Finite Group Databasebeta

← Group #10848588

Character table — Group #10848588

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order12222234444666444444446612121212444422446666881212121212121212121212124444442668242424242224448828
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-11-1-11-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-111-1-111
χ5111111111111111111-1-1-1-1111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-1-11-1-1-1-111
χ7111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-111-11111-1-1
χ911111111111111-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-11-1
χ1011111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-111-1-1-1-111-1-1-11
χ1111111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-11-1-111111-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1111-1
χ1311111111111111-1-1-1-1-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-111-1-1-111-11
χ1411111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111111-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1111-1-11-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-111-1-11111-1-1-1-1-11
χ172222222-2-2-2-22220000000022-2-2-2-222-2-22-20022-2-2000000000000002-200000000000002-20000000
χ182222222-2-2-2-22220000000022-2-2-2-222-2-2-2200-2-222000000000000002-20000000000000-220000000
χ192222222-2-2-2-22220000000022-2-2-2-2-2-2222-20022-2-200000000000000-220000000000000-220000000
χ202222222-2-2-2-22220000000022-2-2-2-2-2-222-2200-2-22200000000000000-2200000000000002-20000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-100002222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000002-1-12-1-1-1-10000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-10000-2-2-2-2111122-1-1-1-11111-1-1-1-1000000-211-2-1-1110000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-100002222-1-1-1-1-2-2-1-1-1-1-1-1-1-11111000000-211-211110000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-10000-2-2-2-21111-2-2-1-1-1-1111111110000002-1-1211-1-10000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1000022-2-2-1-1-1-1-2-211111111-1-1-1-10000002-1-1-211110000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-10000-2-2221111-2-21111-1-1-1-1-1-1-1-1000000-211211-1-10000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1000022-2-2-1-1-1-122111111111111000000-2112-1-1-1-10000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-10000-2-2221111221111-1-1-1-111110000002-1-1-2-1-1110000000000
χ292222-2-222-2-2222222-2-20000-2-22-22-222-2-2000000000022-2-200000000-22000000000000200-2000000
χ302222-2-222-2-2222222-2-20000-2-22-22-2-2-222000000000022-2-2000000002-2000000000000-2002000000
χ312222-2-222-2-22222-2-2220000-2-22-22-222-2-20000000000-2-22200000000-22000000000000-2002000000
χ322222-2-222-2-22222-2-2220000-2-22-22-2-2-2220000000000-2-222000000002-2000000000000200-2000000
χ332222-2-22-222-222200000000-2-2-22-222222002-2000000000022-2-20000-2-200000000000000002-20000
χ342222-2-22-222-222200000000-2-2-22-22222200-220000000000-2-2220000-2-20000000000000000-220000
χ352222-2-22-222-222200000000-2-2-22-22-2-2-2-2002-2000000000022-2-20000220000000000000000-220000
χ362222-2-22-222-222200000000-2-2-22-22-2-2-2-200-220000000000-2-22200002200000000000000002-20000
χ3722-2-22-222-22-22-2-22i−2i2i−2i22-2-2-2222-2-20000000000002i−2i2i−2i2i−2i000022-2-200000000002i−2i000000000000
χ3822-2-22-222-22-22-2-22i−2i2i−2i-2-222-2222-2-2000000000000−2i2i2i−2i2i−2i0000-2-2220000000000−2i2i000000000000
χ3922-2-22-222-22-22-2-2−2i2i−2i2i22-2-2-2222-2-2000000000000−2i2i−2i2i−2i2i000022-2-20000000000−2i2i000000000000
χ4022-2-22-222-22-22-2-2−2i2i−2i2i-2-222-2222-2-20000000000002i−2i−2i2i−2i2i0000-2-22200000000002i−2i000000000000
χ4122-2-22-2-12-22-2-1112i−2i2i−2i22-2-21-1-1-11100000000−i3i3−i3i32i−2i−ii−ii3−33−3-1-1110000000−i3i30−ii3−30000000000
