Finite Group Databasebeta

← Group #10900885

Character table — Group #10900885

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12222222344446666666224466661212121244448888121212121212121212122424242424242424441212121222444444888844
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
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1111-11-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-1-11-1111-1-111-11
χ1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111111-11-1-1-1-1-111-11
χ1211111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-11-111111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-11-11-1-1-1-1111-1
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-11-11-11111-1-1-11
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-111-11-11-1-111-1-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-11-11-111-1-1111-1
χ17222222222-2-2-2-2222222222-2-22222-2-2-2-200000000-2-20000000000000000000000002-2-2200000000
χ18222222222-2-2-2-2222222222-2-22222-2-2-2-200000000-2-2000000000000000000000000-222-200000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-2000000002200000000000000000000000022-2-200000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-20000000022000000000000000000000000-2-22200000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-222-2-211-1-1-1-11111-1-1-1-111112-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-122-2-2-2-22211-1-1-1-111111111-1-1-1-1-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-22222-2-2111111-1-1-1-1-1-1-1-11111-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-21111-1-1-1-1-2-222-2-222111111-1-1-1-11111-1-1-1-12-2-1-11100000000000000
χ292-2-2-2-2222222-2-222-2-2-2-222-22-222-2-2-2-222000000002-200000000000000000000002-200002-2000000
χ302-2-2-2-2222222-2-222-2-2-2-222-22-222-2-2-2-222000000002-20000000000000000000000-220000-22000000
χ312-2-2-2-2222222-2-222-2-2-2-22-22-22-2-222-2-22200000000-2200000000000000000000002-20000-22000000
χ322-2-2-2-2222222-2-222-2-2-2-22-22-22-2-222-2-22200000000-220000000000000000000000-2200002-2000000
χ332-2-2-2-22222-2-22222-2-2-2-222-2-2222-2-222-2-22-22-20000-2222-2-222-2-20000000000000000000000000000
χ342-2-2-2-22222-2-22222-2-2-2-222-2-2222-2-222-2-2-22-220000-22-2-222-2-2220000000000000000000000000000
χ352-2-2-2-22222-2-22222-2-2-2-22-222-2-2-22222-2-22-2-2200002-222-2-2-2-2220000000000000000000000000000
χ362-2-2-2-22222-2-22222-2-2-2-22-222-2-2-22222-2-2-222-200002-2-2-22222-2-20000000000000000000000000000
χ372-2-2-2-2222-1-2-222-1-11111-12-2-22-1-111-1-1112-22-200001-1-1-111-1-11133−3−333−3−3003−33−300000000000000
χ382-2-2-2-2222-1-2-222-1-11111-12-2-22-1-111-1-1112-22-200001-1-1-111-1-111−3−333−3−33300−33−3300000000000000
χ392-2-2-2-2222-1-2-222-1-11111-12-2-22-1-111-1-111-22-2200001-111-1-111-1-133−3−333−3−300−33−3300000000000000
χ402-2-2-2-2222-1-2-222-1-11111-12-2-22-1-111-1-111-22-2200001-111-1-111-1-1−3−333−3−333003−33−300000000000000
χ412-2-2-2-2222-1-2-222-1-11111-1-222-211-1-1-1-1112-2-220000-11-1-11111-1-133−3−3−3−333003−3−3300000000000000
χ422-2-2-2-2222-1-2-222-1-11111-1-222-211-1-1-1-1112-2-220000-11-1-11111-1-1−3−33333−3−300−333−300000000000000
χ432-2-2-2-2222-1-2-222-1-11111-1-222-211-1-1-1-111-222-20000-1111-1-1-1-11133−3−3−3−33300−333−300000000000000
χ442-2-2-2-2222-1-2-222-1-11111-1-222-211-1-1-1-111-222-20000-1111-1-1-1-111−3−33333−3−3003−3−3300000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4442222222200000000-2-2000000000000000000000000000000000000
