Finite Group Databasebeta

← Group #10900881

Character table — Group #10900881

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order122222223444466666662244121212121212121222446666668888121212122424242424242424441212121244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ911111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-11-11-111-1-111-1-11-1
χ1011111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11-111-1-1-11-11-1-111-1-111-11
χ1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-1111-11-111-1-1-1-111-11
χ1211111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111-11-11-1-11111-1-11-1
χ1311111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-1111-11-1-1-11111-1-1-11
χ1411111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-111-11-1111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-11-11-1-1-111-1-1111-1
χ1611111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-1-11-1111-1-111-1-1-11
χ17222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2000022000000000000000000000000002-2-220000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200002200000000000000000000000000-222-20000000000
χ19222222222-2-2-2-22222222-2-222-2-22222-2-20000-2-20000000000000000000000000022-2-20000000000
χ20222222222-2-2-2-22222222-2-222-2-22222-2-20000-2-200000000000000000000000000-2-2220000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-1111122221111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-211111111111122-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-211-1-1-1-122-2-21111-1-1-1-111112-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-122-2-211-1-1-1-1-2-22211111111-1-1-1-1-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-22211111122-2-2-1-1-1-1-1-1-1-11111-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-11111-1-1-2-222111111-2-222-1-1-1-11111-1-1-1-12-2-1-11100000000000000
χ292-2-22-2-222222-2-22-2-2-2-2222-22-2-2-222-2-2222-22-22-222-2-2000022-2-20000000000000000000000000000
χ302-2-22-2-222222-2-22-2-2-2-2222-22-2-2-222-2-222-22-222-2-2-2220000-2-2220000000000000000000000000000
χ312-2-22-2-222222-2-22-2-2-2-222-22-22-2-2-2-222222-2-22-2222-2-20000-2-2220000000000000000000000000000
χ322-2-22-2-222222-2-22-2-2-2-222-22-22-2-2-2-22222-222-2-22-2-222000022-2-20000000000000000000000000000
χ332-2-22-2-2222-2-2222-2-2-2-2222-2-2222-2-222-2-200002-20000000000000000000000000000002-22-2000000
χ342-2-22-2-2222-2-2222-2-2-2-2222-2-2222-2-222-2-200002-2000000000000000000000000000000-22-22000000
χ352-2-22-2-2222-2-2222-2-2-2-222-222-22222-2-2-2-20000-220000000000000000000000000000002-2-22000000
χ362-2-22-2-2222-2-2222-2-2-2-222-222-22222-2-2-2-20000-22000000000000000000000000000000-222-2000000
χ372-2-22-2-222-122-2-2-11111-1-12-22-211-1-111-1-12-22-2-11-1-1110000-1-111−i3−i3i3i3−i3−i3i3i300−i3i3−i3i300000000000000
χ382-2-22-2-222-122-2-2-11111-1-12-22-211-1-111-1-12-22-2-11-1-1110000-1-111i3i3−i3−i3i3i3−i3−i300i3−i3i3−i300000000000000
χ392-2-22-2-222-122-2-2-11111-1-12-22-211-1-111-1-1-22-22-1111-1-1000011-1-1−i3−i3i3i3−i3−i3i3i300i3−i3i3−i300000000000000
χ402-2-22-2-222-122-2-2-11111-1-12-22-211-1-111-1-1-22-22-1111-1-1000011-1-1i3i3−i3−i3i3i3−i3−i300−i3i3−i3i300000000000000
χ412-2-22-2-222-122-2-2-11111-1-1-22-221111-1-1-1-12-2-221-1-1-111000011-1-1−i3−i3i3i3i3i3−i3−i300−i3i3i3−i300000000000000
χ422-2-22-2-222-122-2-2-11111-1-1-22-221111-1-1-1-12-2-221-1-1-111000011-1-1i3i3−i3−i3−i3−i3i3i300i3−i3−i3i300000000000000
χ432-2-22-2-222-122-2-2-11111-1-1-22-221111-1-1-1-1-222-21-111-1-10000-1-111−i3−i3i3i3i3i3−i3−i300i3−i3−i3i300000000000000
