Finite Group Databasebeta

← Group #10858828

Character table — Group #10858828

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order1222222222223444466666666666666644444488888888121212121212121224242424242424242424242424242424444444121212121212121212121212121212124444444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-111-1-11-1
χ1011111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-11-1-111-11
χ1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-111-11
χ1211111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1111-1-11-1
χ1311111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-111-1-1-11
χ1411111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-11-1-1111-1
χ1511111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-1-1111-1
χ1611111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1111-1-1-11
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χ182222222222222-2-2-2-2222222222222222-2-2000000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2000022000000
χ19222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ21222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ22222222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
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χ2522222222-2-2-2-2-12222-1-1-1-111111111-1-1-1-2-222222222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-2-2-2-2-12222-1-1-1-111111111-1-1-1-2-22222-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-2-2-2-2-12222-1-1-1-111111111-1-1-1-2-2-2-2-2-22222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-2-2-2-2-12222-1-1-1-111111111-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ302222-2-2-2-222-2-220000222-22222-2-2-2-2-2-2-200000022−2−222−2−2000000002222−2−2−2−22222−2−2−2−20000000000000000000000-22-22000000−22−2200
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χ362222-2-2-2-2-2-22220000222-2-2-2-2-22222-2-2-2000000−2−22222−2−200000000−2−2−2−222222222−2−2−2−20000000000000000000000-222-20000002−2−2200
χ3722-2-222-2-22-22-2222-2-22-2-2222-2-222-2-22-2-22-200000000000022-222-2-2-20000000000000000000000000000000000000000002-22-200000000
χ3822-2-222-2-22-22-2222-2-22-2-2222-2-222-2-22-2-22-200000000000022-222-2-2-2000000000000000000000000000000000000000000-22-2200000000
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χ4322-2-222-2-22-22-2-1-2-222-111-1-1-111-1-111-111-22−2i−2i2i2i0000000011-111-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−2i2i0000ii−i−iii−i−i−3−333−3−3330000000000000000
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χ4522-2-222-2-2-22-22222-2-22-2-22-2-222-2-2222-2-2-2200000000000022-2-2-222-20000000000000000000000000000000000000000002-2-2200000000
χ4622-2-222-2-2-22-22222-2-22-2-22-2-222-2-2222-2-2-2200000000000022-2-2-222-2000000000000000000000000000000000000000000-222-200000000
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χ4922-2-222-2-2-22-22-1-2-222-111-111-1-111-1-1-1112-22i2i−2i−2i0000000011-1-1-111-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−2i2i0000−i−iiiii−i−i33−3−3−3−3330000000000000000
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χ794444-4-4-4-444-4-4-20000-2-2-22-2-2-2-222222220000002222−22−222222−22−2200000000−2−2−2−22222−2−2−2−2222200000000000000000000000000000000000000
χ804444-4-4-4-444-4-4-20000-2-2-22-2-2-2-22222222000000−22−222222−22−222222000000002222−2−2−2−22222−2−2−2−200000000000000000000000000000000000000
χ814444-4-4-4-4-4-444-20000-2-2-222222-2-2-2-22220000002222−22−22−22−22222200000000−2−2−2−222222222−2−2−2−200000000000000000000000000000000000000
χ824444-4-4-4-4-4-444-20000-2-2-222222-2-2-2-2222000000−22−2222222222−22−22000000002222−2−2−2−2−2−2−2−2222200000000000000000000000000000000000000
χ8344-4-444-4-44-44-4-244-4-4-222-2-2-222-2-222-2224-4000000000000-2-22-2-2222000000000000000000000000000000000000000000000000000000
