Finite Group Databasebeta

← Group #13166017

Character table — Group #13166017

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222333344446666668888888888881212121216161616161616161616161618181818181824242424242424242424242424243636363636363636545454547272108108
order122233666666444436664412121212333666666666121212123336666666664488881212121212121212121212121212441212242424248888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ4111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51-1-1111-111-1-1-1ii−i−i1-1-11-11ii−i−i111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1i−iii−i−i1-1iiiiii−i−i−i−i−i−ii−ii−iii−i−i11-1-1i−i1-1
χ61-1-1111-111-1-1-1ii−i−i1-1-11-11ii−i−i111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1i−i−i−iii1-1iiiiii−i−i−i−i−i−i−iii−i−i−iii-1-111−ii-11
χ71-1-1111-111-1-1-1−i−iii1-1-11-11−i−iii111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−iiii−i−i1-1−i−i−i−i−i−iiiiiiii−i−iiii−i−i-1-111i−i-11
χ81-1-1111-111-1-1-1−i−iii1-1-11-11−i−iii111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−ii−i−iii1-1−i−i−i−i−i−iiiiiii−ii−ii−i−iii11-1-1−ii1-1
χ922222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000022-1-1-1-1-1-1-1-1-1-1-1-10022000000000000
χ10222222222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200002211111111111100-2-2000000000000
χ1122222-122-1-1-122222-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-12-1-122-1-12-1-122-1-1-1-1220000-1-122-1-1-1-122-1-1-1-100-1-1000000000000
χ1222222-122-1-1-122222-1-1-1-122-1-1-1-1-12-1-12-1-12-1-12-12-1-12-12-1-12-1-1-122-1-1220000-1-1-1-122-1-1-1-122-1-100-1-1000000000000
χ1322222-122-1-1-122222-1-1-1-122-1-1-1-1-1-12-1-12-1-12-1-122-1-12-1-12-1-12-1-1-1-122220000-1-1-1-1-1-122-1-1-1-12200-1-1000000000000
χ1422222-122-1-1-12-2-2-2-2-1-1-1-12211112-1-12-1-12-1-12-1-12-1-122-1-12-1-122-1-1-1-1-2-20000-1-1-2-21111-2-211110011000000000000
χ1522222-122-1-1-12-2-2-2-2-1-1-1-1221111-12-1-12-1-12-1-12-12-1-12-12-1-12-1-1-122-1-1-2-20000-1-111-2-21111-2-2110011000000000000
χ1622222-122-1-1-12-2-2-2-2-1-1-1-1221111-1-12-1-12-1-12-1-122-1-12-1-12-1-12-1-1-1-122-2-20000-1-11111-2-21111-2-20011000000000000
χ172222-12-1-1222-10000-1-1-1-1220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1002222-1-10000000000002200-1-1-1-10000-1-100
χ182222-12-1-1222-10000-1-1-1-1220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2-1-1000000000000-2-200111100001100
χ1922-2-2222-2-22-2-22-22-222-2-2002-22-2-1-1-1111111-1-1-10000-1-1-11111-11-11-1002−22−2001-11-11-11-11-11-100002−22−22−22−20000
χ2022-2-2222-2-22-2-22-22-222-2-2002-22-2-1-1-1111111-1-1-10000-1-1-11111-11-11-100−22−22001-11-11-11-11-11-10000−22−22−22−220000
χ2122-2-2222-2-22-2-2-22-2222-2-200-22-22-1-1-1111111-1-1-10000-1-1-11111-11-11-1002−22−200-11-11-11-11-11-1100002−22−2−22−220000
χ2222-2-2222-2-22-2-2-22-2222-2-200-22-22-1-1-1111111-1-1-10000-1-1-11111-11-11-100−22−2200-11-11-11-11-11-110000−22−222−22−20000
