Finite Group Databasebeta

← Group #10697114

Character table — Group #10697114

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666666644888888881212121212121212121212122424242424242424242424242424242444441212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2-2-2-2-222222222-200000000-2-22222-2-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-222222222-200000000-2-22222-2-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ112222222-2-22-2-22222222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000000000000000022-2-20000
χ122222222-2-22-2-22222222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000-2-2220000
χ132222222-2-2-222-2-2-22222222-220000000022-2-2-2-2-2-2-2-22200000000000000002-20022-2-20000000000000000
χ142222222-2-2-222-2-2-22222222-220000000022-2-2-2-2-2-2-2-2220000000000000000-2200-2-2220000000000000000
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-2200000000-1-111111111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200-1-111−i3−i3i3i3000000000000
χ20222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-2200000000-1-111111111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-220011-1-1i3i3−i3−i3000000000000
χ21222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-2200000000-1-111111111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-200-1-111i3i3−i3−i3000000000000
χ22222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-2200000000-1-111111111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i3000000000000
χ232222-2-22222-2-2-2-22-2-2-2-2222-222222-2-2-2-2-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-22222-2-2-2-22-2-2-2-2222-22-2-2-2-22222-2-222-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-2222-22222-2-2-2-2-2222-2-2000000002222-2-2-2-222-2-20000000000000000000000000000000000002-200
χ262222-2-2222-22222-2-2-2-2-2222-2-2000000002222-2-2-2-222-2-2000000000000000000000000000000000000-2200
χ272222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-22222-2-2-2-2000000000000000000000000000022-2-200000000
χ282222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-22222-2-2-2-20000000000000000000000000000-2-22200000000
χ292222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-2-2-222-2-222220000000000000000002-200002-22-2000000000000
χ302222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-2-2-222-2-22222000000000000000000-220000-22-22000000000000
χ312222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-211-1-111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3i3−i3000000000000
χ322222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-211-1-111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3−i3i3000000000000
χ332222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-2222211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3−i3i3000000000000
χ342222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-2222211-1-111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3i3−i3000000000000
χ352222-2-2-1-2-2-2-2-222-21111-1-1-122000000001111-1-111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3002-2−i3i3i3−i3-11-11000000000000
χ362222-2-2-1-2-2-2-2-222-21111-1-1-122000000001111-1-111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300-22i3−i3−i3i31-11-1000000000000
χ372222-2-2-1-2-2-2-2-222-21111-1-1-122000000001111-1-111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3002-2i3−i3−i3i3-11-11000000000000
χ382222-2-2-1-2-2-2-2-222-21111-1-1-122000000001111-1-111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300-22−i3i3i3−i31-11-1000000000000
χ392-2-222-22002002-2-222-2-2-22-200−i2−i2i2i2−i2−i2i2i20000002-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i2002-20000
χ402-2-222-22002002-2-222-2-2-22-200−i2−i2i2i2−i2−i2i2i20000002-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200-220000
χ412-2-222-22002002-2-222-2-2-22-200i2i2−i2−i2i2i2−i2−i20000002-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200-220000
χ422-2-222-22002002-2-222-2-2-22-200i2i2−i2−i2i2i2−i2−i20000002-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i2002-20000
χ432-2-22-22200200-22-2-2-222-22-200−i2−i2i2i2i2i2−i2−i20000002-2-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i22-2000000
χ442-2-22-22200200-22-2-2-222-22-200−i2−i2i2i2i2i2−i2−i20000002-2-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i2-22000000
χ452-2-22-22200200-22-2-2-222-22-200i2i2−i2−i2−i2−i2i2i20000002-2-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i2-22000000
χ462-2-22-22200200-22-2-2-222-22-200i2i2−i2−i2−i2−i2i2i20000002-2-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i22-2000000
χ47444444-244-4-4-4-4-4-4-2-2-2-2-2-2-24-40000000022-2-2-2-22222220000000000000000000000000000000000000000
