Finite Group Databasebeta

← Group #13155504

Character table — Group #13155504

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order124423334666121212121212333666666661212121212121212121212888836666612121212121288882424242424242424242424242424242488882424242424242424242424242424242422448888242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1111-1-11-1-1-1-111111-1-1i−ii−i11111111-1-1-1-1-1-1-1-111-1-1i−ii−ii−ii−iii−i−iii−i−i11-1-1i−ii−i11-1-1-11i−ii−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1111-1-11-1-1-1-111111-1-1i−i−ii11111111-1-1-1-1-1-1-1-1-1-111i−i−iii−i−iiii−i−i−i−iii-1-111i−i−ii-1-1111-1i−i−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1111-1-11-1-1-1-111111-1-1−iii−i11111111-1-1-1-1-1-1-1-1-1-111−iii−i−iii−i−i−iiiii−i−i-1-111−iii−i-1-1111-1−iii−i
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1111-1-11-1-1-1-111111-1-1−ii−ii11111111-1-1-1-1-1-1-1-111-1-1−ii−ii−ii−ii−i−iii−i−iii11-1-1−ii−ii11-1-1-11−ii−ii
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111111-1-1i−ii−i-1-1-1-1-1-1-1-11111111111-1-1i−ii−ii−ii−iii−i−iii−i−i-1-111−ii−ii11-1-11-1−ii−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111111-1-1i−i−ii-1-1-1-1-1-1-1-111111111-1-111i−i−iii−i−iiii−i−i−i−iii11-1-1−iii−i-1-111-11−iii−i
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111111-1-1−iii−i-1-1-1-1-1-1-1-111111111-1-111−iii−i−iii−i−i−iiiii−i−i11-1-1i−i−ii-1-111-11i−i−ii
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-11-1-1111-1-1-1-111111-1-1−ii−ii-1-1-1-1-1-1-1-11111111111-1-1−ii−ii−ii−ii−i−iii−i−iii-1-111i−ii−i11-1-11-1i−ii−i
χ172222222-1222-12222-1-12-1-122-1-1-12-1-1-1-12-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-10000002200-1-10000-1-1-1-10000002200000000-1-1
χ182222222-1222-12222-1-12-1-122-1-1-12-1-1-1-12-1-1-122-1-122222-12-1-1-1-12-1-1-1-1-100-2-222-1-1-1-1-1-122-1-1-1-1-1-1000000-2-2001100001111000000-2-20000000011
χ192222222-1222-12222-1-12-1-122-1-1-12-1-1-1-12-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-10022-2-2111111-2-21111110000002200-1-10000-1-1-1-1000000-2-20000000011
χ202222222-1222-12222-1-12-1-122-1-1-12-1-1-1-12-1-1-122-1-12-2-2-2-2-12-1-1-1-12-1-1-1-1-100-2-2-2-2111111-2-2111111000000-2-20011000011110000002200000000-1-1
χ21222222-1222-1222-1-122-12-12-12-1-1-12-1-1-1-12-1-1-1-12222222-1-12-1-1-1-12-1-1-1-12200-1-122-1-1-1-1-1-122-1-1-1-100002200-1-100-1-1-1-1000000002200000000-1-100
χ22222222-1222-1222-1-122-12-12-12-1-1-12-1-1-1-12-1-1-1-12222222-1-12-1-1-1-12-1-1-1-1-2-200-1-122-1-1-1-1-1-122-1-1-1-10000-2-2001100111100000000-2-2000000001100
χ23222222-1222-1222-1-122-12-12-12-1-1-12-1-1-1-12-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1220011-2-2111111-2-2111100002200-1-100-1-1-1-100000000-2-2000000001100
χ24222222-1222-1222-1-122-12-12-12-1-1-12-1-1-1-12-1-1-1-1222-2-2-2-2-1-12-1-1-1-12-1-1-1-1-2-20011-2-2111111-2-211110000-2-20011001111000000002200000000-1-100
χ2522222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ2622222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-2-1-11122-2-2-1-1-1-11111000000001111000000
χ2722222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-211-1-1-2-2221111-1-1-1-1000000001111000000
χ2822222-1222-122-1-12222-1-12-12222-1-12222222-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000022221111-2-2-2-21111111100000000-1-1-1-1000000
χ292222-2222-2222222222222-2-2-2-2-222222-2-2-2-22222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000222200000000-2-20000
χ302222-2222-2222222222222-2-2-2-2-222222-2-2-2-22222-200002-2-2-2-22-2-2-2-2220000000000000000000000000000000000000000-2-2-2-200000000220000
χ3122-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2000000000000000000000000000000000000000022-2-2000000002-20000
χ3222-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-20000000000000000000000000000000000000000-2-22200000000-220000
χ3322-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-211222-2-2-1-2111-12-1-1-111002i−2i22-1-1-1-1-1-1-2-21111110000002i−2i00−ii0000−i−iii0000002i−2i00000000−ii
χ3422-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-211222-2-2-1-2111-12-1-1-11100−2i2i22-1-1-1-1-1-1-2-2111111000000−2i2i00i−i0000ii−i−i000000−2i2i00000000i−i
χ3522-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-2112-2-222-1-2111-12-1-1-111002i−2i-2-211111122-1-1-1-1-1-10000002i−2i00−ii0000−i−iii000000−2i2i00000000i−i
χ3622-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-1112-1-1-1-2-2112-2-222-1-2111-12-1-1-11100−2i2i-2-211111122-1-1-1-1-1-1000000−2i2i00i−i0000ii−i−i0000002i−2i00000000−ii