χ47444-4-4-44-4400004-444-4-4-4000000000000000022−2200000000000022−2222−22000000000000000000000000
χ48444-4-4-44-4400004-444-4-4-40000000000000000−2222000000000000−2222−2222000000000000000000000000
χ49444-4-4-44-4-20000-22-2-22220000−2i32i3−2i32i30000000022−22000000000000−22−22i6−i6i6−i600000000000000000000
χ50444-4-4-44-4-20000-22-2-22220000−2i32i3−2i32i300000000−22220000000000002−22−2−i6i6−i6i600000000000000000000
χ51444-4-4-44-4-20000-22-2-222200002i3−2i32i3−2i30000000022−22000000000000−22−22−i6i6−i6i600000000000000000000
χ52444-4-4-44-4-20000-22-2-222200002i3−2i32i3−2i300000000−22220000000000002−22−2i6−i6i6−i600000000000000000000
χ5344-44-44-4-440000-444-44-4-4000000000000000000000000000000000000000000000000000022−220000
χ5444-44-44-4-440000-444-44-4-40000000000000000000000000000000000000000000000000000−22220000
χ5544-4-44-4-4444-44-4-4-44-4-444000000004-44-40000000000000000000000000000000000000000000000
χ5644-4-44-4-444-44-44-4-44-4-44400000000-44-440000000000000000000000000000000000000000000000
χ5744-4-44-4-44-24-44-422-222-2-200000000-22-2200000000000000−2i32i3−2i32i30000000000000000000000000000
χ5844-4-44-4-44-24-44-422-222-2-200000000-22-22000000000000002i3−2i32i3−2i30000000000000000000000000000
χ5944-4-44-4-44-2-44-4422-222-2-2000000002-22-20000000000−2i32i3−2i32i300000000000000000000000000000000
χ6044-4-44-4-44-2-44-4422-222-2-2000000002-22-200000000002i3−2i32i3−2i300000000000000000000000000000000
χ614-444-4-4-4444-4-44-4-4-444-4400000000-444-40000000000000000000000000000000000000000000000
χ624-444-4-4-444-444-4-4-4-444-44000000004-4-440000000000000000000000000000000000000000000000
χ634-444-4-4-44-24-4-44222-2-22-2000000002-2-220000000000−2i32i32i3−2i300000000000000000000000000000000
χ644-444-4-4-44-24-4-44222-2-22-2000000002-2-2200000000002i3−2i3−2i32i300000000000000000000000000000000
χ654-444-4-4-44-2-444-4222-2-22-200000000-222-200000000000000−2i32i32i3−2i30000000000000000000000000000
χ664-444-4-4-44-2-444-4222-2-22-200000000-222-2000000000000002i3−2i3−2i32i30000000000000000000000000000
χ674-44-444-4-440000-44-44-44-400000000000000000000000000000000000000000000000000000022−2200
χ684-44-444-4-440000-44-44-44-4000000000000000000000000000000000000000000000000000000−222200
χ694-4-444-44-4400004-4-4-444-4000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000
χ704-4-444-44-4400004-4-4-444-40000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000
χ714-4-444-44-4-20000-2222-2-220000−2i32i32i3−2i30000000000−2i22i200000000006−6−66i2−i2−i2i200000000000000000000
χ724-4-444-44-4-20000-2222-2-220000−2i32i32i3−2i300000000002i2−2i20000000000−666−6−i2i2i2−i200000000000000000000
χ734-4-444-44-4-20000-2222-2-2200002i3−2i3−2i32i30000000000−2i22i20000000000−666−6i2−i2−i2i200000000000000000000
χ744-4-444-44-4-20000-2222-2-2200002i3−2i3−2i32i300000000002i2−2i200000000006−6−66−i2i2i2−i200000000000000000000
χ754-4-4-4-4444-244-4-4-2-22222-24-44-4-2-22222-2-200000000-22000000000000000000000000000000000000
χ764-4-4-4-4444-244-4-4-2-22222-2-44-4422-2-222-2-2000000002-2000000000000000000000000000000000000
χ7788-88-88-8-8-400004-4-44-4440000000000000000000000000000000000000000000000000000000000
χ788-88-888-8-8-400004-44-44-440000000000000000000000000000000000000000000000000000000000

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