Finite Group Databasebeta

← Group #13048751

Character table — Group #13048751

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222222666666661212121212121212121212121212121212121212181818181818181818181818181818181818545454545454545454545454
order1244333366661212121212121212336612121212333336666612121212121212121212246666666612121212121212122244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111
χ611-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1
χ711-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1
χ811-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111
χ9222222222222222222222-12-122-1-12-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000020200-1-100-1-1
χ10222222222222222222222-12-122-1-12-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000-20-200110011
χ1122222222222222222222-12-12-1-122-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10000000000000000002020-1-100-1-100
χ1222222222222222222222-12-12-1-122-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1000000000000000000-20-2011001100
χ1322222-1-1-12-1-1-122-1-1-1-1-1-122222222-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ1422222-1-1-12-1-1-122-1-1-1-1-1-122222222-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111-2-2111111000000000000
χ1522-2-222222222-2-2-2-2-2-2-2-22-12-1-2-2112-1-1-1-12-1-1-1-1-2-211111111000000000000000000020-200-1-10011
χ1622-2-222222222-2-2-2-2-2-2-2-22-12-1-2-2112-1-1-1-12-1-1-1-1-2-2111111110000000000000000000-202001100-1-1
χ1722-2-222222222-2-2-2-2-2-2-2-2-12-1211-2-2-12-1-1-1-12-1-1-111-2-211111100000000000000000020-20-1-1001100
χ1822-2-222222222-2-2-2-2-2-2-2-2-12-1211-2-2-12-1-1-1-12-1-1-111-2-2111111000000000000000000-20201100-1-100
χ1922-2-22-1-1-12-1-1-1-2-21111112222-2-2-2-2-1-12-1-1-1-12-1-11111-2-211112-222-1-1-1-1-1-1-2-2111111000000000000
χ2022-2-22-1-1-12-1-1-1-2-21111112222-2-2-2-2-1-12-1-1-1-12-1-11111-2-21111-22-2-211111122-1-1-1-1-1-1000000000000
χ212-22i−2i2222-2-2-2-22i−2i2i2i2i−2i−2i−2i22-2-22i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000000
χ222-22i−2i2222-2-2-2-22i−2i2i2i2i−2i−2i−2i2-1-212i−2i−ii2-1-1-1-1-211112i−2i−ii−ii−i−iii000000000000000000000000−i3i3003−3
χ232-22i−2i2222-2-2-2-22i−2i2i2i2i−2i−2i−2i2-1-212i−2i−ii2-1-1-1-1-211112i−2i−ii−ii−i−iii000000000000000000000000i3−i300−33
χ242-22i−2i2222-2-2-2-22i−2i2i2i2i−2i−2i−2i-121-2−ii2i−2i-12-1-1-11-2111−ii2i−2i−ii−i−iii0000000000000000000000−i3i3003−300
χ252-22i−2i2222-2-2-2-22i−2i2i2i2i−2i−2i−2i-121-2−ii2i−2i-12-1-1-11-2111−ii2i−2i−ii−i−iii0000000000000000000000i3−i300−3300
χ262-22i−2i2-1-1-1-21112i−2i−i−i−iiii22-2-22i−2i2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000−i3−i3−i3i3i3i300333−3−3−3000000000000
χ272-22i−2i2-1-1-1-21112i−2i−i−i−iiii22-2-22i−2i2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000i3i3i3−i3−i3−i300−3−3−3333000000000000
χ282-2−2i2i2222-2-2-2-2−2i2i−2i−2i−2i2i2i2i22-2-2−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000
