Finite Group Databasebeta

← Group #10689372

Character table — Group #10689372

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444422224444441212121212121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1
χ91-111-1-11-1111-11-1-1-11-1-1111-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i11-1-1ii−i−ii−iii−i−iii−i−ii−i1-111-1-1ii−i−i
χ101-111-1-11-1111-11-1-1-11-1-1111-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-111−i−iiii−iii−i−iii−i−i−ii-11-1-111−i−iii
χ111-111-1-11-1111-11-1-1-11-1-1111-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii11-1-1−i−iii−ii−i−iii−i−iii−ii1-111-1-1−i−iii
χ121-111-1-11-1111-11-1-1-11-1-1111-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-111ii−i−i−ii−i−iii−i−iiii−i-11-1-111ii−i−i
χ131-111-1-11-1111-11-1-1-11-1-1111-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i11-1-1ii−i−i−iiii−i−i−i−iiii−i1-1-1-111−i−iii
χ141-111-1-11-1111-11-1-1-11-1-1111-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i-1-111−i−iii−iiii−i−i−i−iii−ii-1111-1-1ii−i−i
χ151-111-1-11-1111-11-1-1-11-1-1111-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii11-1-1−i−iiii−i−i−iiiii−i−i−ii1-1-1-111ii−i−i
χ161-111-1-11-1111-11-1-1-11-1-1111-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iii-1-111ii−i−ii−i−i−iiiii−i−ii−i-1111-1-1−i−iii
χ17222222222222-2-2-22-22222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000022220000000000000000-2-200000000
χ18222222222222-2-2-22-22222222-2-20000000022-2-222-2-2-2-2-2-200000000000000000000-2-2-2-200000000000000002200000000
χ19222222222-2-2-2222-222222222-2-200000000-2-222-2-222-2-2-2-200000000000000000000000022220000000000-2-20000000000
χ20222222222-2-2-2222-222222222-2-200000000-2-222-2-222-2-2-2-2000000000000000000000000-2-2-2-20000000000220000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-2222200000000000000002-22-200000000002-22-20000000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-222220000000000000000-22-220000000000-22-220000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-20000000000-11-11−i3i3−i3i3000000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2200000000001-11-1i3−i3i3−i3000000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000000000-11-11i3−i3i3−i3000000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2200000000001-11-1−i3i3−i3i3000000000000
χ31222-22-2-2-222-2-2000202-22-2-22-200−i2−i2i2i2−i2−i2i2i22-2002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-22-2000000000000000000−i2i2−i2i20000
χ32222-22-2-2-222-2-2000202-22-2-22-200−i2−i2i2i2−i2−i2i2i22-2002-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-22-22000000000000000000i2−i2i2−i20000
χ33222-22-2-2-222-2-2000202-22-2-22-200i2i2−i2−i2i2i2−i2−i22-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-22-2000000000000000000i2−i2i2−i20000
χ34222-22-2-2-222-2-2000202-22-2-22-200i2i2−i2−i2i2i2−i2−i22-2002-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-22-22000000000000000000−i2i2−i2i20000
χ3522-2-2-2-222200022-20-22-2-22-2-2200−i2i2−i2i2−i2i2−i2i2002-2002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000002-22-2000000000000000000−i2i2−i2i2
χ3622-2-2-2-222200022-20-22-2-22-2-2200−i2i2−i2i2−i2i2−i2i2002-2002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000-22-22000000000000000000i2−i2i2−i2
χ3722-2-2-2-222200022-20-22-2-22-2-2200i2−i2i2−i2i2−i2i2−i2002-2002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000002-22-2000000000000000000i2−i2i2−i2
χ3822-2-2-2-222200022-20-22-2-22-2-2200i2−i2i2−i2i2−i2i2−i2002-2002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000-22-22000000000000000000−i2i2−i2i2
χ392-222-2-22-2222-2-222-2-2-2-2222-2-22-20000000022-2-2-2-22222-2-20000000000000000000022-2-20000000000000000-2200000000
χ402-222-2-22-2222-2-222-2-2-2-2222-2-22-20000000022-2-2-2-22222-2-200000000000000000000-2-22200000000000000002-200000000
χ412-222-2-22-22-2-222-2-222-2-2222-2-22-200000000-2-22222-2-222-2-20000000000000000000000002i2i−2i−2i0000000000−2i2i0000000000
