4-422222−1+3i3−1−3i322222−1+3i3−1−3i322000-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000000000000000000
χ748-88-4-4-444-84-4-42-42222-244-2-2-24-200022-1-1-1-2-2111000000000000000000000000000000000000000
χ758-8-48-4-4444-8-42-42-4222-24-24-2-2-240002-12-1-1-21-211000000000000000000000000000000000000000
χ768-8-4-4-484-844222-4-422-44-244-2-2-2-2000-122-1-11-2-211000000000000000000000000000000000000000
χ778-8-4-4-4-4444422222−1−3i3−1+3i32-2-2-2-21+3i31−3i3-2-2000-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000000000
χ788-8-4-4-4-4444422222−1+3i3−1−3i32-2-2-2-21−3i31+3i3-2-2000-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000000000

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