χ292-2−2i2i2222-2-2-2-2−2i2i−2i−2i−2i2i2i2i2-1-21−2i2ii−i2-1-1-1-1-21111−2i2ii−ii−iii−i−i000000000000000000000000−i3i300−33
χ302-2−2i2i2222-2-2-2-2−2i2i−2i−2i−2i2i2i2i2-1-21−2i2ii−i2-1-1-1-1-21111−2i2ii−ii−iii−i−i000000000000000000000000i3−i3003−3
χ312-2−2i2i2222-2-2-2-2−2i2i−2i−2i−2i2i2i2i-121-2i−i−2i2i-12-1-1-11-2111i−i−2i2ii−iii−i−i0000000000000000000000−i3i300−3300
χ322-2−2i2i2222-2-2-2-2−2i2i−2i−2i−2i2i2i2i-121-2i−i−2i2i-12-1-1-11-2111i−i−2i2ii−iii−i−i0000000000000000000000i3−i3003−300
χ332-2−2i2i2-1-1-1-2111−2i2iiii−i−i−i22-2-2−2i2i−2i2i-1-12-1-111-211i−ii−i−2i2iii−i−i0000−i3−i3−i3i3i3i300−3−3−3333000000000000
χ342-2−2i2i2-1-1-1-2111−2i2iiii−i−i−i22-2-2−2i2i−2i2i-1-12-1-111-211i−ii−i−2i2iii−i−i0000i3i3i3−i3−i3−i300333−3−3−3000000000000
χ3544444444444444444444-2-2-2-2-2-2-2-2-2-2111-2-2111-2-2-2-2111111000000000000000000000000000000
χ3644444-2-2-24-2-2-244-2-2-2-2-2-24-24-244-2-2-21-211-21-211-2-211-2-21111000000000000000000000000000000
χ3744444-2-2-24-2-2-244-2-2-2-2-2-2-24-24-2-2441-2-2111-2-21111-2-2-2-21111000000000000000000000000000000
χ3844444-2-2-24-2-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000
χ3944444-2-2-24-2-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000
χ4044-4-444444444-4-4-4-4-4-4-4-4-2-2-2-22222-2-2111-2-21112222-1-1-1-1-1-1000000000000000000000000000000
χ4144-4-44-2-2-24-2-2-2-4-42222224-24-2-4-422-21-211-21-21122-1-122-1-1-1-1000000000000000000000000000000
χ4244-4-44-2-2-24-2-2-2-4-4222222-24-2422-4-41-2-2111-2-211-1-12222-1-1-1-1000000000000000000000000000000
χ4344-4-44-2-2-24-2-2-2-4-4222222-2-2-2-22222111−1−3i32−1+3i32111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000
χ4444-4-44-2-2-24-2-2-2-4-4222222-2-2-2-22222111−1+3i32−1−3i32111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000
χ454-44i−4i4444-4-4-4-44i−4i4i4i4i−4i−4i−4i-2-222−2i2i−2i2i-2-211122-1-1-1−2i2i−2i2ii−iii−i−i000000000000000000000000000000
χ464-44i−4i4-2-2-2-42224i−4i−2i−2i−2i2i2i2i4-2-424i−4i−2i2i-21-2112-12-1-1−2i2ii−i−2i2iii−i−i000000000000000000000000000000
χ474-44i−4i4-2-2-2-42224i−4i−2i−2i−2i2i2i2i-242-4−2i2i4i−4i1-2-211-122-1-1i−i−2i2i−2i2iii−i−i000000000000000000000000000000
χ484-44i−4i4-2-2-2-42224i−4i−2i−2i−2i2i2i2i-2-222−2i2i−2i2i111−1−3i32−1+3i32-1-1-11+3i321−3i32i−ii−ii−i−ζ7+2ζ112ζ7−ζ11ζ7−2ζ11−2ζ7+ζ11000000000000000000000000000000
χ494-44i−4i4-2-2-2-42224i−4i−2i−2i−2i2i2i2i-2-222−2i2i−2i2i111−1+3i32−1−3i32-1-1-11−3i321+3i32i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11000000000000000000000000000000
χ504-4−4i4i4444-4-4-4-4−4i4i−4i−4i−4i4i4i4i-2-2222i−2i2i−2i-2-211122-1-1-12i−2i2i−2i−ii−i−iii000000000000000000000000000000
χ514-4−4i4i4-2-2-2-4222−4i4i2i2i2i−2i−2i−2i4-2-42−4i4i2i−2i-21-2112-12-1-12i−2i−ii2i−2i−i−iii000000000000000000000000000000
χ524-4−4i4i4-2-2-2-4222−4i4i2i2i2i−2i−2i−2i-242-42i−2i−4i4i1-2-211-122-1-1−ii2i−2i2i−2i−i−iii000000000000000000000000000000