χ232-22-222-2-2-2-2222i−2i−2i2i2-22-2002i−2i−2i2i-1-1-1111-1-1-11110000-1-1-1111-11-11-1100i2−i2−i2i200i−ii−ii−i−ii−ii−ii0000i2−i2−i2i22−2−220000
χ242-22-222-2-2-2-2222i−2i−2i2i2-22-2002i−2i−2i2i-1-1-1111-1-1-11110000-1-1-1111-11-11-1100−i2i2i2−i200i−ii−ii−i−ii−ii−ii0000−i2i2i2−i2−222−20000
χ252-22-222-2-2-2-222−2i2i2i−2i2-22-200−2i2i2i−2i-1-1-1111-1-1-11110000-1-1-1111-11-11-1100i2−i2−i2i200−ii−ii−iii−ii−ii−i0000i2−i2−i2i2−222−20000
χ262-22-222-2-2-2-222−2i2i2i−2i2-22-200−2i2i2i−2i-1-1-1111-1-1-11110000-1-1-1111-11-11-1100−i2i2i2−i200−ii−ii−iii−ii−ii−i0000−i2i2i2−i22−2−220000
χ272-2-2222-222-2-2-22i2i−2i−2i2-2-22-222i2i−2i−2i-1-1-1-1-1-111111122-2-2-1-1-1-1-1-11111112i−2i00002-2−i−i−i−i−i−iiiiiii002i−2i000000000000
χ282-2-2222-222-2-2-2−2i−2i2i2i2-2-22-22−2i−2i2i2i-1-1-1-1-1-111111122-2-2-1-1-1-1-1-1111111−2i2i00002-2iiiiii−i−i−i−i−i−i00−2i2i000000000000
χ292-2-222-1-22-111-22i2i−2i−2i-111-1-22−i−iii2-1-12-1-1-211-2112-11-22-1-12-1-1-2-211112i−2i0000-112i2i−i−i−i−i−2i−2iiiii00−ii000000000000
χ302-2-222-1-22-111-22i2i−2i−2i-111-1-22−i−iii-12-1-12-11-211-212-11-2-12-1-12-111-2-2112i−2i0000-11−i−i2i2i−i−iii−2i−2iii00−ii000000000000
χ312-2-222-1-22-111-22i2i−2i−2i-111-1-22−i−iii-1-12-1-1211-211-22-11-2-1-12-1-121111-2-22i−2i0000-11−i−i−i−i2i2iiiii−2i−2i00−ii000000000000
χ322-2-222-1-22-111-2−2i−2i2i2i-111-1-22ii−i−i2-1-12-1-1-211-2112-11-22-1-12-1-1-2-21111−2i2i0000-11−2i−2iiiii2i2i−i−i−i−i00i−i000000000000
χ332-2-222-1-22-111-2−2i−2i2i2i-111-1-22ii−i−i-12-1-12-11-211-212-11-2-12-1-12-111-2-211−2i2i0000-11ii−2i−2iii−i−i2i2i−i−i00i−i000000000000
χ342-2-222-1-22-111-2−2i−2i2i2i-111-1-22ii−i−i-1-12-1-1211-211-22-11-2-1-12-1-121111-2-2−2i2i0000-11iiii−2i−2i−i−i−i−i2i2i00i−i000000000000
χ352-2-22-121-12-2-210000-111-1-220000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-1111111002i2i−2i−2i-110000000000002i−2i00−i−iii0000−ii00
χ362-2-22-121-12-2-210000-111-1-220000222222-2-2-2-2-2-2-12-21-1-1-1-1-1-111111100−2i−2i2i2i-11000000000000−2i2i00ii−i−i0000i−i00
χ3733333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-11111-1-1000000000000-1-1-1-111111111-1-1-1-1
χ3833333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1-1-1-1-1-1-100000000000011-1-1-1-1-1-1-1-1-1-11111
χ39333333333333-3-3-3-33333-1-1-3-3-3-3000000000000-1-1-1-1000000000000111111-1-1000000000000-1-1111111-1-1-1-1-1-111
χ40333333333333-3-3-3-33333-1-1-3-3-3-3000000000000-1-1-1-100000000000011-1-1-1-1-1-10000000000001111-1-1-1-1111111-1-1
χ413-3-3333-333-3-3-33i3i−3i−3i3-3-331-13i3i−3i−3i000000000000-1-111000000000000−iiii−i−i-11000000000000−ii−iiii−i−i11-1-1−ii-11
χ423-3-3333-333-3-3-33i3i−3i−3i3-3-331-13i3i−3i−3i000000000000-1-111000000000000−ii−i−iii-11000000000000i−i−ii−i−iii-1-111i−i1-1
χ433-3-3333-333-3-3-3−3i−3i3i3i3-3-331-1−3i−3i3i3i000000000000-1-111000000000000i−iii−i−i-11000000000000−iii−iii−i−i-1-111−ii1-1
