Finite Group Databasebeta

← Group #10833990

Character table — Group #10833990

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111111112222222222224444444488888888888888888888121212121212121212121212161616161616161616162424242424244848
order1222222234444666666688881212121244444488121212122424242424242424224444448888246612121212121222448844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-11-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-11-1-111-1-11111-1-111-11
χ61111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-11-1-111-1-111-1-111-1-11-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11-111-1-111-1-1-1-111111-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111111-111-1-111-1-111-1-1-1-1-11
χ911111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1011111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111
χ1111111111111111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1
χ1311111111111111111111-1-1-1-11111-111-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-111111-111-1-1-1-11111-1-1-1-11-1
χ1411111111111111111111-1-1-1-11111-111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11-111-1-1-1-111-1-11111-11
χ1511111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111-11-1-11111-1-1-1-111-1-1-11
χ1611111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-11-1-11111-1-111-1-1111-1
χ17222222222-2-2-2-222222220000-2-2-2-2200-2000022-2-20000000022-2-2-2-2220000000000000000000000
χ18222222222-2-2-2-222222220000-2-2-2-2200-2000022-2-200000000-2-22222-2-20000000000000000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-20020000-2-222000000002222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-20020000-2-22200000000-2-2-2-222220000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-12-2-22-2-222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-1-222-2-2-2-2-21111-1-1-1-11111000000000000-2211-1-111-1-100000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-222-2-21111-1-1-1-111110000000000002-2-1-111-1-11100000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1222222-2-2-1-1-1-111111111000000000000-2-21111-1-1-1-100000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-2-22-2-2-2-2-1-1-1-11111111100000000000022-1-1-1-1111100000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-222-2-2-22211111111-1-1-1-10000000000002-2-1-11111-1-100000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2222211111111-1-1-1-1000000000000-2211-1-1-1-11100000000
χ2922-22-22-2-222-22-22-2-2-22-2200002-2-2202-200000000000000000002i−2i002i−2i0000000000002-2002i−2i0000
χ3022-22-22-2-222-22-22-2-2-22-2200002-2-2202-20000000000000000000−2i2i00−2i2i0000000000002-200−2i2i0000
χ3122-22-22-2-222-22-22-2-2-22-2200002-2-220-2200000000000000000002i−2i002i−2i000000000000-2200−2i2i0000
χ3222-22-22-2-222-22-22-2-2-22-2200002-2-220-220000000000000000000−2i2i00−2i2i000000000000-22002i−2i0000
χ3322-22-22-2-22-22-222-2-2-22-220000-222-200002i−2i00000000000000002i−2i00−2i2i00000000002i−2i002-2000000
χ3422-22-22-2-22-22-222-2-2-22-220000-222-200002i−2i0000000000000000−2i2i002i−2i00000000002i−2i00-22000000
χ3522-22-22-2-22-22-222-2-2-22-220000-222-20000−2i2i00000000000000002i−2i00−2i2i0000000000−2i2i00-22000000
χ3622-22-22-2-22-22-222-2-2-22-220000-222-20000−2i2i0000000000000000−2i2i002i−2i0000000000−2i2i002-2000000
χ372-2-2-2222-2222-2-2-2-222-2-222i2i−2i−2i22-2-20000000000002i2i−2i−2i00002-2002-2000000000000000000002i−2i00
χ382-2-2-2222-2222-2-2-2-222-2-222i2i−2i−2i22-2-20000000000002i2i−2i−2i0000-2200-2200000000000000000000−2i2i00
χ392-2-2-2222-2222-2-2-2-222-2-22−2i−2i2i2i22-2-2000000000000−2i−2i2i2i00002-2002-200000000000000000000−2i2i00
χ402-2-2-2222-2222-2-2-2-222-2-22−2i−2i2i2i22-2-2000000000000−2i−2i2i2i0000-2200-22000000000000000000002i−2i00