χ422-222-2-22-22-2-222-2-222-2-2222-2-22-200000000-2-22222-2-222-2-2000000000000000000000000−2i−2i2i2i00000000002i−2i0000000000
χ432-222-2-22-22-2-22-2222-2-2-2222-2-2-2200000000-2-2-2-22222-2-22200000000000000002i−2i−2i2i00000000002i−2i−2i2i0000000000000000
χ442-222-2-22-22-2-22-2222-2-2-2222-2-2-2200000000-2-2-2-22222-2-2220000000000000000−2i2i2i−2i0000000000−2i2i2i−2i0000000000000000
χ452-222-2-22-2-122-22-2-2-2211-1-1-111-222222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i000000002i−2i−i−iii−i−iii000000000000
χ462-222-2-22-2-122-22-2-2-2211-1-1-111-222222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111−2i−2i2i2i00000000−2i2iii−i−iii−i−i000000000000
χ472-222-2-22-2-122-22-2-2-2211-1-1-111-22-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i00000000−2i2i−i−iiiii−i−i000000000000
χ482-222-2-22-2-122-22-2-2-2211-1-1-111-22-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i000000002i−2iii−i−i−i−iii000000000000
χ492-222-2-22-2-1-2-22-2222-211-1-1-111-22000000001111-1-1-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32i−2i−2i2i0000000000−iii−i3−3−33000000000000
χ502-222-2-22-2-1-2-22-2222-211-1-1-111-22000000001111-1-1-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−2i2i2i−2i0000000000i−i−ii−333−3000000000000
χ512-222-2-22-2-1-2-22-2222-211-1-1-111-22000000001111-1-1-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32i−2i−2i2i0000000000−iii−i−333−3000000000000
χ522-222-2-22-2-1-2-22-2222-211-1-1-111-22000000001111-1-1-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3−2i2i2i−2i0000000000i−i−ii3−3−33000000000000
χ532-22-2-22-2222-22000-20-222-2-2-2200−i2−i2i2i2i2i2−i2−i22-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002-2-22000000000000000000−i2i2i2−i20000
χ542-22-2-22-2222-22000-20-222-2-2-2200−i2−i2i2i2i2i2−i2−i22-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-222-2000000000000000000i2−i2−i2i20000
χ552-22-2-22-2222-22000-20-222-2-2-2200i2i2−i2−i2−i2−i2i2i22-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002-2-22000000000000000000i2−i2−i2i20000
χ562-22-2-22-2222-22000-20-222-2-2-2200i2i2−i2−i2−i2−i2i2i22-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-222-2000000000000000000−i2i2i2−i20000
χ572-2-2-2222-220002-220-2-22-22-22-200−i2i2−i2i2i2−i2i2−i2002-200-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000002i−2i−2i2i0000000000000000002−2−22
χ582-2-2-2222-220002-220-2-22-22-22-200−i2i2−i2i2i2−i2i2−i2002-200-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000−2i2i2i−2i000000000000000000−222−2
χ592-2-2-2222-220002-220-2-22-22-22-200i2−i2i2−i2−i2i2−i2i2002-200-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000002i−2i−2i2i000000000000000000−222−2
χ602-2-2-2222-220002-220-2-22-22-22-200i2−i2i2−i2−i2i2−i2i2002-200-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000−2i2i2i−2i0000000000000000002−2−22
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χ7644-4-4-4-444-200044-40-4-222-222-2002i2−2i22i2−2i22i2−2i22i2−2i200-2200-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
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χ914-4-444-4-44-2000000002222-2-2-200-222-22-2-22000000002i3−2i3−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ924-4-4-4444-44000-44-404-44-44-44-4000000000000-44004-4000000000000000000000000000000000000000000000000000000
χ934-4-4-4444-4-20004-440-42-22-22-2200−2i22i2−2i22i22i2−2i22i2−2i200-22002-20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ944-4-4-4444-4-20004-440-42-22-22-22002i2−2i22i2−2i2−2i22i2−2i22i200-22002-20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ954-4-4-4444-4-2000-44-4042-22-22-220000000000002-200-2200006−66−6−66−66−66−666−66−60000000000000000000000000000000000
χ964-4-4-4444-4-2000-44-4042-22-22-220000000000002-200-220000−66−666−66−66−66−6−66−660000000000000000000000000000000000

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