Finite Group Databasebeta

← Group #10696578

Character table — Group #10696578

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222222444444444888888888888888816161616161616161616161624242424484848484848
order122222344666666644444121212124444121212121212121212121212444412121212121212128888248888
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-11111-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-11111
χ92222222222222222-22-2-2-22222000000000000-2-2-2-2200-222-2-200000000000000
χ102222222222222222-22-2-2-22222000000000000-2-2-2-2-2002-2-22200000000000000
χ112222222-2-222222222-2-22-2-2-2-2-222-2-22222-2-2-2-222-2-20000000000000000000000
χ122222222-2-222222222-2-22-2-2-2-2-2-2-222-2-2-2-2222222-2-20000000000000000000000
χ132222222-2-22222222-2-22-22-2-2-2-2000000000000-2-22202-20000022-2-20000000000
χ142222222-2-22222222-2-22-22-2-2-2-2000000000000-2-2220-2200000-2-2220000000000
χ15222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000
χ16222222-122-1-1-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-211111111-1-1-1-12-2-22-1-1-1-111110000000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-211111111-1-1-1-1-222-21111-1-1-1-10000000000
χ19222222-122-1-1-1-1-1-1-1-22-2-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i31111200-2-1-111−i3i3−i3i30000000000
χ20222222-122-1-1-1-1-1-1-1-22-2-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i31111-200211-1-1i3−i3i3−i30000000000
χ21222222-122-1-1-1-1-1-1-1-22-2-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i31111200-2-1-111i3−i3i3−i30000000000
χ22222222-122-1-1-1-1-1-1-1-22-2-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i31111-200211-1-1−i3i3−i3i30000000000
χ23222222-1-2-2-1-1-1-1-1-1-12-2-22-2111122-2-2-1-1-1-11111-1-1110000−i3i3−i3i3−i3i3i3−i30000000000
χ24222222-1-2-2-1-1-1-1-1-1-12-2-22-2111122-2-2-1-1-1-11111-1-1110000i3−i3i3−i3i3−i3−i3i30000000000
χ25222222-1-2-2-1-1-1-1-1-1-12-2-22-21111-2-2221111-1-1-1-1-1-1110000−i3i3−i3i3i3−i3−i3i30000000000
χ26222222-1-2-2-1-1-1-1-1-1-12-2-22-21111-2-2221111-1-1-1-1-1-1110000i3−i3i3−i3−i3i3i3−i30000000000
χ27222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-102-20−i3i3i3−i3-1-1110000000000
χ28222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000−i3−i3i3i3i3i3−i3−i311-1-10-220i3−i3−i3i311-1-10000000000
χ29222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-102-20i3−i3−i3i3-1-1110000000000
χ30222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000i3i3−i3−i3−i3−i3i3i311-1-10-220−i3i3i3−i311-1-10000000000
χ312222-2-2222-2-2-2-22222-2-2-2222-2-20000000000002-22-200000000000000002-20000
χ322222-2-2222-2-2-2-22222-2-2-2222-2-20000000000002-22-20000000000000000-220000
χ332222-2-2222-2-2-2-2222-2-222-222-2-2000000000000-22-220000000000000000002-200
χ342222-2-2222-2-2-2-2222-2-222-222-2-2000000000000-22-22000000000000000000-2200
χ352222-2-22-2-2-2-2-2-2222222-2-2-2-2220000000000002-2-22000000000000000000002i−2i
χ362222-2-22-2-2-2-2-2-2222222-2-2-2-2220000000000002-2-2200000000000000000000−2i2i
χ372222-2-22-2-2-2-2-2-2222-22-222-2-222000000000000-222-200000000000022-2-2000000
χ382222-2-22-2-2-2-2-2-2222-22-222-2-222000000000000-222-2000000000000-2-222000000
χ394444-4-4-2442222-2-2-24-4-4-44-2-222000000000000-22-220000000000000000000000
χ404444-4-4-2442222-2-2-2-4-444-4-2-2220000000000002-22-20000000000000000000000
χ414444-4-4-2-4-42222-2-2-2444-4-422-2-2000000000000-222-20000000000000000000000
χ424444-4-4-2-4-42222-2-2-2-44-44422-2-20000000000002-2-220000000000000000000000
χ434-44-40044-40000-4-44000004-4002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ444-44-40044-40000-4-44000004-400−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ454-44-4004-440000-4-4400000-44002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ464-44-4004-440000-4-4400000-4400−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ474-44-400-24-4−2i3−2i32i32i322-200000-22−2i32i32i−2i2i−2i2ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ484-44-400-24-4−2i3−2i32i32i322-200000-22−2i32i3−2i2i−2i2i−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ494-44-400-24-42i32i3−2i3−2i322-200000-222i3−2i32i−2i2i−2i2ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ504-44-400-24-42i32i3−2i3−2i322-200000-222i3−2i3−2i2i−2i2i−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ514-44-400-2-44−2i3−2i32i32i322-2000002-22i3−2i32i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ524-44-400-2-44−2i3−2i32i32i322-2000002-22i3−2i3−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ534-44-400-2-442i32i3−2i3−2i322-2000002-2−2i32i32i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ544-44-400-2-442i32i3−2i3−2i322-2000002-2−2i32i3−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ554-4-444-44004-44-44-4-400000000000000000000000000000000000002i−2i2i−2i000000
χ564-4-444-44004-44-44-4-40000000000000000000000000000000000000−2i2i−2i2i000000
χ574-4-44-44400-44-444-4-400000000000000000000000000000000000002i−2i−2i2i000000
χ584-4-44-44400-44-444-4-40000000000000000000000000000000000000−2i2i2i−2i000000
χ5988-8-8008000000-88-800000000000000000000000000000000000000000000000
χ6088-8-800-400−4i34i34i3−4i34-4400000000000000000000000000000000000000000000000
χ6188-8-800-4004i3−4i3−4i34i34-4400000000000000000000000000000000000000000000000
χ628-8-888-8-400-44-44-44400000000000000000000000000000000000000000000000
χ638-8-88-88-4004-44-4-44400000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.