Finite Group Databasebeta

← Group #10695860

Character table — Group #10695860

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order1222222234466666662444666612121212222266666666888812122424242424242424246612128888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-222222222-2-2-22222-2-2-2-20000000000000000-2-200000000000000000000002i−2i
χ10222222222-2-222222222-2-2-22222-2-2-2-20000000000000000-2-20000000000000000000000−2i2i
χ1122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ1222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-211110000000000
χ1322222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-1-2-211110000000000
χ1422222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2-1-11111111122-1-1-1-10000000000
χ15222222-2-22222222222-22-2-2-2-2-2-222220000000000000000-2-2000000002-222-2-20000000000
χ16222222-2-22222222222-22-2-2-2-2-2-222220000000000000000-2-200000000-22-2-2220000000000
χ17222222-2-22-2-22222222-2-222-2-2-2-2-2-2-2-20000000000000000220000000000000022-2-2000000
χ18222222-2-22-2-22222222-2-222-2-2-2-2-2-2-2-200000000000000002200000000000000-2-222000000
χ19222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000011−i3−i3−i3−i3i3i3i3i32-2-1-1110000000000
χ20222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000011i3i3i3i3−i3−i3−i3−i3-2211-1-10000000000
χ21222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000011−i3−i3−i3−i3i3i3i3i3-2211-1-10000000000
χ22222222-2-2-122-1-1-1-1-1-1-1-22-2-21111-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000011i3i3i3i3−i3−i3−i3−i32-2-1-1110000000000
χ232222-2-2222222-2-2-2-222-2-22-222-2-222-2-200000000000000002-20000000000000000002-20000
χ242222-2-2222222-2-2-2-222-2-22-222-2-222-2-200000000000000002-2000000000000000000-220000
χ252222-2-2222-2-22-2-2-2-222-22-2222-2-2-2-22200000000000022-2-2-2222-2-222-2-20000000000000000
χ262222-2-2222-2-22-2-2-2-222-22-2222-2-2-2-222000000000000-2-222-22-2-222-2-2220000000000000000
χ272222-2-222-1-2-2-11111-1-1-22-22-1-11111-1-10000−i3−i3i3i3−i3−i3i3i322-2-21-1-1-111-1-11100−i3i3−i3i30000000000
χ282222-2-222-1-2-2-11111-1-1-22-22-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3-2-2221-111-1-111-1-100i3−i3i3−i30000000000
χ292222-2-222-1-2-2-11111-1-1-22-22-1-11111-1-10000i3i3−i3−i3i3i3−i3−i322-2-21-1-1-111-1-11100i3−i3i3−i30000000000
χ302222-2-222-1-2-2-11111-1-1-22-22-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3-2-2221-111-1-111-1-100−i3i3−i3i30000000000
χ312222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-20000000000000000-22000000000000000000002-200
χ322222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-20000000000000000-2200000000000000000000-2200
χ332222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-22222-2-222-2-2-2-22200002-2000000000000000000000000
χ342222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-222-2-222-2-22222-2-200002-2000000000000000000000000
χ352222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-122-2-2-1-11111-1-10000-11−i3−i3i3i3i3i3−i3−i300−i3i3i3−i30000000000
χ362222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-122-2-2-1-11111-1-10000-11i3i3−i3−i3−i3−i3i3i300i3−i3−i3i30000000000
χ372222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-1-2-22211-1-1-1-1110000-11−i3−i3i3i3i3i3−i3−i300i3−i3−i3i30000000000
χ382222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-1-2-22211-1-1-1-1110000-11i3i3−i3−i3−i3−i3i3i300−i3i3i3−i30000000000
χ3944444444-2-4-4-2-2-2-2-2-2-24-4-4-4-2-2-2-22222000000000000000022000000000000000000000000
