Finite Group Databasebeta

← Group #10858789

Character table — Group #10858789

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666226666888888881212121212121212242424242424242424242424242424242244444444444466121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1
χ911111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-11-111-1-111-1-111-1-1-1-11-1-1-111
χ1011111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-111-1-111-1-1-1-11111-1111-1-1
χ1111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-11-1-111-1-11111-1-1-1-1-1111-1-1
χ1211111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-111-1-111-1-111111-1-1-111
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1111-1-1-1-111-1-1-1-1111-111-1-1
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1111-1-1-1-1111111-1-1-11-1-111
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-1-1111-1-1-11111-1-1-1-1-1-111-11-1-111
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11-1-1-11111-1-11111-1-11-111-1-1
χ17222222222-2-22222-2-22222222-2-2-2-2-2-200000000-2-2-22222-200000000000000000000000022220000000000000000-2-20000
χ18222222222-2-22222-2-22222222-2-2-2-2-2-200000000-2-2-22222-2000000000000000000000000-2-2-2-20000000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000022-2-20000000000000000-220000
χ20222222222-2-2-2-2-2-2-2-2222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000-2-22200000000000000002-20000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ292222-2-2-2-222222-2-2-2-22-2-222-2-22-222-2-20000000022-222-2-2-200000000000000002-22-200000000002-22-20000000000000000
χ302222-2-2-2-222222-2-2-2-22-2-222-2-22-222-2-20000000022-222-2-2-20000000000000000-22-220000000000-22-220000000000000000
χ312222-2-2-2-2222-2-222-2-22-2-222-2-2-22-2-2220000000022-2-2-222-200000000000000002-2-2200000000002-2-220000000000000000
χ322222-2-2-2-2222-2-222-2-22-2-222-2-2-22-2-2220000000022-2-2-222-20000000000000000-222-20000000000-222-20000000000000000
χ332222-2-2-2-22-2-222-2-2222-2-222-2-2-22-2-22200000000-2-2222-2-22000000000000000000002i2i−2i−2i00000000000000002i−2i00000000
χ342222-2-2-2-22-2-222-2-2222-2-222-2-2-22-2-22200000000-2-2222-2-2200000000000000000000−2i−2i2i2i0000000000000000−2i2i00000000
χ352222-2-2-2-22-2-2-2-222222-2-222-2-22-222-2-200000000-2-22-2-2222000000000000000000002i2i−2i−2i0000000000000000−2i2i00000000
χ362222-2-2-2-22-2-2-2-222222-2-222-2-22-222-2-200000000-2-22-2-222200000000000000000000−2i−2i2i2i00000000000000002i−2i00000000
χ372222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-11100000000-1-11-1-11113333−3−3−3−33333−3−3−3−32-22-20000000000-11-113−33−3000000000000
χ382222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-11100000000-1-11-1-11113333−3−3−3−33333−3−3−3−3-22-2200000000001-11-1−33−33000000000000
χ392222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-11100000000-1-11-1-1111−3−3−3−33333−3−3−3−333332-22-20000000000-11-11−33−33000000000000
χ402222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-11100000000-1-11-1-1111−3−3−3−33333−3−3−3−33333-22-2200000000001-11-13−33−3000000000000
χ412222-2-2-2-2-122-2-222-2-2-111-1-111-2211-1-100000000-1-1111-1-113333−3−3−3−3−3−3−3−333332-2-220000000000-111-13−3−33000000000000
χ422222-2-2-2-2-122-2-222-2-2-111-1-111-2211-1-100000000-1-1111-1-113333−3−3−3−3−3−3−3−33333-222-200000000001-1-11−333−3000000000000
χ432222-2-2-2-2-122-2-222-2-2-111-1-111-2211-1-100000000-1-1111-1-11−3−3−3−333333333−3−3−3−32-2-220000000000-111-1−333−3000000000000
χ442222-2-2-2-2-122-2-222-2-2-111-1-111-2211-1-100000000-1-1111-1-11−3−3−3−333333333−3−3−3−3-222-200000000001-1-113−3−33000000000000
