Finite Group Databasebeta

← Group #10855218

Character table — Group #10855218

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order1222222234444444466666661212121212121212222244888888881212121212121212242424242424242424242424242424242244446666666612121212121212124444444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-111-1-1-1-1111-1
χ101111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-11-1-11111-1-1-11
χ111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-111-1-111-1-1-11
χ121111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1111-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-11-1-1-111-1-111-11
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1-111-1-11-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-11-1-1-11111-1-11-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1111-1-1-1-111-11
χ17222222222-22222-2-2-22222222222222220000-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002222-2-20000000000
χ18222222222-22222-2-2-22222222222222220000-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-2-2-2-2220000000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000-2-22222-2-20000000000000000000000000000000000000022-2-2-220000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200002200000000-2-22222-2-200000000000000000000000000000000000000-2-2222-20000000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1111111112222-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1111111112222-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-111111111-2-2-2-2-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
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χ4422-22-2-2-22202i2i−2i−2i0002-22-2-22-22i2i−2i−2i2i2i−2i−2i000000i2−i2i2−i2−2−22200000000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000000000−2i2i-22000000−i2i22−200
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χ502-222-2-22-2222i−2i2i−2i-2-22-2-2222-2-22i−2i2i−2i2i−2i2i−2i-22-222i−2i00000000-222i−2i2i−2i2-2000000000000000000−2i2i00-22-220000−2i2i−2i2i00000000000000000000
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χ652-22-2-22-222-200002-22-2-2-2-2222000000002-2-220000002-22-2-2-2000022000000002-22-2-22-222-200002-2-222-2-22000000000000000000000000
χ662-22-2-22-222-200002-22-2-2-2-2222000000002-2-22000000-22-22-2-200002200000000-22-222-22-2-2200002-2-22-222-2000000000000000000000000
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χ762-22-2-22-22-1-200002-221111-1-1-1i3−i3i3−i3−i3i3−i3i3-222-2000000-22-2211i3−i3−i3i3-1-1−i3i3−i3i3i3−i3i3−i31-11-1-11-112-200001-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ7744444444-2-44444-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000-4-40000000022222222000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2222222220000440000000022-2-2-2-222000000000000000000000000000000000000000000000000000000
χ79444-44-4-4-44400004-4-444-4-44-4-40000000000000000000000-440000-44000000000000000000000000000000000000000000000000000000
χ80444-44-4-4-4-2400004-4-4-2-222-22223232323−23−23−23−23000000000000002-2−23−2323232-2000000000000000000000000000000000000000000000000000000
χ81444-44-4-4-4-2400004-4-4-2-222-222−23−23−23−2323232323000000000000002-22323−23−232-2000000000000000000000000000000000000000000000000000000
χ8244-44-4-4-44-204i4i−4i−4i000-22-222-22−2i−2i2i2i−2i−2i2i2i000000−2i22i2−2i22i22222−22−2200000000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000000000000000000000
χ8344-44-4-4-44-204i4i−4i−4i000-22-222-22−2i−2i2i2i−2i−2i2i2i0000002i2−2i22i2−2i2−22−22222200000000−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000000000000000000000
χ8444-44-4-4-44-20−4i−4i4i4i000-22-222-222i2i−2i−2i2i2i−2i−2i000000−2i22i2−2i22i2−22−22222200000000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000000000000000000000
χ8544-44-4-4-44-20−4i−4i4i4i000-22-222-222i2i−2i−2i2i2i−2i−2i0000002i2−2i22i2−2i22222−22−2200000000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000000000000000000000
χ8644-4-4-444-44000000004-4-44-4-440000000000000022−22−22220000000000002222−22−22−22−2222220000000000000000000000000000000000000000000000
χ8744-4-4-444-44000000004-4-44-4-4400000000000000−222222−22000000000000−22−2222222222−22−220000000000000000000000000000000000000000000000
χ8844-4-4-444-4-200000000-222-222-2−2i3−2i32i32i32i32i3−2i3−2i300000022−22−2222000000000000−2−22222−2−2i6i6−i6−i6−i6−i6i6i600000000000000000000000000000000000000
χ8944-4-4-444-4-200000000-222-222-2−2i3−2i32i32i32i32i3−2i3−2i3000000−222222−2200000000000022−2−2−2−222−i6−i6i6i6i6i6−i6−i600000000000000000000000000000000000000
χ9044-4-4-444-4-200000000-222-222-22i32i3−2i3−2i3−2i3−2i32i32i300000022−22−2222000000000000−2−22222−2−2−i6−i6i6i6i6i6−i6−i600000000000000000000000000000000000000
χ9144-4-4-444-4-200000000-222-222-22i32i3−2i3−2i3−2i3−2i32i32i3000000−222222−2200000000000022−2−2−2−222i6i6−i6−i6−i6−i6i6i600000000000000000000000000000000000000
χ924-444-4-44-4-2-44i−4i4i−4i44-422-2-2-222−2i2i−2i2i−2i2i−2i2i0000−4i4i00000000-222i−2i2i−2i2-2000000000000000000000000000000000000000000000000000000
χ934-444-4-44-4-2-4−4i4i−4i4i44-422-2-2-2222i−2i2i−2i2i−2i2i−2i00004i−4i00000000-22−2i2i−2i2i2-2000000000000000000000000000000000000000000000000000000
χ944-44-4-44-44440000-44-4-4-4-4-44440000000000000000000000440000-4-4000000000000000000000000000000000000000000000000000000
χ954-44-4-44-44-240000-44-42222-2-2-2−2i32i3−2i32i32i3−2i32i3−2i300000000000000-2-22i3−2i3−2i32i322000000000000000000000000000000000000000000000000000000
χ964-44-4-44-44-240000-44-42222-2-2-22i3−2i32i3−2i3−2i32i3−2i32i300000000000000-2-2−2i32i32i3−2i322000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-4404-4-44000-444-4-4-444-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-440-444-4000-444-4-4-44-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-4444-4-4-204-4-440002-2-2222-2-222-2-222-20000000000000000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ1004-4-4444-4-4-204-4-440002-2-2222-2-222-2-222-20000000000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ1014-4-4444-4-4-20-444-40002-2-2222-22-2-222-2-220000000000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ1024-4-4444-4-4-20-444-40002-2-2222-22-2-222-2-220000000000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ1034-4-4-44-444400000000-44-44-44-400000000000000000022−22−2222000000000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ1044-4-4-44-444400000000-44-44-44-4000000000000000000−222222−220000000000000000−222222−2222−22−222200000000000000000000000000000000000000
χ1054-4-4-44-444-2000000002-22-22-2223−23−2323−232323−23000000000022−22−222200000000−666−66−6−66−222−22−2−2200000000000000000000000000000000000000
χ1064-4-4-44-444-2000000002-22-22-2223−23−2323−232323−230000000000−222222−22000000006−6−66−666−62−2−22−222−200000000000000000000000000000000000000
χ1074-4-4-44-444-2000000002-22-22-22−232323−2323−23−2323000000000022−22−2222000000006−6−66−666−6−222−22−2−2200000000000000000000000000000000000000
χ1084-4-4-44-444-2000000002-22-22-22−232323−2323−23−23230000000000−222222−2200000000−666−66−6−662−2−22−222−200000000000000000000000000000000000000

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