χ3722-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-2222-2-2-11-211-1-12-1-1112i−2i00-1-122-1-1-1-111-2-2111100002i−2i00−ii00−i−iii000000002i−2i00000000−ii00
χ3822-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-2222-2-2-11-211-1-12-1-111−2i2i00-1-122-1-1-1-111-2-211110000−2i2i00i−i00ii−i−i00000000−2i2i00000000i−i00
χ3922-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-22-2-222-11-211-1-12-1-1112i−2i0011-2-21111-1-122-1-1-1-100002i−2i00−ii00−i−iii00000000−2i2i00000000i−i00
χ4022-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-111-12-1-111-2-22-2-222-11-211-1-12-1-111−2i2i0011-2-21111-1-122-1-1-1-10000−2i2i00i−i00ii−i−i000000002i−2i00000000−ii00
χ4122-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-12-2-222221111-10000-11111-1-1-1-1-1112i−2i2i−2i000000000000000022-2-2−ii−ii2i−2i2i−2i−i−iii−i−iii00000000-1-111000000
χ4222-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-12-2-222221111-10000-11111-1-1-1-1-1112i−2i−2i2i0000000000000000-2-222−iii−i2i−2i−2i2i−i−iiiii−i−i0000000011-1-1000000
χ4322-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-12-2-222221111-10000-11111-1-1-1-1-111−2i2i2i−2i0000000000000000-2-222i−i−ii−2i2i2i−2iii−i−i−i−iii0000000011-1-1000000
χ4422-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-12-2-222221111-10000-11111-1-1-1-1-111−2i2i−2i2i000000000000000022-2-2i−ii−i−2i2i−2i2iii−i−iii−i−i00000000-1-111000000
χ452-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-22i−2i00002i−2i2i−2i0i2−i22−220000-200002i−2i0000i2−i2i2−i2i2i2−i2−i22−22−222−2−2i2−i22−200000000000000002-22i−2i0000i2−i22−2000000
χ462-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-22i−2i00002i−2i2i−2i0i2−i22−220000-200002i−2i0000i2−i2i2−i2i2i2−i2−i22−22−222−2−2−i2i2−220000000000000000-22−2i2i0000−i2i2−22000000
χ472-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-22i−2i00002i−2i2i−2i0−i2i2−2220000-200002i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−2−222i2−i22−20000000000000000-22−2i2i0000i2−i22−2000000
χ482-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-22i−2i00002i−2i2i−2i0−i2i2−2220000-200002i−2i0000−i2i2−i2i2−i2−i2i2i2−22−22−2−222−i2i2−2200000000000000002-22i−2i0000−i2i2−22000000
χ492-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-2−2i2i0000−2i2i−2i2i0i2−i2−2220000-20000−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−2−222i2−i2−2200000000000000002-2−2i2i0000i2−i2−22000000
χ502-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-2−2i2i0000−2i2i−2i2i0i2−i2−2220000-20000−2i2i0000i2−i2i2−i2i2i2−i2−i2−22−22−2−222−i2i22−20000000000000000-222i−2i0000−i2i22−2000000
χ512-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-2−2i2i0000−2i2i−2i2i0−i2i22−220000-20000−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−222−2−2i2−i2−220000000000000000-222i−2i0000i2−i2−22000000
χ522-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-2−2i2i0000−2i2i−2i2i0−i2i22−220000-20000−2i2i0000−i2i2−i2i2−i2−i2i2i22−22−222−2−2−i2i22−200000000000000002-2−2i2i0000−i2i22−2000000
χ53444444-2-244-2-244-2-2-2-2-2-214-2-211-2-2111-2-211-2-2-2-2444441-2-2111-2-211110000-2-2-2-21111-2-2-2-2111100000000000000000000000000000000000000
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χ5544444-24-24-24-2-2-244-2-2-21-2-24-2-2-2-21-2-2-24-2-2-2-2-211-200001-21111-21111100440000000000000000000000-2-200-2-200001111000000000000000000
χ5644444-24-24-24-2-2-244-2-2-21-2-24-2-2-2-21-2-2-24-2-2-2-2-211-200001-21111-21111100-4-400000000000000000000002200220000-1-1-1-1000000000000000000
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χ5844444-2-244-2-24-2-2-2-2441-2-2-2-24-2-21-2-2-2-2-24-2-211-2-2-2000011-21111-21111-4-4000000000000000000000022002200-1-1-1-10000000000000000000000
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χ7544-4-44-2-24-4-2-242222-4-41-2-2-2-24-2-21-2-2222-422-1-1222000011-2111-12-1-1-1-1000000000000000000000000000000003i−3i−3i3i0000000000000000000000
χ7644-4-44-2-24-4-2-242222-4-41-2-2-2-24-2-21-2-2222-422-1-1222000011-2111-12-1-1-1-100000000000000000000000000000000−3i3i3i−3i0000000000000000000000
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χ7944-4-4-4-24-24-24-222-4-422-21-22-4222-21-2224-2-2-222-1-1-2000012-1-1-11-2111-1-1004i−4i0000000000000000000000−2i2i00−2i2i0000ii−i−i000000000000000000
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χ1148-8−8i8i0-4-4-404444i−4i4i−4i4i−4i222000-66-2-2-2−2i2i006i−6i−2i2i−2i2i00000-1003-3100−3i3ii−i0000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.