χ4522-2-22-22-22002i−2i2i−2i0022-2-2-22-2000000−i2−i2i2i222−2−20002i−2i2i−2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000002i−2i2-2000000000000000000−i2i22−2
χ4622-2-22-22-22002i−2i2i−2i0022-2-2-22-2000000−i2−i2i2i222−2−20002i−2i2i−2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000−2i2i-22000000000000000000i2−i2−22
χ4722-2-22-22-22002i−2i2i−2i0022-2-2-22-2000000i2i2−i2−i2−2−2220002i−2i2i−2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000002i−2i2-2000000000000000000i2−i2−22
χ4822-2-22-22-22002i−2i2i−2i0022-2-2-22-2000000i2i2−i2−i2−2−2220002i−2i2i−2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000−2i2i-22000000000000000000−i2i22−2
χ4922-2-22-22-2200−2i2i−2i2i0022-2-2-22-2000000−i2−i2i2i2−2−222000−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000002i−2i-22000000000000000000i2−i22−2
χ5022-2-22-22-2200−2i2i−2i2i0022-2-2-22-2000000−i2−i2i2i2−2−222000−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000−2i2i2-2000000000000000000−i2i2−22
χ5122-2-22-22-2200−2i2i−2i2i0022-2-2-22-2000000i2i2−i2−i222−2−2000−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000002i−2i-22000000000000000000−i2i2−22
χ5222-2-22-22-2200−2i2i−2i2i0022-2-2-22-2000000i2i2−i2−i222−2−2000−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000−2i2i2-2000000000000000000i2−i22−2
χ532-22-22-2-2222-200002-2-22-22-2-2200000000002i−2i2i−2i2-220000-2000000002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i0000000000000000002-2000000
χ542-22-22-2-2222-200002-2-22-22-2-2200000000002i−2i2i−2i2-220000-2000000002i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i000000000000000000-22000000
χ552-22-22-2-2222-200002-2-22-22-2-220000000000−2i2i−2i2i2-220000-200000000−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i000000000000000000-22000000
χ562-22-22-2-2222-200002-2-22-22-2-220000000000−2i2i−2i2i2-220000-200000000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i0000000000000000002-2000000
χ572-22-2-222-22-2200002-2-2-222-22-20000002i−2i2i−2i0000-2220000-22i−2i2i−2i2i−2i2i−2i0000000000002-2-22000000000000002i−2i0000000000
χ582-22-2-222-22-2200002-2-2-222-22-20000002i−2i2i−2i0000-2220000-22i−2i2i−2i2i−2i2i−2i000000000000-222-200000000000000−2i2i0000000000
χ592-22-2-222-22-2200002-2-2-222-22-2000000−2i2i−2i2i0000-2220000-2−2i2i−2i2i−2i2i−2i2i0000000000002-2-2200000000000000−2i2i0000000000
χ602-22-2-222-22-2200002-2-2-222-22-2000000−2i2i−2i2i0000-2220000-2−2i2i−2i2i−2i2i−2i2i000000000000-222-2000000000000002i−2i0000000000
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222200000000222-2-2-2-2200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-2-4-444-4-444-222-2-222-4422-2-20000000022-2-2-222-200000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-4-4-44444-222-2-2224-4-2-2220000000022-222-2-2-200000000000000000000000000000000000000000000000000
χ6544-4-44-44-4-2004i−4i4i−4i00-2-2222-22000000−2i2−2i22i22i22222−22−22000−2i2i−2i2i0i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000000000000000000000
χ6644-4-44-44-4-2004i−4i4i−4i00-2-2222-220000002i22i2−2i2−2i2−22−222222000−2i2i−2i2i0−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000000000000000000000
χ6744-4-44-44-4-200−4i4i−4i4i00-2-2222-22000000−2i2−2i22i22i2−22−2222220002i−2i2i−2i0i2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000000000000000000000
χ6844-4-44-44-4-200−4i4i−4i4i00-2-2222-220000002i22i2−2i2−2i22222−22−220002i−2i2i−2i0−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000000000000000000000
