Finite Group Databasebeta

← Group #10698464

Character table — Group #10698464

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12222222222236666666444466661212121244448888121212121212121212122424242424242424441212121222444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-2000000000000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000-2-2220000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-200000000000000002-222-2-200000000000000
χ1622222222-2-2-2-2222222222-22-2-2-2-2-2222200000000-2-20000000000000000-22-2-22200000000000000
χ1722222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000002-2
χ1822222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000220000000000000000000000000000000000-22
χ1922222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000000011−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-2-1-11100000000000000
χ2022222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000000011−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-2211-1-100000000000000
χ2122222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000000011i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-2211-1-100000000000000
χ2222222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000000011i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-2-1-11100000000000000
χ2322-2-2-222-222-2-2222-2-2-2-22000022-2-200000000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i2000000002i−2i000022−2−200
χ2422-2-2-222-222-2-2222-2-2-2-22000022-2-200000000−i2−i2i2i20000000000−i2−i2i2i2−i2−i2i2i200000000−2i2i0000−2−22200
χ2522-2-2-222-222-2-2222-2-2-2-22000022-2-200000000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i2000000002i−2i0000−2−22200
χ2622-2-2-222-222-2-2222-2-2-2-22000022-2-200000000i2i2−i2−i20000000000i2i2−i2−i2i2i2−i2−i200000000−2i2i000022−2−200
χ272-222-2-22-22-22-222-2-222-2-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000002-2000000−i2i2−i2i200
χ282-222-2-22-22-22-222-2-222-2-200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000-22000000i2−i2i2−i200
χ292-222-2-22-22-22-222-2-222-2-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000002-2000000i2−i2i2−i200
χ302-222-2-22-22-22-222-2-222-2-200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000-22000000−i2i2−i2i200
χ312-2-2-22-2222-2-2222-22-2-22-222-2-22-2-2222-2-2000000002-20000000000000000000000000000002i−2i−2i2i00
χ322-2-2-22-2222-2-2222-22-2-22-222-2-22-2-2222-2-2000000002-2000000000000000000000000000000−2i2i2i−2i00
χ332-2-2-22-2222-2-2222-22-2-22-2-2-2222-2-22-2-22200002-2-22-22000000002-2-222-2-2200000000000000000000
χ342-2-2-22-2222-2-2222-22-2-22-2-2-2222-2-22-2-2220000-222-2-2200000000-222-2-222-200000000000000000000
χ352-2-2-22-2222-2-22-1-11-111-11-2-222-111-111-1-100002-2-221-133−3−333−3−3-111-1-111-1003−33−300000000000000
χ362-2-2-22-2222-2-22-1-11-111-11-2-222-111-111-1-100002-2-221-1−3−333−3−333-111-1-111-100−33−3300000000000000
χ372-2-2-22-2222-2-22-1-11-111-11-2-222-111-111-1-10000-222-21-133−3−333−3−31-1-111-1-1100−33−3300000000000000
χ382-2-2-22-2222-2-22-1-11-111-11-2-222-111-111-1-10000-222-21-1−3−333−3−3331-1-111-1-11003−33−300000000000000
χ392-2-2-22-222-222-222-22-2-22-22-2-22-222-222-2-200000000-22000000000000000000000000002i2i−2i−2i000000
χ402-2-2-22-222-222-222-22-2-22-22-2-22-222-222-2-200000000-2200000000000000000000000000−2i−2i2i2i000000
χ412-2-2-22-222-222-222-22-2-22-2-222-2-222-2-2-2222i2i−2i−2i00002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422-2-2-22-222-222-222-22-2-22-2-222-2-222-2-2-222−2i−2i2i2i00002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432-2-2-22-222-222-2-1-11-111-11-222-21-1-1111-1-12i2i−2i−2i0000-11−i−iiiii−i−i−i3i3i3−i3i3−i3−i3i3003−3−3300000000000000
χ442-2-2-22-222-222-2-1-11-111-11-222-21-1-1111-1-12i2i−2i−2i0000-11−i−iiiii−i−ii3−i3−i3i3−i3i3i3−i300−333−300000000000000
