Finite Group Databasebeta

← Group #10844809

Character table — Group #10844809

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order122222223444466666668888121212124444444444881212121224242424242424244488884412121212121212124444448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-111-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-111-1-1-1-1
χ311111111111111111111111111111111-1-11-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-11-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1
χ911111111111111111111-1-1-1-111111111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-11111-1-1-1-111-1-1-1-1111-1
χ1111111111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-11111-1-1-1-11111-1-11-1
χ1211111111111111111111-1-1-1-111111111-1-1-111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-11
χ1311111111111111111111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111111-1
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111-11111-1-1-1-1-1-11111-1-1-11
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-111-1-1-1-111-11
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-11111-1-11111-11-1-1-1-111111111-1-1-1-11-1
χ17222222222-2-2-2-222222220000-2-2-2-2222200200-20022-2-200000000-2-200000000000000002-2000000
χ18222222222-2-2-2-222222220000-2-2-2-2222200-200200-2-22200000000-2-20000000000000000-22000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-200200-20022-2-200000000220000000000000000-22000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-200-200200-2-222000000002200000000000000002-2000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-1000022-222-2-2-21111-1-1-1-11111000000-2-2-1-111-1-1110000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-22-2-2222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-2-2-2-21111-1-1-1-111110000002211-1-111-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000222-2-22-2-2-1-1-1-111111111000000-22-1-11111-1-10000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-2-22211111111-1-1-1-10000002-2-1-1-1-111110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22222-2-2-1-1-1-1111111110000002-211-1-1-1-1110000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-2-222-22211111111-1-1-1-1000000-221111-1-1-1-10000000000
χ2922-22-2-2-2222-2-2222-2-2-22-200002-2-2200002i−2i000000000000000000002i2i−2i−2i002i−2i00000000002-20000
χ3022-22-2-2-2222-2-2222-2-2-22-200002-2-2200002i−2i00000000000000000000−2i−2i2i2i002i−2i0000000000-220000
χ3122-22-2-2-2222-2-2222-2-2-22-200002-2-220000−2i2i000000000000000000002i2i−2i−2i00−2i2i0000000000-220000
χ3222-22-2-2-2222-2-2222-2-2-22-200002-2-220000−2i2i00000000000000000000−2i−2i2i2i00−2i2i00000000002-20000
χ332-22-2-22-2222-22-2-2-2-2222-2000022-2-200000002i−2i000000000000000002-22-20000002i−2i002i−2i00000000
χ342-22-2-22-2222-22-2-2-2-2222-2000022-2-200000002i−2i00000000000000000-22-220000002i−2i00−2i2i00000000
χ352-22-2-22-2222-22-2-2-2-2222-2000022-2-20000000−2i2i000000000000000002-22-2000000−2i2i00−2i2i00000000
χ362-22-2-22-2222-22-2-2-2-2222-2000022-2-20000000−2i2i00000000000000000-22-22000000−2i2i002i−2i00000000
χ372-2-2-22-222222-2-2-2-22-2-2222i2i−2i−2i2-22-222-2-20000000000002i2i−2i−2i00002-22i−2i−2i2i00000000000000000000
χ382-2-2-22-222222-2-2-2-22-2-2222i2i−2i−2i2-22-2-2-2220000000000002i2i−2i−2i0000-22−2i2i2i−2i00000000000000000000
χ392-2-2-22-222222-2-2-2-22-2-222−2i−2i2i2i2-22-222-2-2000000000000−2i−2i2i2i00002-2−2i2i2i−2i00000000000000000000
χ402-2-2-22-222222-2-2-2-22-2-222−2i−2i2i2i2-22-2-2-222000000000000−2i−2i2i2i0000-222i−2i−2i2i00000000000000000000
χ412-2-2-22-2222-2-222-2-22-2-2220000-22-2222-2-20000002-20000000022-2-2-22000000000000000000002-200
