Finite Group Databasebeta

← Group #13170573

Character table — Group #13170573

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order124423334666121212121212333666666661212121212121212121212888836666612121212121222442244666612121212242424242424242424242424242424242466121266666612121212121222446128888661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11-11-111-1-111-1-11111111111111111-1-1-1-1-1-11-111-1-11-111-1-11-11-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-11-11-1-111-1-1111111111111111111-1-1-1-1-1-1-11-1-111-11-1-111-11-11-1-1-1-1-1-1-11-11
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-111-1-1-11-11-1-11111-11-11
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1111-11-1-1-111111-11-1
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-1-111111-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-111-1-1-1111-1-111-1-1
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-1-111111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-111-1111-1-1-1-111
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111-111-1-1-11-1-1111-1-111-1-1-1111-1-11
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1111111-1-11-1-1-1-111111-1-1-1-111-111-1-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-111-11-1-1111-111-1-1-111-11-1-1-111-111-1
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1111111-1-1-1-1-1-1-1-111-11-1-111-1-111
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-1-1-111111111-1-1-11-1-11111-1-1
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1111-111-1-1-11-1-111-111-11-111-1-1-111-1
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-11-1-1111-111-1-11-1-111-111-1-11-1-11
χ172222222-1222-12222-1-12-1-122-1222-1-1-122-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000000022-1-1-1-122-1-1-1-122-1-1-1-10000-1-100000000
χ182222222-1222-12222-1-12-1-122-1222-1-1-122-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111000000000000000022-1-1-1-1-2-21111-2-211110000-1-100000000
χ192222222-1222-12222-1-12-1-122-1222-1-1-122-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22-22-2-1-111-1-1110000000000000000-2-211112-2-1-1112-2-1-11100001100000000
χ202222222-1222-12222-1-12-1-122-1222-1-1-122-1-1-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22-2211-1-111-1-10000000000000000-2-21111-2211-1-1-2211-1-100001100000000
χ21222222-1222-1222-1-122-12-12-12-1-1-12-12-1-122-1-12-1-1-12222-12-1-1-1-12-1-1-1-1-1000002020022002222-1-1-1-1-1-122-1-1-1-1-1-10000000-100-1-10-100-1-102020000000-10-1
χ22222222-1222-1222-1-122-12-12-12-1-1-12-12-1-122-1-12-1-1-12222-12-1-1-1-12-1-1-1-1-100000-20-200-2-200-2-222-1-1-1-1-1-122-1-1-1-1-1-10000000100110100110-20-20000000101
χ23222222-1222-1222-1-122-12-12-12-1-1-12-12-1-122-1-12-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1-1-10000020200220022-2-2111111-2-21111110000000-100-1-10-100-1-10-20-20000000101
χ24222222-1222-1222-1-122-12-12-12-1-1-12-12-1-122-1-12-1-1-1-2-2-2-2-12-1-1-1-12-1-1-1-1-100000-20-200-2-200-2-2-2-2111111-2-211111100000001001101001102020000000-10-1
χ2522222-1222-122-1-12222-1-12-122-1-1-1-122-1-1-1-122-12-1-12222-1-12-1-1-1-12-1-1-1-10000202022002200-1-122-1-1-1-1-1-122-1-1-1-1000000-10-1-100-10-1-1002020000000-10-10
