Finite Group Databasebeta

← Group #72267866

Character table — Group #72267866

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111111122222222222244444444888888888888888888881616161616161616161616161616161616163232323232323232323232323232323232323232323232323232323232323232323232323232323264646464
order12222222222222222222222222224444444444444444444444444444444444444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1
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χ1011111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111-1-1-1-1iiii−i−i−i−iζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−i−i−i−iiiii-1-111
χ1111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−i−i−i−iiiii-1-111
χ1211111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111-1-1-1-1iiii−i−i−i−i−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζiiii−i−i−i−i11-1-1
χ1311111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3−i−i−i−iiiii11-1-1
χ1411111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiiiζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3ζζζζ−ζ−ζ−ζ−ζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3iiii−i−i−i−i-1-111
χ1511111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζζζζζ−ζ−ζ−ζ−ζζ3ζ3ζ3ζ3−ζ3−ζ3−ζ3−ζ3iiii−i−i−i−i-1-111
χ1611111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−iiiii−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ−ζ−ζ−ζζζζζ−ζ−ζ−ζ−ζζζζζ−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζ3ζ3−i−i−i−iiiii11-1-1
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χ844-4-44-444-44-44-44-4000-440000000-4400002i2i00−2i−2i0000−2i−2i002i2i0000000000002i−2i00−2i2i0000000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i000000000000
χ854-4-44-444-44-44-44-4000-440000000-440000−2i−2i002i2i00002i2i00−2i−2i000000000000−2i2i002i−2i00000000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i000000000000
χ864-4-44-444-44-44-44-4000-440000000-440000−2i−2i002i2i00002i2i00−2i−2i000000000000−2i2i002i−2i0000000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i000000000000
χ874-4-44-444-4-44-44-440004-40000000-4400002i2i00−2i−2i0000−2i−2i002i2i000000000000−2i2i002i−2i00000000000000001+i−1−i−1−i1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000
χ884-4-44-444-4-44-44-440004-40000000-4400002i2i00−2i−2i0000−2i−2i002i2i000000000000−2i2i002i−2i0000000000000000−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000000000
χ894-4-44-444-4-44-44-440004-40000000-440000−2i−2i002i2i00002i2i00−2i−2i0000000000002i−2i00−2i2i00000000000000001−i−1+i−1+i1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i000000000000
χ904-4-44-444-4-44-44-440004-40000000-440000−2i−2i002i2i00002i2i00−2i−2i0000000000002i−2i00−2i2i0000000000000000−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i000000000000
χ914-4-44-444-4-44-4-44-40004400000004-400002200220000-2-200-2-2000000000000-2200-220000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ924-4-44-444-4-44-4-44-40004400000004-400002200220000-2-200-2-2000000000000-2200-220000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ934-4-44-444-4-44-4-44-40004400000004-40000-2-200-2-200002200220000000000002-2002-200000000000000002−2−22−222−2−222−22−2−22000000000000
χ944-4-44-444-4-44-4-44-40004400000004-40000-2-200-2-200002200220000000000002-2002-20000000000000000−222−22−2−222−2−22−222−2000000000000
χ958888-8-8-8-800088-8-8-880-8800-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ968888-8-8-8-8000-8-8888-808-800-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-888-8-8000000000000-880000008i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-888-8-8000000000000-88000000−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-8-8888-8-80000008000000000000000000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ10088-8-8-8-8888-8-8000000800000000000000000000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ10188-8-8-8-888-888000000-80000000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ10288-8-8-8-888-888000000-8000000000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ1038-88-8-88-880000008-8-80080000000000004-4004-40000-4400-4400000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-88-880000008-8-8008000000000000-4400-4400004-4004-400000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-88-88000000-88800-80000000000004i−4i00−4i4i0000−4i4i004i−4i00000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-88-88000000-88800-8000000000000−4i4i004i−4i00004i−4i00−4i4i00000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-8-880008-8-800008000000000004-4004-40000-4400-440000000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-8-880008-8-80000800000000000-4400-4400004-4004-40000000000000000000000000000000000000000000000000000000000000000
χ1098-8-888-8-88000-8880000-8000000000004i−4i00−4i4i0000−4i4i004i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1108-8-888-8-88000-8880000-800000000000−4i4i004i−4i00004i−4i00−4i4i0000000000000000000000000000000000000000000000000000000000000000

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