χ452-2-2-22-222-222-2-1-11-111-11-222-21-1-1111-1-1−2i−2i2i2i0000-11ii−i−i−i−iii−i3i3i3−i3i3−i3−i3i300−333−300000000000000
χ462-2-2-22-222-222-2-1-11-111-11-222-21-1-1111-1-1−2i−2i2i2i0000-11ii−i−i−i−iiii3−i3−i3i3−i3i3i3−i3003−3−3300000000000000
χ47444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2-2-2-2-44-442222222200000000-2-2000000000000000000000000000000000000
χ49444-44-4-4-400004-44-44-44-40000000000002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ50444-44-4-4-400004-44-44-44-4000000000000−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ51444-44-4-4-40000-22-22-22-2200000000−2i32i3−2i32i32i−2i2i−2i0000002ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ220000000000000000000000000000
χ52444-44-4-4-40000-22-22-22-2200000000−2i32i3−2i32i3−2i2i−2i2i000000−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ220000000000000000000000000000
χ53444-44-4-4-40000-22-22-22-22000000002i3−2i32i3−2i32i−2i2i−2i0000002ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ140000000000000000000000000000
χ54444-44-4-4-40000-22-22-22-22000000002i3−2i32i3−2i3−2i2i−2i2i000000−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ140000000000000000000000000000
χ5544-44-4-4-4400004-444-44-4-40000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ5644-44-4-4-4400004-444-44-4-4000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ5744-4-4-444-444-4-4-2-2-22222-20000-2-22200000000−2i2−2i22i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000
χ5844-4-4-444-444-4-4-2-2-22222-20000-2-222000000002i22i2−2i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000
χ5944-4-4-444-4-4-444444-4-4-4-440000-4-44400000000000000000000000000000000000000000000000000
χ6044-4-4-444-4-4-444-2-2-22222-2000022-2-2000000000000000000000066−6−6−6−66600000000000000000000
χ6144-4-4-444-4-4-444-2-2-22222-2000022-2-20000000000000000000000−6−66666−6−600000000000000000000
χ624-444-4-44-44-44-4-2-222-2-2220000-22-2200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000
χ634-444-4-44-44-44-4-2-222-2-2220000-22-22000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000
χ644-444-4-44-4-44-4444-4-444-4-40000-44-4400000000000000000000000000000000000000000000000000
χ654-444-4-44-4-44-44-2-222-2-22200002-22-200000000000000000000006−66−6−66−6600000000000000000000
χ664-444-4-44-4-44-44-2-222-2-22200002-22-20000000000000000000000−66−666−66−600000000000000000000
χ674-44-4-44-4400004-4-444-4-440000000000000000000000000000000000000000000000002-2-22000000
χ684-44-4-44-4400004-4-444-4-44000000000000000000000000000000000000000000000000-222-2000000
χ694-4-4444-4-400004-4-4-4-44440000000000002-2-220000002-2-22-222-20000000000000000000000000000
χ704-4-4444-4-400004-4-4-4-4444000000000000-222-2000000-222-22-2-220000000000000000000000000000
χ714-4-4444-4-40000-22222-2-2-200000000−2i32i32i3−2i32-2-22000000−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i30000000000000000000000000000
χ724-4-4444-4-40000-22222-2-2-200000000−2i32i32i3−2i3-222-20000001+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i30000000000000000000000000000
χ734-4-4444-4-40000-22222-2-2-2000000002i3−2i3−2i32i32-2-22000000−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i30000000000000000000000000000
χ744-4-4444-4-40000-22222-2-2-2000000002i3−2i3−2i32i3-222-20000001−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i30000000000000000000000000000
χ754-4-4-44-4444-4-44-2-22-222-2244-4-4-222-2-2-22200000000-22000000000000000000000000000000000000
χ764-4-4-44-444-444-4-2-22-222-224-4-442-2-22-2-222000000002-2000000000000000000000000000000000000
χ7788-88-8-8-880000-44-4-44-4440000000000000000000000000000000000000000000000000000000000
χ788-88-8-88-880000-444-4-444-40000000000000000000000000000000000000000000000000000000000

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