Finite Group Databasebeta

← Group #10690504

Character table — Group #10690504

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order12224444344444444666121212122466888888881212121212121212121224242424242424242424242424242424444488888888441212121212121212888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1-111-1-111-1-1i−ii−iii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1-111-1-111-1-1−ii−ii−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-11-1-111-1-111i−i−iiii−i−i−i−iii
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-11-1-111-1-111−iii−i−i−iiiii−i−i
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1ii−i−iii−i−i-1111-1-1-1-111i−ii−i−i−iii−i−iii
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1−i−iii−i−iii-1111-1-1-1-111−ii−iiii−i−iii−i−i
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111ii−i−i−i−iii1-1-1-11111-1-1i−i−ii−i−iiiii−i−i
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111−i−iiiii−i−i1-1-1-11111-1-1−iii−iii−i−i−i−iii
χ1722222222222-2-222-2-22222222-2-2-2-20000000022-2-222-2-2-2-20000000000000000000000002222000000000000-2-200000000
χ1822222222222-2-222-2-22222222-2-2-2-20000000022-2-222-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ19222222222-2-222-2-2222222222-2-2-2-200000000-2-222-2-222-2-200000000000000000000222200000000000000-2-20000000000
χ20222222222-2-222-2-2222222222-2-2-2-200000000-2-222-2-222-2-200000000000000000000-2-2-2-200000000000000220000000000
χ21222222222-2-2-2-2-2-2-2-22222222222200000000-2-2-2-2-2-2-2-22200000000000000002-22-200000000002-22-20000000000000000
χ22222222222-2-2-2-2-2-2-2-22222222222200000000-2-2-2-2-2-2-2-2220000000000000000-22-220000000000-22-220000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-20000000000-11-11−i3i3−i3i3000000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2200000000001-11-1i3−i3i3−i3000000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000000000-11-11i3−i3i3−i3000000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2200000000001-11-1−i3i3−i3i3000000000000
χ312222-2-2-2-2222-2-2-2-222222-2-2-2-22-2220000000022-2-2-2-222-2-20000000000000000000000002i2i−2i−2i000000000000−2i2i00000000
χ322222-2-2-2-2222-2-2-2-222222-2-2-2-22-2220000000022-2-2-2-222-2-2000000000000000000000000−2i−2i2i2i0000000000002i−2i00000000
χ332222-2-2-2-22-2-22222-2-2222-2-2-2-22-22200000000-2-22222-2-2-2-2000000000000000000002i2i−2i−2i00000000000000−2i2i0000000000
χ342222-2-2-2-22-2-22222-2-2222-2-2-2-22-22200000000-2-22222-2-2-2-200000000000000000000−2i−2i2i2i000000000000002i−2i0000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2-2-222222200000000000000002-2-2200000000002-2-220000000000000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-200000000-2-2-2-22222220000000000000000-222-20000000000-222-20000000000000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-111-1-111000000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-22200000000-2211-1-111-1-1000000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-11111-1-1000000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-1-1-111000000000000
χ412222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-220000000000-111-1−i3i3i3−i3000000000000
χ422222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-200000000001-1-11i3−i3−i3i3000000000000
χ432222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-220000000000-111-1i3−i3−i3i3000000000000
χ442222-2-2-2-2-1-2-2-2-22222-1-1-11111-2211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-200000000001-1-11−i3i3i3−i3000000000000
χ452-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i000022−2−2−i2−i2i2i2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000001+i−1−i1−i−1+i0000
χ462-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i000022−2−2−i2−i2i2i2002-2002i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000−1−i1+i−1+i1−i0000
χ472-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i0000−2−222i2i2−i2−i2002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000−1−i1+i−1+i1−i0000
χ482-22-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i0000−2−222i2i2−i2−i2002-2002i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000001+i−1−i1−i−1+i0000
χ492-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i000022−2−2i2i2−i2−i2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000001−i−1+i1+i−1−i0000
χ502-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i000022−2−2i2i2−i2−i2002-200−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000−1+i1−i−1−i1+i0000
χ512-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i0000−2−222−i2−i2i2i2002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000−1+i1−i−1−i1+i0000
χ522-22-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i0000−2−222−i2−i2i2i2002-200−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000001−i−1+i1+i−1−i0000
χ532-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i00002−22−2−i2i2−i2i22-2002i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000001−i−1+i1+i−1−i
χ542-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i00002−22−2−i2i2−i2i22-2002i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i2000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000−1+i1−i−1−i1+i
χ552-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i0000−22−22i2−i2i2−i22-2002i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000−1+i1−i−1−i1+i