χ442-2-22-2-222-122-2-2-11111-1-1-22-221111-1-1-1-1-222-21-111-1-10000-1-111i3i3−i3−i3−i3−i3i3i300−i3i3i3−i300000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4222222220000-2-20000000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-44422-2-2-2-2220000220000000000000000000000000000000000000000
χ47444-4-4-44-440000-444-4-44-4000000000000000000000022−2200000022−2222−22000000000000000000000000
χ48444-4-4-44-440000-444-4-44-40000000000000000000000−2222000000−2222−2222000000000000000000000000
χ49444-4-4-44-4-200002-2-222-2200000023−2323−2300000000000022−22000000−22−226−66−600000000000000000000
χ50444-4-4-44-4-200002-2-222-2200000023−2323−23000000000000−22220000002−22−2−66−6600000000000000000000
χ51444-4-4-44-4-200002-2-222-22000000−2323−232300000000000022−22000000−22−22−66−6600000000000000000000
χ52444-4-4-44-4-200002-2-222-22000000−2323−2323000000000000−22220000002−22−26−66−600000000000000000000
χ5344-444-4-4-44000044-44-4-4-400000000000000000000000000000000000000000000000000000022−2200
χ5444-444-4-4-44000044-44-4-4-4000000000000000000000000000000000000000000000000000000−222200
χ5544-4-4-44-4444-44-4-44-4-44-4400004-400004-40000000000000000000000000000000000000000000000
χ5644-4-4-44-444-44-44-44-4-44-440000-440000-440000000000000000000000000000000000000000000000
χ5744-4-4-44-44-24-44-42-222-22-20000-220000-2200000000000000−2i32i3−2i32i30000000000000000000000000000
χ5844-4-4-44-44-24-44-42-222-22-20000-220000-22000000000000002i3−2i32i3−2i30000000000000000000000000000
χ5944-4-4-44-44-2-44-442-222-22-200002-200002-2000000−2i32i3−2i32i3000000000000000000000000000000000000
χ6044-4-4-44-44-2-44-442-222-22-200002-200002-20000002i3−2i32i3−2i3000000000000000000000000000000000000
χ614-444-44-4-4400004-44-44-4-4000000000000000000000000000000000000000000000000000022−220000
χ624-444-44-4-4400004-44-44-4-40000000000000000000000000000000000000000000000000000−22220000
χ634-44-44-4-4444-4-44-4-444-4-440000-4400004-40000000000000000000000000000000000000000000000
χ644-44-44-4-444-444-4-4-444-4-4400004-40000-440000000000000000000000000000000000000000000000
χ654-44-44-4-44-24-4-4422-2-222-200002-20000-2200000000000000−2i32i32i3−2i30000000000000000000000000000
χ664-44-44-4-44-24-4-4422-2-222-200002-20000-22000000000000002i3−2i3−2i32i30000000000000000000000000000
χ674-44-44-4-44-2-444-422-2-222-20000-2200002-2000000−2i32i32i3−2i3000000000000000000000000000000000000
χ684-44-44-4-44-2-444-422-2-222-20000-2200002-20000002i3−2i3−2i32i3000000000000000000000000000000000000
χ694-4-44-4-444-2-4-444-22222-2-24-4-44-2-222-2-2220000-220000000000000000000000000000000000000000
χ704-4-44-4-444-2-4-444-22222-2-2-444-4-2-2-2-2222200002-20000000000000000000000000000000000000000
χ714-4-4-4444-440000-4-4-4444-4000000000000000000000000−2i22i200000000−2i22i22i2−2i200000000000000000000
χ724-4-4-4444-440000-4-4-4444-40000000000000000000000002i2−2i2000000002i2−2i2−2i22i200000000000000000000
χ734-4-4-4444-4-20000222-2-2-2200000023−23−232300000000000000−2i22i20000i6−i6−i6i6i2−i2−i2i200000000000000000000
χ744-4-4-4444-4-20000222-2-2-2200000023−23−2323000000000000002i2−2i20000−i6i6i6−i6−i2i2i2−i200000000000000000000
χ754-4-4-4444-4-20000222-2-2-22000000−232323−2300000000000000−2i22i20000−i6i6i6−i6i2−i2−i2i200000000000000000000
χ764-4-4-4444-4-20000222-2-2-22000000−232323−23000000000000002i2−2i20000i6−i6−i6i6−i2i2i2−i200000000000000000000
χ7788-888-8-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000
χ788-888-88-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000

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