χ4222-2-22-2-12-22-2-1112i−2i2i−2i22-2-21-1-1-11100000000i3−i3i3−i32i−2i−ii−ii−33−33-1-1110000000i3−i30−ii−330000000000
χ4322-2-22-2-12-22-2-1112i−2i2i−2i-2-2221-1-1-11100000000−i3i3−i3i3−2i2i−ii−ii3−33−311-1-10000000i3−i30i−i−330000000000
χ4422-2-22-2-12-22-2-1112i−2i2i−2i-2-2221-1-1-11100000000i3−i3i3−i3−2i2i−ii−ii−33−3311-1-10000000−i3i30i−i3−30000000000
χ4522-2-22-2-12-22-2-111−2i2i−2i2i22-2-21-1-1-11100000000−i3i3−i3i3−2i2ii−ii−i−33−33-1-1110000000−i3i30i−i−330000000000
χ4622-2-22-2-12-22-2-111−2i2i−2i2i22-2-21-1-1-11100000000i3−i3i3−i3−2i2ii−ii−i3−33−3-1-1110000000i3−i30i−i3−30000000000
χ4722-2-22-2-12-22-2-111−2i2i−2i2i-2-2221-1-1-11100000000−i3i3−i3i32i−2ii−ii−i−33−3311-1-10000000i3−i30−ii3−30000000000
χ4822-2-22-2-12-22-2-111−2i2i−2i2i-2-2221-1-1-11100000000i3−i3i3−i32i−2ii−ii−i3−33−311-1-10000000−i3i30−ii−330000000000
χ4922-2-2-22222-2-22-2-22i−2i−2i2i00002-22-2-22000000000000002i−2i−2i2i000000000022-2-2000000000000002i−2i00
χ5022-2-2-22222-2-22-2-22i−2i−2i2i00002-22-2-22000000000000002i−2i−2i2i0000000000-2-22200000000000000−2i2i00
χ5122-2-2-22222-2-22-2-2−2i2i2i−2i00002-22-2-2200000000000000−2i2i2i−2i000000000022-2-200000000000000−2i2i00
χ5222-2-2-22222-2-22-2-2−2i2i2i−2i00002-22-2-2200000000000000−2i2i2i−2i0000000000-2-222000000000000002i−2i00
χ53444444-2-4-4-4-4-2-2-200000000-2-2222200004-400-2-22200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-200000000-2-222220000-440022-2-200000000000000000000000000000000000000
χ554444-4-4-24-4-44-2-2-244-4-4000022-22-2200000000000000-2-22200000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-444000022-22-220000000000000022-2-200000000000000000000000000000000
χ574444-4-4-2-444-4-2-2-200000000222-22-20000004-40000000000-2-2220000000000000000000000000000
χ584444-4-4-2-444-4-2-2-200000000222-22-2000000-44000000000022-2-20000000000000000000000000000
χ5944-4-44-44-44-444-4-400000000-44-4-44400000000000000000000000000000000000000000000000000
χ6044-4-44-4-2-44-44-222000000002-222-2-200000000−2i32i32i3−2i300000000000000000000000000000000000000
χ6144-4-44-4-2-44-44-222000000002-222-2-2000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ6244-4-4-444-4-4444-4-4000000004-4-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-244-4-4-2224i−4i−4i4i0000-22-222-200000000000000−2i2i2i−2i00000000000000000000000000000000
χ6444-4-4-44-244-4-4-222−4i4i4i−4i0000-22-222-2000000000000002i−2i−2i2i00000000000000000000000000000000
χ6544-4-4-44-2-4-444-22200000000-222-2-2200000000000000000023−23−23230000000000000000000000000000
χ6644-4-4-44-2-4-444-22200000000-222-2-22000000000000000000−232323−230000000000000000000000000000
χ674-44-40040000-44-400002-22-20000004-4000000000000000000002-22-2002-22-2000000000000000000
χ684-44-40040000-44-400002-22-2000000-44000000000000000000002-22-200-22-22000000000000000000
χ694-44-40040000-44-40000-22-220000004-400000000000000000000-22-2200-22-22000000000000000000
χ704-44-40040000-44-40000-22-22000000-4400000000000000000000-22-22002-22-2000000000000000000
χ714-4-440040000-4-4400002-2-22000000004-40000000000000000002-2-22002-2-22000000000000000000
χ724-4-440040000-4-4400002-2-2200000000-440000000000000000002-2-2200-222-2000000000000000000
χ734-4-440040000-4-440000-222-2000000004-4000000000000000000-222-200-222-2000000000000000000
χ744-4-440040000-4-440000-222-200000000-44000000000000000000-222-2002-2-22000000000000000000
χ758-88-800-400004-4400004-44-40000000000000000000000000000-22-22000000000000000000000000
χ768-88-800-400004-440000-44-4400000000000000000000000000002-22-2000000000000000000000000
χ778-8-8800-4000044-400004-4-440000000000000000000000000000-222-2000000000000000000000000
χ788-8-8800-4000044-40000-444-400000000000000000000000000002-2-22000000000000000000000000

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