χ443-3-3333-333-3-3-3−3i−3i3i3i3-3-331-1−3i−3i3i3i000000000000-1-111000000000000i−i−i−iii-11000000000000i−ii−i−i−iii11-1-1i−i-11
χ454444-24-2-2444-20000-2-2-2-2440000-2-2-2-2-2-2-2-2-2-2-2-2-244-2111111111111000000-2-20000000000000000000000000000
χ464444-2-2-2-2-2-2-2-2000011114400004-2-24-2-24-2-24-2-2-2-2-2-2-211-211-2-21111000000110000000000000000000000000000
χ474444-2-2-2-2-2-2-2-200001111440000-24-2-24-2-24-2-24-2-2-2-2-21-211-2111-2-211000000110000000000000000000000000000
χ484444-2-2-2-2-2-2-2-200001111440000-2-24-2-24-2-24-2-24-2-2-2-211-211-21111-2-2000000110000000000000000000000000000
χ4944-4-4444-4-44-4-44-44-444-4-4004-44-4111-1-1-1-1-1-11110000111-1-1-1-11-11-1100000000-11-11-11-11-11-110000000000000000
χ5044-4-4444-4-44-4-4-44-4444-4-400-44-44111-1-1-1-1-1-11110000111-1-1-1-11-11-11000000001-11-11-11-11-11-10000000000000000
χ5144-4-44-24-42-22-44-44-4-2-22200-22-2211-2-1-12-1-1211-2000011-2-1-12-11-112-200000000-11-112-2-11-112-20000000000000000
χ5244-4-44-24-42-22-44-44-4-2-22200-22-221-21-12-1-12-11-2100001-21-12-1-112-2-1100000000-112-2-11-112-2-110000000000000000
χ5344-4-44-24-42-22-44-44-4-2-22200-22-22-2112-1-12-1-1-2110000-2112-1-12-2-11-11000000002-2-11-112-2-11-110000000000000000
χ5444-4-44-24-42-22-4-44-44-2-222002-22-211-2-1-12-1-1211-2000011-2-1-12-11-112-2000000001-11-1-221-11-1-220000000000000000
χ5544-4-44-24-42-22-4-44-44-2-222002-22-21-21-12-1-12-11-2100001-21-12-1-112-2-11000000001-1-221-11-1-221-10000000000000000
χ5644-4-44-24-42-22-4-44-44-2-222002-22-2-2112-1-12-1-1-2110000-2112-1-12-2-11-1100000000-221-11-1-221-11-10000000000000000
χ5744-4-4-24-22-44-420000-2-222000000-2-2-2222222-2-2-20000111-1-1-1-11-11-110022−2222−22000000000000000000−22−2200000000
χ5844-4-4-24-22-44-420000-2-222000000-2-2-2222222-2-2-20000111-1-1-1-11-11-1100−2222−22220000000000000000002−22−200000000
χ594-44-444-4-4-4-4444i−4i−4i4i4-44-4004i−4i−4i4i111-1-1-1111-1-1-10000111-1-1-11-11-11-100000000−ii−ii−iii−ii−ii−i0000000000000000
χ604-44-444-4-4-4-444−4i4i4i−4i4-44-400−4i4i4i−4i111-1-1-1111-1-1-10000111-1-1-11-11-11-100000000i−ii−ii−i−ii−ii−ii0000000000000000
χ614-44-44-2-4-422-244i−4i−4i4i-22-2200−2i2i2i−2i11-2-1-1211-2-1-12000011-2-1-121-11-1-2200000000−ii−ii2i−2ii−ii−i−2i2i0000000000000000
χ624-44-44-2-4-422-244i−4i−4i4i-22-2200−2i2i2i−2i1-21-12-11-21-12-100001-21-12-11-1-221-100000000−ii2i−2i−iii−i−2i2ii−i0000000000000000
χ634-44-44-2-4-422-244i−4i−4i4i-22-2200−2i2i2i−2i-2112-1-1-2112-1-10000-2112-1-1-221-11-1000000002i−2i−ii−ii−2i2ii−ii−i0000000000000000
χ644-44-44-2-4-422-24−4i4i4i−4i-22-22002i−2i−2i2i11-2-1-1211-2-1-12000011-2-1-121-11-1-2200000000i−ii−i−2i2i−ii−ii2i−2i0000000000000000
χ654-44-44-2-4-422-24−4i4i4i−4i-22-22002i−2i−2i2i1-21-12-11-21-12-100001-21-12-11-1-221-100000000i−i−2i2ii−i−ii2i−2i−ii0000000000000000
χ664-44-44-2-4-422-24−4i4i4i−4i-22-22002i−2i−2i2i-2112-1-1-2112-1-10000-2112-1-1-221-11-100000000−2i2ii−ii−i2i−2i−ii−ii0000000000000000