χ2622222-1222-122-1-12222-1-12-122-1-1-1-122-1-1-1-122-12-1-12222-1-12-1-1-1-12-1-1-1-10000-20-20-2-200-2-200-1-122-1-1-1-1-1-122-1-1-1-1000000101100101100-20-200000001010
χ2722222-1222-122-1-12222-1-12-122-1-1-1-122-1-1-1-122-12-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-1000020202200220011-2-2111111-2-21111000000-10-1-100-10-1-100-20-200000001010
χ2822222-1222-122-1-12222-1-12-122-1-1-1-122-1-1-1-122-12-1-1-2-2-2-2-1-12-1-1-1-12-1-1-1-10000-20-20-2-200-2-20011-2-2111111-2-211110000001011001011002020000000-10-10
χ292222-2222-2222222222222-2-2-2-2-2222-2222222-2-2-2-200002-2-2-2-22-2-2-2-22222220000000000000000000000000000-2-222220000000000000000-2-200000000
χ302222-2222-2222222222222-2-2-2-2-2222-2222222-2-2-2-200002-2-2-2-22-2-2-2-222-2-2-2-2000000000000000000000000000022-2-2-2-200000000000000002200000000
χ312222-222-1-222-12222-1-12-1-1-2-21-2-22-1-1122-1-1-1-1-2-2-2-20000-11111-11111-1-122220000−i3i3−i3i3−i3i3−i3i30000000000000000-2-2-1-1-1-100−i3i3−i3i300−i3i3−i3i300001100000000
χ322222-222-1-222-12222-1-12-1-1-2-21-2-22-1-1122-1-1-1-1-2-2-2-20000-11111-11111-1-122220000i3−i3i3−i3i3−i3i3−i30000000000000000-2-2-1-1-1-100i3−i3i3−i300i3−i3i3−i300001100000000
χ332222-222-1-222-12222-1-12-1-1-2-21-2-22-1-1122-1-1-1-1-2-2-2-20000-11111-11111-1-1-2-2-2-20000−i3i3i3−i3−i3i3i3−i3000000000000000022111100−i3i3i3−i300−i3i3i3−i30000-1-100000000
χ342222-222-1-222-12222-1-12-1-1-2-21-2-22-1-1122-1-1-1-1-2-2-2-20000-11111-11111-1-1-2-2-2-20000i3−i3−i3i3i3−i3−i3i3000000000000000022111100i3−i3−i3i300i3−i3−i3i30000-1-100000000
χ3522-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-222-2-200000000000000000000000000002-222-2-200000000000000002-200000000
χ3622-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-20000222222-2-2-2-2-2-2-2-2220000000000000000000000000000-22-2-2220000000000000000-2200000000
χ3722-2-2222-1-222-1-2-2-2-2112-1-122-1222-1-11-2-21111-2-2-2-20000-1-1-1-1-1-111111122-2-20000−i3i3−i3i3i3−i3i3−i300000000000000002-2-1-11100−i3i3−i3i300i3−i3i3−i30000-1100000000
χ3822-2-2222-1-222-1-2-2-2-2112-1-122-1222-1-11-2-21111-2-2-2-20000-1-1-1-1-1-111111122-2-20000i3−i3i3−i3−i3i3−i3i300000000000000002-2-1-11100i3−i3i3−i300−i3i3−i3i30000-1100000000
χ3922-2-2222-1-222-1-2-2-2-2112-1-122-1222-1-11-2-21111-2-2-2-20000-1-1-1-1-1-1111111-2-2220000−i3i3i3−i3i3−i3−i3i30000000000000000-2211-1-100−i3i3i3−i300i3−i3−i3i300001-100000000
χ4022-2-2222-1-222-1-2-2-2-2112-1-122-1222-1-11-2-21111-2-2-2-20000-1-1-1-1-1-1111111-2-2220000i3−i3−i3i3−i3i3i3−i30000000000000000-2211-1-100i3−i3−i3i300−i3i3i3−i300001-100000000
χ4122-2-2-222-1222-1-2-2-2-2112-1-1-2-21-2-22-1-1-1-2-2111122220000-11111-1-1-1-1-11122-2-222-2-2-1-1-1-111110000000000000000-22-1-11122-1-1-1-1-2-2111100001-100000000
χ4222-2-2-222-1222-1-2-2-2-2112-1-1-2-21-2-22-1-1-1-2-2111122220000-11111-1-1-1-1-11122-2-2-2-2221111-1-1-1-10000000000000000-22-1-111-2-2111122-1-1-1-100001-100000000
χ4322-2-2-222-1222-1-2-2-2-2112-1-1-2-21-2-22-1-1-1-2-2111122220000-11111-1-1-1-1-111-2-2222-2-22-1-11111-1-100000000000000002-211-1-12-2-1-111-2211-1-10000-1100000000