χ422-2-2-22-2222-2-222-2-22-2-2220000-22-2222-2-2000000-2200000000-2-222-2200000000000000000000-2200
χ432-2-2-22-2222-2-222-2-22-2-2220000-22-22-2-2220000002-20000000022-2-22-200000000000000000000-2200
χ442-2-2-22-2222-2-222-2-22-2-2220000-22-22-2-222000000-2200000000-2-2222-2000000000000000000002-200
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000400-400-2-2220000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000-40040022-2-20000000000000000000000000000000000
χ47444-4-4-44-4400004-4-44-4-4422−2222−220000000000000000000022−2222−22000000000000000000000000000000
χ48444-4-4-44-4400004-4-44-4-44−2222−222200000000000000000000−2222−2222000000000000000000000000000000
χ49444-4-4-44-4-20000-222-222-222−2222−22000000000000000023−2300−22−226−66−600000000000000000000000000
χ50444-4-4-44-4-20000-222-222-222−2222−220000000000000000−232300−22−22−66−6600000000000000000000000000
χ51444-4-4-44-4-20000-222-222-2−2222−2222000000000000000023−23002−22−2−66−6600000000000000000000000000
χ52444-4-4-44-4-20000-222-222-2−2222−22220000000000000000−2323002−22−26−66−600000000000000000000000000
χ5344-44-4-4-444-444-444-4-4-44-40000-444-400000000000000000000000000000000000000000000000000
χ5444-44-4-4-44-24-4-44-2-2222-220000-222-200004i−4i00000000000000000000000000−2i2i0000000000000000
χ5544-44-4-4-44-24-4-44-2-2222-220000-222-20000−4i4i000000000000000000000000002i−2i0000000000000000
χ5644-44-4-4-44-2-444-4-2-2222-2200002-2-2200000000000000000000000000000000000000−2i32i30000000000
χ5744-44-4-4-44-2-444-4-2-2222-2200002-2-22000000000000000000000000000000000000002i3−2i30000000000
χ5844-4-444-4-4400004-44-44-4-4000000004-44-40000000000000000000000000000000000000000000000
χ5944-4-444-4-4400004-44-44-4-400000000-44-440000000000000000000000000000000000000000000000
χ604-4444-4-4-440000-4444-4-4-4000000004-4-440000000000000000000000000000000000000000000000
χ614-4444-4-4-440000-4444-4-4-400000000-444-40000000000000000000000000000000000000000000000
χ624-44-4-44-444-44-44-4-4-4444-40000-4-44400000000000000000000000000000000000000000000000000
χ634-44-4-44-44-24-44-4222-2-2-220000-2-22200000004i−4i000000000000000000000000000−2i2i000000000000
χ644-44-4-44-44-24-44-4222-2-2-220000-2-2220000000−4i4i0000000000000000000000000002i−2i000000000000
χ654-44-4-44-44-2-44-44222-2-2-22000022-2-20000000000000000000000000000000000−2i32i300000000000000
χ664-44-4-44-44-2-44-44222-2-2-22000022-2-200000000000000000000000000000000002i3−2i300000000000000
χ674-4-44-444-440000-44-4-44-44−2i22i22i2−2i200000000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ684-4-44-444-440000-44-4-44-442i2−2i2−2i22i2000000000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ694-4-44-444-4-200002-222-22-2−2i22i22i2−2i2000000000000000000−2i32i3i2−i2−i2i26−6−6600000000000000000000000000
χ704-4-44-444-4-200002-222-22-2−2i22i22i2−2i20000000000000000002i3−2i3i2−i2−i2i2−666−600000000000000000000000000
χ714-4-44-444-4-200002-222-22-22i2−2i2−2i22i2000000000000000000−2i32i3−i2i2i2−i2−666−600000000000000000000000000
χ724-4-44-444-4-200002-222-22-22i2−2i2−2i22i20000000000000000002i3−2i3−i2i2i2−i26−6−6600000000000000000000000000
χ734-4-4-44-444-244-4-422-222-2-24i4i−4i−4i-22-220000000000000000−2i−2i2i2i000000000000000000000000000000
χ744-4-4-44-444-244-4-422-222-2-2−4i−4i4i4i-22-2200000000000000002i2i−2i−2i000000000000000000000000000000
χ754-4-4-44-444-2-4-44422-222-2-200002-22-200000000004-400000000-2-22200000000000000000000000000
χ764-4-4-44-444-2-4-44422-222-2-200002-22-20000000000-440000000022-2-200000000000000000000000000
χ7788-8-888-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000
χ788-8888-8-8-8-400004-4-4-44440000000000000000000000000000000000000000000000000000000000

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