χ674-44-4-2422-4-44-20000-22-22000000-2-2-2222-2-2-22220000111-1-1-11-11-11-1002i2−2i2−2i22i2000000000000000000−i2i2i2−i200000000
χ684-44-4-2422-4-44-20000-22-22000000-2-2-2222-2-2-22220000111-1-1-11-11-11-100−2i22i22i2−2i2000000000000000000i2−i2−i2i200000000
χ694-4-44-242-24-4-420000-222-2-440000-2-2-2-2-2-2222222-24-42111111-1-1-1-1-1-1000000-220000000000000000000000000000
χ704-4-44-2-22-2-222200001-1-11-4400004-2-24-2-2-422-422-2-222-211-21122-1-1-1-10000001-10000000000000000000000000000
χ714-4-44-2-22-2-222200001-1-11-440000-24-2-24-22-422-42-2-2221-211-21-1-122-1-10000001-10000000000000000000000000000
χ724-4-44-2-22-2-222200001-1-11-440000-2-24-2-2422-422-4-2-22211-211-2-1-1-1-1220000001-10000000000000000000000000000
χ7366666-366-3-3-366666-3-3-3-3-2-2-3-3-3-3000000000000-211-2000000000000-2-20000110000000000000011000000000000
χ7466666-366-3-3-36-6-6-6-6-3-3-3-3-2-23333000000000000-211-20000000000002200001100000000000000-1-1000000000000
χ756666-36-3-3666-30000-3-3-3-3-2-200000000000000001-2-2100000000000000222211000000000000-2-200-1-1-1-100001100
χ766666-36-3-3666-30000-3-3-3-3-2-200000000000000001-2-2100000000000000-2-2-2-211000000000000220011110000-1-100
χ776-6-666-3-66-333-66i6i−6i−6i-333-32-2−3i−3i3i3i000000000000-21-12000000000000−2i2i00001-100000000000000i−i000000000000
χ786-6-666-3-66-333-6−6i−6i6i6i-333-32-23i3i−3i−3i000000000000-21-120000000000002i−2i00001-100000000000000−ii000000000000
χ796-6-66-363-36-6-630000-333-32-200000000000000001-22-1000000000000002i2i−2i−2i1-1000000000000−2i2i00−i−iii0000i−i00
χ806-6-66-363-36-6-630000-333-32-200000000000000001-22-100000000000000−2i−2i2i2i1-10000000000002i−2i00ii−i−i0000−ii00
χ8188-8-8-48-44-88-840000-4-444000000222-2-2-2-2-2-22220000-1-1-11111-11-11-1000000000000000000000000000000000000
χ8288-8-8-4-4-444-444000022-2-200000022-4-2-24-2-2422-40000-1-1211-21-11-1-22000000000000000000000000000000000000
χ8388-8-8-4-4-444-444000022-2-20000002-42-24-2-24-22-420000-12-11-211-1-221-1000000000000000000000000000000000000
χ8488-8-8-4-4-444-444000022-2-2000000-4224-2-24-2-2-42200002-1-1-211-221-11-1000000000000000000000000000000000000
χ858-88-8-4844-8-88-40000-44-44000000222-2-2-2222-2-2-20000-1-1-1111-11-11-11000000000000000000000000000000000000
χ868-88-8-4-44444-4-400002-22-200000022-4-2-2422-4-2-240000-1-1211-2-11-112-2000000000000000000000000000000000000
χ878-88-8-4-44444-4-400002-22-20000002-42-24-22-42-24-20000-12-11-21-112-2-11000000000000000000000000000000000000
χ888-88-8-4-44444-4-400002-22-2000000-4224-2-2-4224-2-200002-1-1-2112-2-11-11000000000000000000000000000000000000
χ8912121212-6-6-6-6-6-6-6-600003333-4-400000000000000002222000000000000000000-1-10000000000000000000000000000
χ9012-12-1212-6-66-6-666600003-3-334-4000000000000000022-2-2000000000000000000-110000000000000000000000000000

Here i is the imaginary unit (i² = −1).