χ4422-2-2-222-1222-1-2-2-2-2112-1-1-2-21-2-22-1-1-1-2-2111122220000-11111-1-1-1-1-111-2-222-222-211-1-1-1-11100000000000000002-211-1-1-2211-1-12-2-1-1110000-1100000000
χ4522-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1211-2-2112-1-1-122-2-2-1-2111-12-1-1-1110000020-2002200-2-222-1-1-1-1-1-1-2-21111110000000-100-1-1010011020-20000000-101
χ4622-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1211-2-2112-1-1-122-2-2-1-2111-12-1-1-11100000-20200-2-2002222-1-1-1-1-1-1-2-21111110000000100110-100-1-10-202000000010-1
χ4722-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1211-2-2112-1-1-1-2-222-1-2111-12-1-1-1110000020-2002200-2-2-2-211111122-1-1-1-1-1-10000000-100-1-10100110-202000000010-1
χ4822-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1211-2-2112-1-1-1-2-222-1-2111-12-1-1-11100000-20200-2-20022-2-211111122-1-1-1-1-1-10000000100110-100-1-1020-20000000-101
χ4922-2-2-2-1222-12211-2-2-2-2-1-121-2-211-1-1221111-2-2-12-1-122-2-2-11-211-1-12-1-111000020-202200-2-200-1-122-1-1-1-111-2-21111000000-10-1-10010110020-20000000-1010
χ5022-2-2-2-1222-12211-2-2-2-2-1-121-2-211-1-1221111-2-2-12-1-122-2-2-11-211-1-12-1-1110000-2020-2-2002200-1-122-1-1-1-111-2-21111000000101100-10-1-100-202000000010-10
χ5122-2-2-2-1222-12211-2-2-2-2-1-121-2-211-1-1221111-2-2-12-1-1-2-222-11-211-1-12-1-111000020-202200-2-20011-2-21111-1-122-1-1-1-1000000-10-1-100101100-202000000010-10
χ5222-2-2-2-1222-12211-2-2-2-2-1-121-2-211-1-1221111-2-2-12-1-1-2-222-11-211-1-12-1-1110000-2020-2-200220011-2-21111-1-122-1-1-1-1000000101100-10-1-10020-20000000-1010
χ532-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i2i−2i2i−2i00002−2−i2i220000-200002i−2i2-22i−2i0000000000002−22−222−2−2−i2i2−i2i2−i2−i2i2i2002-22i−2i0000000000000000002−2−i2i20000
χ542-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i2i−2i2i−2i00002−2−i2i220000-200002i−2i-22−2i2i0000000000002−22−222−2−2−i2i2−i2i2−i2−i2i2i200-22−2i2i000000000000000000−22i2−i20000
χ552-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i2i−2i2i−2i0000−22i2−i220000-200002i−2i2-22i−2i000000000000−22−22−2−222i2−i2i2−i2i2i2−i2−i2002-22i−2i000000000000000000−22i2−i20000
χ562-22i−2i02220-2-2-22i−2i2i−2i2i−2i22200000-2-2-202i−2i2i−2i2i−2i0000−22i2−i220000-200002i−2i-22−2i2i000000000000−22−22−2−222i2−i2i2−i2i2i2−i2−i200-22−2i2i0000000000000000002−2−i2i20000
χ572-2−2i2i02220-2-2-2−2i2i−2i2i−2i2i22200000-2-2-20−2i2i−2i2i−2i2i00002−2i2−i220000-20000−2i2i2-2−2i2i0000000000002−22−222−2−2i2−i2i2−i2i2i2−i2−i2002-2−2i2i0000000000000000002−2i2−i20000
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χ61444444-2-244-2-244-2-2-2-2-2-214-2-2-2-2-2-21-2-2-2-2-2114-2-2-200001-21111-2111110000040400-2-200-2-200000000000000000000000-200110-2001100000000000000
χ62444444-2-244-2-244-2-2-2-2-2-214-2-2-2-2-2-21-2-2-2-2-2114-2-2-200001-21111-21111100000-40-40022002200000000000000000000000200-1-10200-1-100000000000000
χ6344444-24-24-24-2-2-244-2-2-21-2-24-2-2-2-21-2-2-2-211-2-2-24-2-2000011-21111-2111100004040-2-200-2-2000000000000000000000000-201100-20110000000000000000
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χ704444-4-244-4-244-2-24444-2-242-4-422-2-24-4-2-2-2-2442-4220000-22-422-22-422-2-20000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.