χ562-2-222i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i0000−22−22i2−i2i2−i22-2002i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i2000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000001−i−1+i1+i−1−i
χ572-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i00002−22−2i2−i2i2−i22-200−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000001+i−1−i1−i−1+i
χ582-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i00002−22−2i2−i2i2−i22-200−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000−1−i1+i−1+i1−i
χ592-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i0000−22−22−i2i2−i2i22-200−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000−1−i1+i−1+i1−i
χ602-2-22−2i2i−2i2i22-200−2i2i00-2-22−2i2i−2i2i0000−22−22−i2i2−i2i22-200−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000001+i−1−i1−i−1+i
χ6144444444-244-4-444-4-4-2-2-2-2-2-2-2-4-42200000000-2-222-2-2222200000000000000000000000000000000000000000000000000
χ6244444444-2-4-444-4-444-2-2-2-2-2-2-2-4-4220000000022-2-222-2-22200000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-244-4-4-4-444-2-2-222224-4-2-200000000-2-22222-2-22200000000000000000000000000000000000000000000000000
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χ6544-4-44-4-444000000004-4-44-4-4400002-2-222-2-2200000000002-2-222-2-222-2-222-2-220000000000000000000000000000000000
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χ6844-4-44-4-44-200000000-222-222-200−2i32i3-222-2-222-200000000−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ6944-4-44-4-44-200000000-222-222-2002i3−2i32-2-222-2-22000000002i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ7044-4-44-4-44-200000000-222-222-2002i3−2i3-222-2-222-2000000002i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ7144-4-4-444-44000000004-4-4-444-400002-2-22-222-200000000002-2-222-2-22-222-2-222-20000000000000000000000000000000000
χ7244-4-4-444-44000000004-4-4-444-40000-222-22-2-220000000000-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ7344-4-4-444-4-200000000-2222-2-2200−2i32i32-2-22-222-2000000002i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ7444-4-4-444-4-200000000-2222-2-2200−2i32i3-222-22-2-22000000002i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ7544-4-4-444-4-200000000-2222-2-22002i3−2i32-2-22-222-200000000−2i32i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ7644-4-4-444-4-200000000-2222-2-22002i3−2i3-222-22-2-2200000000−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ774-44-44i4i−4i−4i400-4400−4i4i-44-44i4i−4i−4i00000000000000-4400−4i4i0000000000000000000000000000000000000000000000000000
χ784-44-44i4i−4i−4i-2004-4004i−4i2-22−2i−2i2i2i00002222−22−22−2i2−2i22i22i200-2200−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ794-44-44i4i−4i−4i-2004-4004i−4i2-22−2i−2i2i2i0000−22−2222222i22i2−2i2−2i200-2200−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ804-44-44i4i−4i−4i-200-4400−4i4i2-22−2i−2i2i2i000000000000002-2002i−2i00i6i6−i6−i6−i6−i6i6i666−6−6−6−6660000000000000000000000000000000000
χ814-44-44i4i−4i−4i-200-4400−4i4i2-22−2i−2i2i2i000000000000002-2002i−2i00−i6−i6i6i6i6i6−i6−i6−6−66666−6−60000000000000000000000000000000000
χ824-44-4−4i−4i4i4i400-44004i−4i-44-4−4i−4i4i4i00000000000000-44004i−4i0000000000000000000000000000000000000000000000000000
χ834-44-4−4i−4i4i4i-2004-400−4i4i2-222i2i−2i−2i00002222−22−222i22i2−2i2−2i200-22002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ844-44-4−4i−4i4i4i-2004-400−4i4i2-222i2i−2i−2i0000−22−222222−2i2−2i22i22i200-22002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ854-44-4−4i−4i4i4i-200-44004i−4i2-222i2i−2i−2i000000000000002-200−2i2i00i6i6−i6−i6−i6−i6i6i6−6−66666−6−60000000000000000000000000000000000
χ864-44-4−4i−4i4i4i-200-44004i−4i2-222i2i−2i−2i000000000000002-200−2i2i00−i6−i6i6i6i6i6−i6−i666−6−6−6−6660000000000000000000000000000000000
χ874-4-444i−4i4i−4i4-4400−4i4i00-4-444i−4i4i−4i000000000000-4400−4i4i000000000000000000000000000000000000000000000000000000
χ884-4-444i−4i4i−4i-24-4004i−4i0022-2−2i2i−2i2i000022−2222−22−2i22i2−2i22i2-2200−2i2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ894-4-444i−4i4i−4i-24-4004i−4i0022-2−2i2i−2i2i0000−2222−22222i2−2i22i2−2i2-2200−2i2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ904-4-444i−4i4i−4i-2-4400−4i4i0022-2−2i2i−2i2i0000000000002-2002i−2i0000i6−i6i6−i6−i6i6−i6i66−66−6−66−660000000000000000000000000000000000
χ914-4-444i−4i4i−4i-2-4400−4i4i0022-2−2i2i−2i2i0000000000002-2002i−2i0000−i6i6−i6i6i6−i6i6−i6−66−666−66−60000000000000000000000000000000000
χ924-4-44−4i4i−4i4i4-44004i−4i00-4-44−4i4i−4i4i000000000000-44004i−4i000000000000000000000000000000000000000000000000000000
χ934-4-44−4i4i−4i4i-24-400−4i4i0022-22i−2i2i−2i000022−2222−222i2−2i22i2−2i2-22002i−2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ944-4-44−4i4i−4i4i-24-400−4i4i0022-22i−2i2i−2i0000−2222−2222−2i22i2−2i22i2-22002i−2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ954-4-44−4i4i−4i4i-2-44004i−4i0022-22i−2i2i−2i0000000000002-200−2i2i0000i6−i6i6−i6−i6i6−i6i6−66−666−66−60000000000000000000000000000000000
χ964-4-44−4i4i−4i4i-2-44004i−4i0022-22i−2i2i−2i0000000000002-200−2i2i0000−i6i6−i6i6i6−i6i6−i66−66−6−66−660000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.