χ40444444-4-4-2-4-4-2-2-2-2-2-2-2-4-444222222220000000000000000-2-2000000000000000000000000
χ414444-4-444-244-22222-2-2-4-44-4-2-222-2-2220000000000000000-22000000000000000000000000
χ424444-4-4-4-4-244-22222-2-24-4-4422-2-2-2-22200000000000000002-2000000000000000000000000
χ4344-4-44-400400444-4-4-4-40000000000000000000000000000000000000000000000−2i22i2000000
χ4444-4-44-400400444-4-4-4-400000000000000000000000000000000000000000000002i2−2i2000000
χ4544-4-4-44004004-4-444-4-400000000000000000000000000000000000000000000−2i22i200000000
χ4644-4-4-44004004-4-444-4-4000000000000000000000000000000000000000000002i2−2i200000000
χ474-44-4000044-4-400004-4000000004-4002-22-22-22-22-22-2000000000000000000000000000000
χ484-44-4000044-4-400004-4000000004-400-22-22-22-22-22-22000000000000000000000000000000
χ494-44-400004-44-400004-400000000-44002-2-222-2-22-222-2000000000000000000000000000000
χ504-44-400004-44-400004-400000000-4400-222-2-222-22-2-22000000000000000000000000000000
χ514-44-40000-24-42−2i32i3−2i32i3-2200000000-22−2i32i32-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3000000000000000000000000000000
χ524-44-40000-24-42−2i32i3−2i32i3-2200000000-22−2i32i3-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i3000000000000000000000000000000
χ534-44-40000-24-422i3−2i32i3−2i3-2200000000-222i3−2i32-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i3000000000000000000000000000000
χ544-44-40000-24-422i3−2i32i3−2i3-2200000000-222i3−2i3-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i3000000000000000000000000000000
χ554-44-40000-2-442−2i32i3−2i32i3-22000000002-22i3−2i32-2-22−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i3000000000000000000000000000000
χ564-44-40000-2-442−2i32i3−2i32i3-22000000002-22i3−2i3-222-21−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3000000000000000000000000000000
χ574-44-40000-2-4422i3−2i32i3−2i3-22000000002-2−2i32i32-2-22−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i3000000000000000000000000000000
χ584-44-40000-2-4422i3−2i32i3−2i3-22000000002-2−2i32i3-222-21+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3000000000000000000000000000000
χ594-4-44004-4400-40000-4400004-40000000000000000000022−22000022−220022−220000000000000000
χ604-4-44004-4400-40000-4400004-400000000000000000000−22220000−222200−22220000000000000000
χ614-4-44004-4-2002−2i32i32i3−2i32-20000-22−2i32i300000000000000000022−2200i6−i6−22i6−i6−220000000000000000
χ624-4-44004-4-2002−2i32i32i3−2i32-20000-22−2i32i3000000000000000000−222200−i6i62−2−i6i62−20000000000000000
χ634-4-44004-4-20022i3−2i3−2i32i32-20000-222i3−2i300000000000000000022−2200−i6i6−22−i6i6−220000000000000000
χ644-4-44004-4-20022i3−2i3−2i32i32-20000-222i3−2i3000000000000000000−222200i6−i62−2i6−i62−20000000000000000
χ654-4-4400-44400-40000-440000-4400000000000000000022−22000022−2200−2222000000000000000000
χ664-4-4400-44400-40000-440000-44000000000000000000−22220000−22220022−22000000000000000000
χ674-4-4400-44-2002−2i32i32i3−2i32-200002-22i3−2i3000000000000000022−220000−22i6−i62−2−i6i60000000000000000
χ684-4-4400-44-2002−2i32i32i3−2i32-200002-22i3−2i30000000000000000−222200002−2−i6i6−22i6−i60000000000000000
χ694-4-4400-44-20022i3−2i3−2i32i32-200002-2−2i32i3000000000000000022−220000−22−i6i62−2i6−i60000000000000000
χ704-4-4400-44-20022i3−2i3−2i32i32-200002-2−2i32i30000000000000000−222200002−2i6−i6−22−i6i60000000000000000
χ7188-8-88-800-400-4-4-44444000000000000000000000000000000000000000000000000000000
χ7288-8-8-8800-400-444-4-444000000000000000000000000000000000000000000000000000000

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