χ8444-4-444-4-4-44-44-244-4-4-222-222-2-222-2-2-222-44000000000000-2-2222-2-22000000000000000000000000000000000000000000000000000000
χ8544-4-4-4-4444-4-44400004-4-4-444-4-4-4-444-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ8644-4-4-4-4444-4-44-20000-2222-2-22222-2-22-2-20000000000000000000000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i600000000000000000000000000000000000000
χ8744-4-4-4-4444-4-44-20000-2222-2-22222-2-22-2-20000000000000000000000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i600000000000000000000000000000000000000
χ8844-4-4-4-444-444-4400004-4-4-4-4-44444-4-4-4440000000000000000000000000000000000000000000000000000000000000000000000000000
χ8944-4-4-4-444-444-4-20000-222222-2-2-2-2222-2-20000000000000000000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i600000000000000000000000000000000000000
χ9044-4-4-4-444-444-4-20000-222222-2-2-2-2222-2-20000000000000000000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i600000000000000000000000000000000000000
χ914-44-44-4-44000040000-44-4400000000-4-44000000−2i22i22i2−2i2000000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ924-44-44-4-44000040000-44-4400000000-4-440000002i2−2i2−2i22i20000000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ934-44-44-4-440000-200002-22-2−2i32i3−2i32i32i3−2i32i3−2i322-2000000−2i22i22i2−2i2000000000000i2−i2i2−i2−i2i2−i2i2−66−666−66−600000000000000000000000000000000000000
χ944-44-44-4-440000-200002-22-2−2i32i3−2i32i32i3−2i32i3−2i322-20000002i2−2i2−2i22i2000000000000−i2i2−i2i2i2−i2i2−i26−66−6−66−6600000000000000000000000000000000000000
χ954-44-44-4-440000-200002-22-22i3−2i32i3−2i3−2i32i3−2i32i322-2000000−2i22i22i2−2i2000000000000i2−i2i2−i2−i2i2−i2i26−66−6−66−6600000000000000000000000000000000000000
χ964-44-44-4-440000-200002-22-22i3−2i32i3−2i3−2i32i3−2i32i322-20000002i2−2i2−2i22i2000000000000−i2i2−i2i2i2−i2i2−i2−66−666−66−600000000000000000000000000000000000000
χ974-44-4-444-400004-44-44-44-4-40000000044-400000000000000-44-400004000000000000000000000000000000000000000000000000000000
χ984-44-4-444-40000-2-44-442-222−2i32i3−2i32i3−2i32i3−2i32i3-2-22000000000000002-222i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ994-44-4-444-40000-2-44-442-2222i3−2i32i3−2i32i3−2i32i3−2i3-2-22000000000000002-22−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000000000
χ1004-4-444-44-4000040000-4-44400000000-44-40000000000−2i22i22i2−2i20000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ1014-4-444-44-4000040000-4-44400000000-44-400000000002i2−2i2−2i22i200000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ1024-4-444-44-40000-2000022-2-2−2i32i32i3−2i32i3−2i3−2i32i32-220000000000−2i22i22i2−2i200000000−666−66−6−66i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000000000
χ1034-4-444-44-40000-2000022-2-2−2i32i32i3−2i32i3−2i3−2i32i32-2200000000002i2−2i2−2i22i2000000006−6−66−666−6−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000000000
χ1044-4-444-44-40000-2000022-2-22i3−2i3−2i32i3−2i32i32i3−2i32-220000000000−2i22i22i2−2i2000000006−6−66−666−6i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000000000
χ1054-4-444-44-40000-2000022-2-22i3−2i3−2i32i3−2i32i32i3−2i32-2200000000002i2−2i2−2i22i200000000−666−66−6−66−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000000000
χ1064-4-44-44-44000044-4-44-4-44-4000000004-44000000000000004-4-400004000000000000000000000000000000000000000000000000000000
χ1074-4-44-44-440000-24-4-4422-22−2i32i32i3−2i3−2i32i32i3−2i3-22-200000000000000-222−2i32i32i3−2i3-2000000000000000000000000000000000000000000000000000000
χ1084-4-44-44-440000-24-4-4422-222i3−2i3−2i32i32i3−2i3−2i32i3-22-200000000000000-2222i3−2i3−2i32i3-2000000000000000000000000000000000000000000000000000000

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