Finite Group Databasebeta

← Group #10909525

Character table — Group #10909525

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222244444444448888888888888888888888888888812121616161616242424242424242424484848
order122222223444466666664412121212121212124444444888812121212121212121212242424242424242422412121212244448888444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-111-1
χ411111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11
χ61111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111111-1
χ71111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1111-1-11111-1-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111
χ911111111111111111111-1-1-1-1-1-11111-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-111-11-111-1-1111-1-1
χ1011111111111111111111-1-1-1-1-1-11111-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-11-1-111-1-1-111
χ1111111111111111111111-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-11-1-1-111-1-11-11
χ1211111111111111111111-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11-1111-1-111-11-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-11-11111-1-1-11-1
χ1411111111111111111111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-11-1-1-1-1111-11
χ1511111111111111111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-11-1-1-1-1-111-111
χ1611111111111111111111-1-1-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11-111111-1-11-1-1
χ17222222222-2-2-2-22222222222222-2-2-2-2-20000000000-2-200000000000000002200000-2-22000000000
χ18222222222-2-2-2-22222222222222-2-2-2-2-20000000000-2-20000000000000000-2-20000022-2000000000
χ19222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22000000000022000000000000000022000002-2-2000000000
χ20222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-220000000000220000000000000000-2-200000-222000000000
χ2122222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-2-2-2-222-2-2-2-2-1-11111111111111111002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-222-2-22222-2-211-1-1-1-11111-1-1-1-1111100-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-222-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-1002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2-22222-2-222111111-1-1-1-11111-1-1-1-100-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2-222-2-222-2-2111111-1-1-1-1-1-1-1-11111002-1-111000000000000
χ2922-22-2-2-2222-22-22-2-2-22-2200000022-2-202i−2i00000000002i2i−2i−2i00000000000000000000002-2002i−2i000
χ3022-22-2-2-2222-22-22-2-2-22-2200000022-2-202i−2i00000000002i2i−2i−2i0000000000000000000000-2200−2i2i000
χ3122-22-2-2-2222-22-22-2-2-22-2200000022-2-20−2i2i0000000000−2i−2i2i2i00000000000000000000002-200−2i2i000
χ3222-22-2-2-2222-22-22-2-2-22-2200000022-2-20−2i2i0000000000−2i−2i2i2i0000000000000000000000-22002i−2i000
χ332-2-2-2-22222-2-222-222-2-2-220000002-22-20002-22-2002-200000022-2-2000022-2-2000002-2000000000000
χ342-2-2-2-22222-2-222-222-2-2-220000002-22-20002-2-2200-2200000022-2-20000-2-22200000-22000000000000
χ352-2-2-2-22222-2-222-222-2-2-220000002-22-2000-222-200-22000000-2-2220000-2-222000002-2000000000000
χ362-2-2-2-22222-2-222-222-2-2-220000002-22-2000-22-22002-2000000-2-222000022-2-200000-22000000000000
χ372-2-2-2-2222-1-2-2221-1-1111-10033−3−3-11-110002-22-2002-23−33−33−3-1-11133−3−3-1-1110003−3-11000000000000
χ382-2-2-2-2222-1-2-2221-1-1111-10033−3−3-11-110002-2-2200-223−33−33−3-1-111−3−33311-1-1000−331-1000000000000
χ392-2-2-2-2222-1-2-2221-1-1111-10033−3−3-11-11000-222-200-223−3−33−3311-1-1−3−33311-1-10003−3-11000000000000
χ402-2-2-2-2222-1-2-2221-1-1111-10033−3−3-11-11000-22-22002-23−3−33−3311-1-133−3−3-1-111000−331-1000000000000
χ412-2-2-2-2222-1-2-2221-1-1111-100−3−333-11-110002-22-2002-2−33−33−33-1-111−3−333-1-111000−33-11000000000000