χ48444444-2-4-44-4-4444-2-2-2-2-2-2-2-4-400000000222222-2-2-2-2220000000000000000000000000000000000000000
χ494444-4-4-244-44444-42222-2-2-2-4-400000000-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4-4444-4-442222-2-2-24-400000000-2-222-2-2-2-222220000000000000000000000000000000000000000
χ5144-4-40040004-400000004-4-4002-22-22-22-24-400000000002-22-22-22-22-22-22-22-2000000000000000000000000
χ5244-4-40040004-400000004-4-400-22-22-22-224-40000000000-22-22-22-22-22-22-22-22000000000000000000000000
χ5344-4-4004000-4400000004-4-4002-22-2-22-22-4400000000002-22-2-22-222-22-2-22-22000000000000000000000000
χ5444-4-4004000-4400000004-4-400-22-222-22-2-440000000000-22-222-22-2-22-222-22-2000000000000000000000000
χ5544-4-400-20004-4000−2i32i3−2i32i3-222002-22-22-22-2-2200000000−2i32i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000000000000000
χ5644-4-400-20004-4000−2i32i3−2i32i3-22200-22-22-22-22-2200000000−2i32i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i3000000000000000000000000
χ5744-4-400-20004-40002i3−2i32i3−2i3-222002-22-22-22-2-22000000002i3−2i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000000000000000
χ5844-4-400-20004-40002i3−2i32i3−2i3-22200-22-22-22-22-22000000002i3−2i31−i3−1+i31−i3−1+i31−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3−1−i3000000000000000000000000
χ5944-4-400-2000-44000−2i32i3−2i32i3-222002-22-2-22-222-2000000002i3−2i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i3000000000000000000000000
χ6044-4-400-2000-44000−2i32i3−2i32i3-22200-22-222-22-22-2000000002i3−2i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i3000000000000000000000000
χ6144-4-400-2000-440002i3−2i32i3−2i3-222002-22-2-22-222-200000000−2i32i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i3000000000000000000000000
χ6244-4-400-2000-440002i3−2i32i3−2i3-22200-22-222-22-22-200000000−2i32i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i3000000000000000000000000
χ634-44-40044-40000000000-4-44000000−2i22i22i2−2i2004-4000000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000
χ644-44-40044-40000000000-4-440000002i2−2i2−2i22i2004-40000000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000
χ654-44-4004-440000000000-4-4400−2i22i22i2−2i2000000-4400000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ664-44-4004-440000000000-4-44002i2−2i2−2i22i2000000-44000000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ674-44-400-24-4000000−2i32i32i3−2i322-2000000−2i22i22i2−2i200-22−2i32i3000000−666−6i2−i2−i2i26−6−66i2−i2−i2i2000000000000000000000000
χ684-44-400-24-4000000−2i32i32i3−2i322-20000002i2−2i2−2i22i200-22−2i32i30000006−6−66−i2i2i2−i2−666−6−i2i2i2−i2000000000000000000000000
χ694-44-400-24-40000002i3−2i3−2i32i322-2000000−2i22i22i2−2i200-222i3−2i30000006−6−66i2−i2−i2i2−666−6i2−i2−i2i2000000000000000000000000
χ704-44-400-24-40000002i3−2i3−2i32i322-20000002i2−2i2−2i22i200-222i3−2i3000000−666−6−i2i2i2−i26−6−66−i2i2i2−i2000000000000000000000000
χ714-44-400-2-44000000−2i32i32i3−2i322-200−2i22i22i2−2i20000002-22i3−2i3000000i2−i2−i2i2−666−6i2−i2−i2i26−6−66000000000000000000000000
χ724-44-400-2-44000000−2i32i32i3−2i322-2002i2−2i2−2i22i20000002-22i3−2i3000000−i2i2i2−i26−6−66−i2i2i2−i2−666−6000000000000000000000000
χ734-44-400-2-440000002i3−2i3−2i32i322-200−2i22i22i2−2i20000002-2−2i32i3000000i2−i2−i2i26−6−66i2−i2−i2i2−666−6000000000000000000000000
χ744-44-400-2-440000002i3−2i3−2i32i322-2002i2−2i2−2i22i20000002-2−2i32i3000000−i2i2i2−i2−666−6−i2i2i2−i26−6−66000000000000000000000000
χ754-4-444-4400-400-44444-4-4-44-40000000000000000-44-44000000000000000000000000000000000000000000
χ764-4-444-4-2004004-4-4-2-2222-2200−2i2−2i22i22i2−2i2−2i22i22i2000000-22-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ774-4-444-4-2004004-4-4-2-2222-22002i22i2−2i2−2i22i22i2−2i2−2i2000000-22-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ784-4-444-4-200-400-444-2-2222-2200000000000000002-22-20066−6−666−6−6−6−666−6−666000000000000000000000000
χ794-4-444-4-200-400-444-2-2222-2200000000000000002-22-200−6−666−6−66666−6−666−6−6000000000000000000000000
χ804-4-44-44400-4004-44-4-444-44-40000000000000000-444-4000000000000000000000000000000000000000000
χ814-4-44-44-200400-44-422-2-22-2200−2i2−2i22i22i22i22i2−2i2−2i2000000-222-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ824-4-44-44-200400-44-422-2-22-22002i22i2−2i2−2i2−2i2−2i22i22i2000000-222-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ834-4-44-44-200-4004-4422-2-22-2200000000000000002-2-220066−6−6−6−666−6−66666−6−6000000000000000000000000
χ844-4-44-44-200-4004-4422-2-22-2200000000000000002-2-2200−6−66666−6−666−6−6−6−666000000000000000000000000

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