Finite Group Databasebeta

← Group #10729233

Character table — Group #10729233

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222222222222234444444466666666666666644444444121212121212121212121212121212121212121212121212224444446666121212121212121212121212444444444444444422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ911111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1211111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1511111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1611111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ172222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-222-1-1-1-1-1-1-1-111111111000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-22222-2-211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
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χ772-2-222-222-2-22-22-22-222i−2i−2i2i2i−2i−2i2i-2-222-22-22-2-222-22-2000000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ782-2-222-222-2-22-22-22-222i−2i−2i2i2i−2i−2i2i-2-222-22-22-2-222-22-2000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ792-2-222-222-2-22-22-22-22−2i2i2i−2i−2i2i2i−2i-2-222-22-22-2-222-22-200000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ802-2-222-222-2-22-22-22-22−2i2i2i−2i−2i2i2i−2i-2-222-22-22-2-222-22-200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000-222-22i−2i−2i2i0000000000000000
χ812-2-22-22-2222-2-22-2-2222-2-22-222-2-2-22-22-2-22-22-2-2222000000002-2-22-222-200000000000000002-200002-22-2-222-2-2200000000000000000000000000000000
χ822-2-22-22-2222-2-22-2-2222-2-22-222-2-2-22-22-2-22-22-2-2222000000002-2-22-222-20000000000000000-220000-22-222-2-222-200000000000000000000000000000000
χ832-2-22-22-2222-2-22-2-222-222-22-2-22-2-22-22-2-22-22-2-222200000000-222-22-2-2200000000000000002-20000-222-2-22-222-200000000000000000000000000000000
χ842-2-22-22-2222-2-22-2-222-222-22-2-22-2-22-22-2-22-22-2-222200000000-222-22-2-220000000000000000-2200002-2-222-22-2-2200000000000000000000000000000000
χ852-2-22-22-2222-2-22-2-22-12-2-22-222-211-11-111-11-111-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i32-200002-2-111-1-111-1−i3i3i3−i3−i3i3i3−i3000000000000000000000000
χ862-2-22-22-2222-2-22-2-22-12-2-22-222-211-11-111-11-111-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3−i3i3i3−i3i3−i3-220000-221-1-111-1-11i3−i3−i3i3i3−i3−i3i3000000000000000000000000
χ872-2-22-22-2222-2-22-2-22-12-2-22-222-211-11-111-11-111-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i32-200002-2-111-1-111-1i3−i3−i3i3i3−i3−i3i3000000000000000000000000
χ882-2-22-22-2222-2-22-2-22-12-2-22-222-211-11-111-11-111-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3i3−i3−i3i3−i3i3-220000-221-1-111-1-11−i3i3i3−i3−i3i3i3−i3000000000000000000000000
χ892-2-22-22-2222-2-22-2-22-1-222-22-2-2211-11-111-11-111-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i32-20000-22-111-11-1-11−i3i3i3−i3i3−i3−i3i3000000000000000000000000
χ902-2-22-22-2222-2-22-2-22-1-222-22-2-2211-11-111-11-111-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3-2200002-21-1-11-111-1i3−i3−i3i3−i3i3i3−i3000000000000000000000000
χ912-2-22-22-2222-2-22-2-22-1-222-22-2-2211-11-111-11-111-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i32-20000-22-111-11-1-11i3−i3−i3i3−i3i3i3−i3000000000000000000000000
χ922-2-22-22-2222-2-22-2-22-1-222-22-2-2211-11-111-11-111-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3-2200002-21-1-11-111-1−i3i3i3−i3i3−i3−i3i3000000000000000000000000
χ9344444-4-4-4-444-4-4-4-44-200000000-2-2-2-2-2-2222222-2224i4i−4i−4i000000000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ9444444-4-4-4-444-4-4-4-44-200000000-2-2-2-2-2-2222222-222−4i−4i4i4i0000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ954444-444-44-4-4-4-4-44-4400000000444-4-4-4-4-4-4444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964444-444-44-4-4-4-4-44-4-200000000-2-2-2222222-2-2-222-200000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000000000
χ974444-444-44-4-4-4-4-44-4-200000000-2-2-2222222-2-2-222-2000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000000000
χ984444-4-4-44-4-4-4444-4-4-24i4i4i4i−4i−4i−4i−4i-2-2-2222-2-2-22222-2200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ994444-4-4-44-4-4-4444-4-4-2−4i−4i−4i−4i4i4i4i4i-2-2-2222-2-2-22222-22000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ10044-4-4444-4-4-4-444-4-44-200000000-222-222-2-22-2-22-2224i−4i4i−4i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ10144-4-4444-4-4-4-444-4-44-200000000-222-222-2-22-2-22-222−4i4i−4i4i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ10244-4-4-4444-444-4-44-4-4-24i4i−4i−4i−4i−4i4i4i-2222-2-222-2-2-222-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ10344-4-4-4444-444-4-44-4-4-2−4i−4i4i4i4i4i−4i−4i-2222-2-222-2-2-222-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ10444-4-4-4-4-4-444444-44-44000000004-4-4-44444-4-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10544-4-4-4-4-4-444444-44-4-200000000-2222-2-2-2-2222-222-200000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000000000000000
χ10644-4-4-4-4-4-444444-44-4-200000000-2222-2-2-2-2222-222-2000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ1074-44-444-44-44-44-4-44-4-24i−4i4i−4i4i−4i4i−4i2-22-2-22-222-22-22-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1084-44-444-44-44-44-4-44-4-2−4i4i−4i4i−4i4i−4i4i2-22-2-22-222-22-22-22000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1094-44-44-44-444-4-444-4-4-2000000002-22-2-222-2-22-2222-200004i−4i4i−4i0000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ1104-44-44-44-444-4-444-4-4-2000000002-22-2-222-2-22-2222-20000−4i4i−4i4i00000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ1114-44-4-44-4-4-4-44-44444400000000-44-4-4-44-4444-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1124-44-4-44-4-4-4-44-44444-2000000002-2222-22-2-2-22-2-222000000000000000023−2323−23−2323−232300000000000000000000000000000000000000000000000000000000
χ1134-44-4-44-4-4-4-44-44444-2000000002-2222-22-2-2-22-2-2220000000000000000−2323−232323−2323−2300000000000000000000000000000000000000000000000000000000
χ1144-4-4444-4-44-444-44-4-4-20000000022-2-22-2-22-2-22222-200004i−4i−4i4i0000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ1154-4-4444-4-44-444-44-4-4-20000000022-2-22-2-22-2-22222-20000−4i4i4i−4i00000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ1164-4-444-444-4-44-44-44-4-24i−4i−4i4i4i−4i−4i4i22-2-22-22-222-2-22-2200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1174-4-444-444-4-44-44-44-4-2−4i4i4i−4i−4i4i4i−4i22-2-22-22-222-2-22-22000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1184-4-44-4-44-4-44-44-4444400000000-4-44-44-44-44-4444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1194-4-44-4-44-4-44-44-4444-20000000022-22-22-22-22-2-2-222000000000000000023−23−232323−23−232300000000000000000000000000000000000000000000000000000000
χ1204-4-44-4-44-4-44-44-4444-20000000022-22-22-22-22-2-2-2220000000000000000−232323−23−232323−2300000000000000000000000000000000000000000000000000000000

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