χ422-2-2-2-2222-1-2-2221-1-1111-100−3−333-11-110002-2-2200-22−33−33−33-1-11133−3−311-1-10003−31-1000000000000
χ432-2-2-2-2222-1-2-2221-1-1111-100−3−333-11-11000-222-200-22−333−33−311-1-133−3−311-1-1000−33-11000000000000
χ442-2-2-2-2222-1-2-2221-1-1111-100−3−333-11-11000-22-22002-2−333−33−311-1-1−3−333-1-1110003−31-1000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-2-2-2-22222-400000000002200000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-42222222240000000000-2-200000000000000000000000000000000000
χ47444-4-4-44-44000044-44-4-4-40000000000000000022−2200000000000022−2222−2200000000000000000000000
χ48444-4-4-44-44000044-44-4-4-400000000000000000−2222000000000000−2222−222200000000000000000000000
χ49444-4-4-44-4-20000-2-22-222200−2i32i3−2i32i30000000000022−22000000000000−22−22i6−i6i6−i60000000000000000000
χ50444-4-4-44-4-20000-2-22-222200−2i32i3−2i32i300000000000−22220000000000002−22−2−i6i6−i6i60000000000000000000
χ51444-4-4-44-4-20000-2-22-2222002i3−2i32i3−2i30000000000022−22000000000000−22−22−i6i6−i6i60000000000000000000
χ52444-4-4-44-4-20000-2-22-2222002i3−2i32i3−2i300000000000−22220000000000002−22−2i6−i6i6−i60000000000000000000
χ5344-44-4-4-444-44-444-4-4-44-44000000-4-444000000000000000000000000000000000000000000000000
χ5444-44-4-4-44-24-44-4-2222-22-2000000-2-22204i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ5544-44-4-4-44-24-44-4-2222-22-2000000-2-2220−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ5644-44-4-4-44-2-44-44-2222-22-200000022-2-200000000000000000−2i32i3−2i32i3000000000000000000000000000
χ5744-44-4-4-44-2-44-44-2222-22-200000022-2-2000000000000000002i3−2i32i3−2i3000000000000000000000000000
χ5844-4-444-4-4400004-44-4-44-40000000000000000000000000000000000000004-400000000000000000
χ5944-4-444-4-4400004-44-4-44-4000000000000000000000000000000000000000-4400000000000000000
χ604-444-44-4-440000-4-4444-4-400000000000000000000000000000000000000000000000000022−2200000
χ614-444-44-4-440000-4-4444-4-4000000000000000000000000000000000000000000000000000−222200000
χ624-44-44-4-4444-4-44-4-4-44-444000000-444-4000000000000000000000000000000000000000000000000
χ634-44-44-4-444-444-4-4-4-44-4440000004-4-44000000000000000000000000000000000000000000000000
χ644-44-44-4-44-24-4-44222-22-2-20000002-2-2200000000000000000−2i32i32i3−2i3000000000000000000000000000
χ654-44-44-4-44-24-4-44222-22-2-20000002-2-22000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ664-44-44-4-44-2-444-4222-22-2-2000000-222-20000000000000−2i32i32i3−2i30000000000000000000000000000000
χ674-44-44-4-44-2-444-4222-22-2-2000000-222-200000000000002i3−2i3−2i32i30000000000000000000000000000000
χ684-4-444-44-440000-44-4-444-44i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ694-4-444-44-440000-44-4-444-4−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ704-4-444-44-4-200002-222-2-224i−4i−2i2i2i−2i00000000000000000000000006−6−66i6−i6−i6i60000000000000000000
χ714-4-444-44-4-200002-222-2-224i−4i−2i2i2i−2i0000000000000000000000000−666−6−i6i6i6−i60000000000000000000
χ724-4-444-44-4-200002-222-2-22−4i4i2i−2i−2i2i00000000000000000000000006−6−66−i6i6i6−i60000000000000000000
χ734-4-444-44-4-200002-222-2-22−4i4i2i−2i−2i2i0000000000000000000000000−666−6i6−i6−i6i60000000000000000000
χ744-4-4-4-4444444-4-4-444-4-4-44000000-44-44000000000000000000000000000000000000000000000000
χ754-4-4-4-4444-244-4-42-2-2222-2002323−23−232-22-200000000000−232300000000000000000000000000000000000
χ764-4-4-4-4444-244-4-42-2-2222-200−23−2323232-22-20000000000023−2300000000000000000000000000000000000
χ7788-8-888-8-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000
χ788-888-88-8-8-4000044-4-4-4440000000000000000000000000000000000000000000000000000000000

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