χ6944-4-4-44-444004i−4i−4i4i004-44-4-4-44000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000
χ7044-4-4-44-44400−4i4i4i−4i004-44-4-4-4400000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ7144-4-4-44-44-2004i−4i−4i4i00-22-2222-200000000000000000−2i2i2i−2i0i6i6−i6−i6−i6−i6i6i6−6−66666−6−60000000000000000000000000000000000
χ7244-4-4-44-44-2004i−4i−4i4i00-22-2222-200000000000000000−2i2i2i−2i0−i6−i6i6i6i6i6−i6−i666−6−6−6−6660000000000000000000000000000000000
χ7344-4-4-44-44-200−4i4i4i−4i00-22-2222-2000000000000000002i−2i−2i2i0i6i6−i6−i6−i6−i6i6i666−6−6−6−6660000000000000000000000000000000000
χ7444-4-4-44-44-200−4i4i4i−4i00-22-2222-2000000000000000002i−2i−2i2i0−i6−i6i6i6i6i6−i6−i6−6−66666−6−60000000000000000000000000000000000
χ754-44-44-4-444-440000-44-44-44-4-4400000000000000-44-40000400000000000000000000000000000000000000000000000000
χ764-44-44-4-44-24-400004-42-22-222-200000000004i−4i4i−4i-22-20000200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ774-44-44-4-44-24-400004-42-22-222-20000000000−4i4i−4i4i-22-200002000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ784-44-44-4-44-2-440000-442-22-222-2000000000000002-220000-2−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000
χ794-44-44-4-44-2-440000-442-22-222-2000000000000002-220000-22i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000
χ804-44-4-444-444-40000-44-4-444-44-4000000000000004-4-40000400000000000000000000000000000000000000000000000000
χ814-44-4-444-4-24-40000-4422-2-22-2200000000000000-2220000-200000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000
χ824-44-4-444-4-24-40000-4422-2-22-2200000000000000-2220000-2000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000
χ834-44-4-444-4-2-4400004-422-2-22-220000004i−4i4i−4i00002-2-200002−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ844-44-4-444-4-2-4400004-422-2-22-22000000−4i4i−4i4i00002-2-2000022i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000
χ854-4-4444-4-4400000000-444-44-4-40000000000−2i22i22i2−2i20000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000
χ864-4-4444-4-4400000000-444-44-4-400000000002i2−2i2−2i22i200000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000
χ874-4-4444-4-4-2000000002-2-22-22200−2i32i3−2i32i30000−2i22i22i2−2i2000000006−6−66−666−6i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ884-4-4444-4-4-2000000002-2-22-22200−2i32i3−2i32i300002i2−2i2−2i22i200000000−666−66−6−66−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ894-4-4444-4-4-2000000002-2-22-222002i3−2i32i3−2i30000−2i22i22i2−2i200000000−666−66−6−66i2−i2−i2i2i2−i2−i2i20000000000000000000000000000000000
χ904-4-4444-4-4-2000000002-2-22-222002i3−2i32i3−2i300002i2−2i2−2i22i2000000006−6−66−666−6−i2i2i2−i2−i2i2i2−i20000000000000000000000000000000000
χ914-4-44-4-444400000000-4-4-4-444400000022−22−222200000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ924-4-44-4-444400000000-4-4-4-4444000000−222222−22000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ934-4-44-4-444-2000000002222-2-2-200−2i32i32i3−2i322−22−2222000000000000−222−2−222−2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000
χ944-4-44-4-444-2000000002222-2-2-200−2i32i32i3−2i3−222222−220000000000002−2−222−2−22−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ954-4-44-4-444-2000000002222-2-2-2002i3−2i3−2i32i322−22−2222000000000000−222−2−222−2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000
χ964-4-44-4-444-2000000002222-2-2-2002i3−2i3−2i32i3−222222−220000000000002−2−222−2−22i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000

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