χ412-2-2-2222-22-2-222-2-222-2-220000-2-2220000002-20000000022-2-22-200-220022-2-2000000000000000000
χ422-2-2-2222-22-2-222-2-222-2-220000-2-2220000002-20000000022-2-2-22002-200-2-222000000000000000000
χ432-2-2-2222-22-2-222-2-222-2-220000-2-222000000-2200000000-2-2222-200-2200-2-222000000000000000000
χ442-2-2-2222-22-2-222-2-222-2-220000-2-222000000-2200000000-2-222-22002-20022-2-2000000000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-200002222400-40000-2-22200000000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-200002222-4004000022-2-200000000000000000000000000000000000000
χ47444-44-4-4-440000444-4-4-4-400000000000000000000000000000000000022−2222−22000000000000000000
χ48444-44-4-4-440000444-4-4-4-4000000000000000000000000000000000000−2222−2222000000000000000000
χ4944-44-44-4-4-24-44-4-2222-22-20000-222-204-40000000000000000000000000000000000000-2200000000
χ5044-44-44-4-4-24-44-4-2222-22-20000-222-20-4400000000000000000000000000000000000002-200000000
χ5144-44-44-4-4-2-44-44-2222-22-200002-2-2200004i−4i00000000000000000000000000000000−2i2i0000000000
χ5244-44-44-4-4-2-44-44-2222-22-200002-2-220000−4i4i000000000000000000000000000000002i−2i0000000000
χ5344-4-4-4-444400004-4-44-44-422−2222−22000000000000000022−2222−220000000000000000000000000000000000
χ5444-4-4-4-444400004-4-44-44-4−2222−22220000000000000000−2222−22220000000000000000000000000000000000
χ5544-4-4-4-444-20000-222-22-2222−2222−2200000000000023−2300−22−226−66−6000000000000000000000000000000
χ5644-4-4-4-444-20000-222-22-2222−2222−22000000000000−232300−22−22−66−66000000000000000000000000000000
χ5744-4-4-4-444-20000-222-22-22−2222−222200000000000023−23002−22−2−66−66000000000000000000000000000000
χ5844-4-4-4-444-20000-222-22-22−2222−2222000000000000−2323002−22−26−66−6000000000000000000000000000000
χ594-444-4-44-440000-44-444-4-4−2i22i22i2−2i20000000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ604-444-4-44-440000-44-444-4-42i2−2i2−2i22i200000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ614-444-4-44-4-200002-22-2-222−2i22i22i2−2i200000000000000−2i32i3i2−i2−i2i26−6−66000000000000000000000000000000
χ624-444-4-44-4-200002-22-2-222−2i22i22i2−2i2000000000000002i3−2i3i2−i2−i2i2−666−6000000000000000000000000000000
χ634-444-4-44-4-200002-22-2-2222i2−2i2−2i22i200000000000000−2i32i3−i2i2i2−i2−666−6000000000000000000000000000000
χ644-444-4-44-4-200002-22-2-2222i2−2i2−2i22i2000000000000002i3−2i3−i2i2i2−i26−6−66000000000000000000000000000000
χ654-44-4-44-4444-4-44-44-4-4-44400004-44-400000000000000000000000000000000000000000000000000
χ664-44-4-44-444-444-4-44-4-4-4440000-44-4400000000000000000000000000000000000000000000000000
χ674-44-4-44-44-24-4-442-2222-2-20000-22-2200000000000000000000000000000000000023−23000000000000
χ684-44-4-44-44-24-4-442-2222-2-20000-22-22000000000000000000000000000000000000−2323000000000000
χ694-44-4-44-44-2-444-42-2222-2-200002-22-20000000000000000000000000000000000−2i32i300000000000000
χ704-44-4-44-44-2-444-42-2222-2-200002-22-200000000000000000000000000000000002i3−2i300000000000000
χ714-4-444-4-4440000-4-44-444-400000000000000000000000000000000000022−22−2222000000000000000000
χ724-4-444-4-4440000-4-44-444-4000000000000000000000000000000000000−222222−22000000000000000000
χ734-4-4-4444-4-244-4-422-2-222-24i4i−4i−4i-2-222000000000000−2i−2i2i2i0000000000000000000000000000000000
χ744-4-4-4444-4-244-4-422-2-222-2−4i−4i4i4i-2-2220000000000002i2i−2i−2i0000000000000000000000000000000000
χ754-4-4-4444-4-2-4-44422-2-222-2000022-2-20000004-400000000-2-222000000000000000000000000000000
χ764-4-4-4444-4-2-4-44422-2-222-2000022-2-2000000-440000000022-2-2000000000000000000000000000000
χ77888-88-8-8-8-40000-4-4-444440000000000000000000000000000000000000000000000000000000000
χ788-8-888-8-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000

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