χ534-4−4i4i4-2-2-2-4222−4i4i2i2i2i−2i−2i−2i-2-2222i−2i2i−2i111−1−3i32−1+3i32-1-1-11+3i321−3i32−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11000000000000000000000000000000
χ544-4−4i4i4-2-2-2-4222−4i4i2i2i2i−2i−2i−2i-2-2222i−2i2i−2i111−1+3i32−1−3i32-1-1-11−3i321+3i32−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11000000000000000000000000000000
χ556666-36-3-3-36-3-3-3-36-3-36-3-3000000000000000000000000000022-1-12-1-12-1-1-1-12-1-12-1-1000000000000
χ566666-36-3-3-36-3-3-3-36-3-36-3-30000000000000000000000000000-2-211-211-21111-211-211000000000000
χ576666-3-36-3-3-36-3-3-3-36-3-36-3000000000000000000000000000022-1-1-12-1-12-1-1-1-12-1-12-1000000000000
χ586666-3-36-3-3-36-3-3-3-36-3-36-30000000000000000000000000000-2-2111-211-21111-211-21000000000000
χ596666-3-3-36-3-3-36-3-3-3-36-3-36000000000000000000000000000022-1-1-1-12-1-12-1-1-1-12-1-12000000000000
χ606666-3-3-36-3-3-36-3-3-3-36-3-360000000000000000000000000000-2-21111-211-21111-211-2000000000000
χ6166-6-6-36-3-3-36-3-333-633-63300000000000000000000000000002-2-1-12-1-12-1-111-211-211000000000000
χ6266-6-6-36-3-3-36-3-333-633-6330000000000000000000000000000-2211-211-211-1-12-1-12-1-1000000000000
χ6366-6-6-3-36-3-3-36-3333-633-6300000000000000000000000000002-2-1-1-12-1-12-1111-211-21000000000000
χ6466-6-6-3-36-3-3-36-3333-633-630000000000000000000000000000-22111-211-21-1-1-12-1-12-1000000000000
χ6566-6-6-3-3-36-3-3-363333-633-600000000000000000000000000002-2-1-1-1-12-1-121111-211-2000000000000
χ6666-6-6-3-3-36-3-3-363333-633-60000000000000000000000000000-221111-211-2-1-1-1-12-1-12000000000000
χ676-66i−6i-36-3-33-633−3i3i6i−3i−3i−6i3i3i000000000000000000000000000000−i3i30−i3i30i3−i33−303−30−33000000000000
χ686-66i−6i-36-3-33-633−3i3i6i−3i−3i−6i3i3i000000000000000000000000000000i3−i30i3−i30−i3i3−330−3303−3000000000000
χ696-66i−6i-3-36-333-63−3i3i−3i6i−3i3i−6i3i000000000000000000000000000000−i3i3i30−i3−i30i33−3−30330−3000000000000
χ706-66i−6i-3-36-333-63−3i3i−3i6i−3i3i−6i3i000000000000000000000000000000i3−i3−i30i3i30−i3−3330−3−303000000000000
χ716-66i−6i-3-3-36333-6−3i3i−3i−3i6i3i3i−6i000000000000000000000000000000−i3i3−i3i30i3−i303−33−30−330000000000000
χ726-66i−6i-3-3-36333-6−3i3i−3i−3i6i3i3i−6i000000000000000000000000000000i3−i3i3−i30−i3i30−33−3303−30000000000000
χ736-6−6i6i-36-3-33-6333i−3i−6i3i3i6i−3i−3i000000000000000000000000000000−i3i30−i3i30i3−i3−330−3303−3000000000000
χ746-6−6i6i-36-3-33-6333i−3i−6i3i3i6i−3i−3i000000000000000000000000000000i3−i30i3−i30−i3i33−303−30−33000000000000
χ756-6−6i6i-3-36-333-633i−3i3i−6i3i−3i6i−3i000000000000000000000000000000−i3i3i30−i3−i30i3−3330−3−303000000000000
χ766-6−6i6i-3-36-333-633i−3i3i−6i3i−3i6i−3i000000000000000000000000000000i3−i3−i30i3i30−i33−3−30330−3000000000000
χ776-6−6i6i-3-3-36333-63i−3i3i3i−6i−3i−3i6i000000000000000000000000000000−i3i3−i3i30i3−i30−33−3303−30000000000000
χ786-6−6i6i-3-3-36333-63i−3i3i3i−6i−3i−3i6i000000000000000000000000000000i3−i3i3−i30−i3i303−33−30−330000000000000

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