Finite Group Databasebeta

← Group #10828811

Character table — Group #10828811

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212122244446666888888881212121224242424242424242424242424242424444444121212121212121212121212121212124444222444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1111111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1-1-11111-1-11-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1111-1-1-1-111-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-111-1-11-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1111-1-1-111-1-1-11
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1111-1-1111-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1-1111-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111111-1-1-11
χ17222222222-22222-2-2-2222222222222222-2-20000-2-2-2-200000000-2-2-2-2000000000000000000000000000000000000002222-200-200000000
χ18222222222-22222-2-2-2222222222222222-2-20000-2-2-2-200000000-2-2-2-200000000000000000000000000000000000000-2-2-2-2200200000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000222200000000-2-2-2-20000000000000000000000000000000000000022-2-2-200200000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000222200000000-2-2-2-200000000000000000000000000000000000000-2-222200-200000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-2222211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-222221111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-2-2-2-2-211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-2-2-2-2-21111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ3022-222-2-2-22-2000022-222-2-22-2-200000000002i2i−2i−2i00000000-2-2222-2-2200000000-2-2-2-222220000−2i2i2i2i−2i−2i00000000−2i−2i2i2i0000000000000000
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χ652-2-22-2-2222-22-22-2-222-2-2-2-22222-22-2-22-22-220000-222-20000000022-2-200000000000000000000000000000000000000000002-202-2000000
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χ672-2-22-2-2222-2-22-22-222-2-2-2-2222-22-222-22-22-200002-2-220000000022-2-200000000000000000000000000000000000000000002-20-22000000
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χ7744444444-2-44444-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-400002222000000002222000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-222222222440000-2-2-2-2000000002222000000000000000000000000000000000000000000000000000000
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χ81444-4-4-4-44-200000000-222-222-22323−23−23−23−23232300000000000000−2i22i22i2−2i20000−i6−i6i6i6i6i6−i6−i6i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000000000
χ82444-4-4-4-44-200000000-222-222-22323−23−23−23−232323000000000000002i2−2i2−2i22i20000i6i6−i6−i6−i6−i6i6i6−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000000000
χ83444-4-4-4-44-200000000-222-222-2−23−2323232323−23−2300000000000000−2i22i22i2−2i20000i6i6−i6−i6−i6−i6i6i6i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000000000
χ84444-4-4-4-44-200000000-222-222-2−23−2323232323−23−23000000000000002i2−2i2−2i22i20000−i6−i6i6i6i6i6−i6−i6−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000000000
χ8544-444-4-4-4440000-4-4444-4-44-4-400000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000
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χ8744-444-4-4-4-240000-4-44-2-222-2222i32i32i32i3−2i3−2i3−2i3−2i3000000−2i3−2i32i32i3000000002-2-22000000000000000000000000000000000000000000000000000000
χ8844-4-4-444-4-204i4i−4i−4i000-22-222-22−2i−2i2i2i−2i−2i2i2i00000000002222−22−22−2i22i2−2i22i20000−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ8944-4-4-444-4-204i4i−4i−4i000-22-222-22−2i−2i2i2i−2i−2i2i2i0000000000−22−2222222i2−2i22i2−2i2000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000000000
χ9044-4-4-444-4-20−4i−4i4i4i000-22-222-222i2i−2i−2i2i2i−2i−2i00000000002222−22−222i2−2i22i2−2i20000−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000000000
χ9144-4-4-444-4-20−4i−4i4i4i000-22-222-222i2i−2i−2i2i2i−2i−2i0000000000−22−222222−2i22i2−2i22i2000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ924-444-44-4-4440000-44-4-4-4444-4-4000000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000
χ934-444-44-4-4-240000-44-422-2-2-222−2i32i3−2i32i3−2i32i3−2i32i30000002i3−2i32i3−2i300000000-22-22000000000000000000000000000000000000000000000000000000
χ944-444-44-4-4-240000-44-422-2-2-2222i3−2i32i3−2i32i3−2i32i3−2i3000000−2i32i3−2i32i300000000-22-22000000000000000000000000000000000000000000000000000000
χ954-44-44-44-4404i−4i−4i4i000-44-44-44-44i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-440−4i4i4i−4i000-44-44-44-4−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-4-204i−4i−4i4i0002-22-22-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000i6−i6−i6i6−i6i6i6−i66−6−66−666−600000000000000000000000000000000000000
χ984-44-44-44-4-204i−4i−4i4i0002-22-22-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000−i6i6i6−i6i6−i6−i6i6−666−66−6−6600000000000000000000000000000000000000
χ994-44-44-44-4-20−4i4i4i−4i0002-22-22-222i−2i−2i2i−2i2i2i−2i0000000000000000000000i6−i6−i6i6−i6i6i6−i6−666−66−6−6600000000000000000000000000000000000000
χ1004-44-44-44-4-20−4i4i4i−4i0002-22-22-222i−2i−2i2i−2i2i2i−2i0000000000000000000000−i6i6i6−i6i6−i6−i6i66−6−66−666−600000000000000000000000000000000000000
χ1014-4-44-4-444-2-44-44-4-4442222-2-2-2-22-222-22-2-4400002-2-2200000000-2-222000000000000000000000000000000000000000000000000000000
χ1024-4-44-4-444-2-4-44-44-4442222-2-2-22-22-2-22-224-40000-222-200000000-2-222000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-44400000000-444-4-4-4400000000000000000022−22−22220000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ1044-4-4-444-44400000000-444-4-4-44000000000000000000−222222−2200000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ1054-4-4-444-44-2000000002-2-2222-223−23−232323−23−2323000000000022−22−222200000000−222−2−222−2−666−6−666−600000000000000000000000000000000000000
χ1064-4-4-444-44-2000000002-2-2222-223−23−232323−23−23230000000000−222222−22000000002−2−222−2−226−6−666−6−6600000000000000000000000000000000000000
χ1074-4-4-444-44-2000000002-2-2222-2−232323−23−232323−23000000000022−22−222200000000−222−2−222−26−6−666−6−6600000000000000000000000000000000000000
χ1084-4-4-444-44-2000000002-2-2222-2−232323−23−232323−230000000000−222222−22000000002−2−222−2−22−666−6−666−600000000000000000000000000000000000000

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