Finite Group Databasebeta

← Group #10695614

Character table — Group #10695614

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222222234466666664446666121212122222444466666666121212121212121212124412121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111
χ411111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ922222222222-2-22222222-2-2-22222-2-2-2-2000022-2-2000000002222-2-2-2-2-2-2000000000000000000
χ1022222222222-2-22222222-2-2-22222-2-2-2-20000-2-22200000000-2-2-2-22222-2-2000000000000000000
χ112222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ122222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-2-21111000000000000
χ132222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-2-21111000000000000
χ142222222222-122-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-122-1-1-1-1000000000000
χ152222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111000022-2-2−i3−i3−i3−i3i3i3i3i3-1-1-1-111111100−i3i3−i3i3000000000000
χ162222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-11111000022-2-2i3i3i3i3−i3−i3−i3−i3-1-1-1-111111100i3−i3i3−i3000000000000
χ172222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-111110000-2-222−i3−i3−i3−i3i3i3i3i31111-1-1-1-11100i3−i3i3−i3000000000000
χ182222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-1-1-1-111110000-2-222i3i3i3i3−i3−i3−i3−i31111-1-1-1-11100−i3i3−i3i3000000000000
χ19222222-2-2-2-22222-2-2-2-222-2-2222-2-222-2-20000000000000000000000002-2000000000000002-200
χ20222222-2-2-2-22222-2-2-2-222-2-2222-2-222-2-20000000000000000000000002-200000000000000-2200
χ21222222-2-2-2-22-2-22-2-2-2-22222-222-2-2-2-222000000000000000000000000-2200000000000000002i−2i
χ22222222-2-2-2-22-2-22-2-2-2-22222-222-2-2-2-222000000000000000000000000-220000000000000000−2i2i
χ232222-2-22-2-222222-2-2-2-2222-2-2-2-22222-2-2000000000000000000000000-2200000022-2-200000000
χ242222-2-22-2-222222-2-2-2-2222-2-2-2-22222-2-2000000000000000000000000-22000000-2-22200000000
χ252222-2-22-2-222-2-22-2-2-2-222-222-2-222-2-2220000000000000000000000002-2000000000022-2-20000
χ262222-2-22-2-222-2-22-2-2-2-222-222-2-222-2-2220000000000000000000000002-20000000000-2-2220000
χ272222-2-2-222-22222222222-22-2-2-2-2-22222000000000000000000000000-2-22-222-2-2000000000000
χ282222-2-2-222-22222222222-22-2-2-2-2-22222000000000000000000000000-2-2-22-2-222000000000000
χ292222-2-2-222-22-2-222222222-22-2-2-2-2-2-2-2-222-2-2000022-2-222-2-20000000022000000000000000000
χ302222-2-2-222-22-2-222222222-22-2-2-2-2-2-2-2-2-2-2220000-2-222-2-2220000000022000000000000000000
χ312222-2-2-222-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3112-2-1-111000000000000
χ322222-2-2-222-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311-2211-1-1000000000000
χ332222-2-2-222-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311-2211-1-1000000000000
χ342222-2-2-222-2-122-1-1-1-1-1-1-1-22-21111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3112-2-1-111000000000000
χ352222-2-2-222-2-1-2-2-1-1-1-1-1-1-12-221111111122-2-20000-1-111-1-111−i3−i3i3i3i3i3−i3−i3-1-100−i3i3i3−i3000000000000
χ362222-2-2-222-2-1-2-2-1-1-1-1-1-1-12-221111111122-2-20000-1-111-1-111i3i3−i3−i3−i3−i3i3i3-1-100i3−i3−i3i3000000000000
χ372222-2-2-222-2-1-2-2-1-1-1-1-1-1-12-2211111111-2-222000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3-1-100i3−i3−i3i3000000000000
χ382222-2-2-222-2-1-2-2-1-1-1-1-1-1-12-2211111111-2-222000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3-1-100−i3i3i3−i3000000000000
χ392-2-222-222-2-2200222-2-2-2-20002-22-200000000002i−2i0000000000002i−2i2i−2i00000000−i2i2−i2i22−22−20000
χ402-2-222-222-2-2200222-2-2-2-20002-22-200000000002i−2i0000000000002i−2i2i−2i00000000i2−i2i2−i2−22−220000
χ412-2-222-222-2-2200222-2-2-2-20002-22-20000000000−2i2i000000000000−2i2i−2i2i00000000−i2i2−i2i2−22−220000
χ422-2-222-222-2-2200222-2-2-2-20002-22-20000000000−2i2i000000000000−2i2i−2i2i00000000i2−i2i2−i22−22−20000
χ432-2-22-222-22-22002-2-222-2-2000-222-2000000002i−2i00000000002i−2i2i−2i000000000000−i2i2i2−i22−2−220000
χ442-2-22-222-22-22002-2-222-2-2000-222-2000000002i−2i00000000002i−2i2i−2i000000000000i2−i2−i2i2−222−20000
χ452-2-22-222-22-22002-2-222-2-2000-222-200000000−2i2i0000000000−2i2i−2i2i000000000000−i2i2i2−i2−222−20000
χ462-2-22-222-22-22002-2-222-2-2000-222-200000000−2i2i0000000000−2i2i−2i2i000000000000i2−i2−i2i22−2−220000
χ47444444-4-4-4-4-244-22222-2-2-4-44-2-222-2-222000000000000000000000000-22000000000000000000
χ48444444-4-4-4-4-2-4-4-22222-2-244-4-2-22222-2-20000000000000000000000002-2000000000000000000
χ494444-4-44-4-44-244-22222-2-24-4-422-2-2-2-2220000000000000000000000002-2000000000000000000
χ504444-4-44-4-44-2-4-4-22222-2-2-44422-2-222-2-2000000000000000000000000-22000000000000000000
χ514-44-400000044-4-40000-4400000004-4002-22-200002-22-22-22-20000000000000000000000000000
χ524-44-400000044-4-40000-4400000004-400-22-220000-22-22-22-220000000000000000000000000000
χ534-44-40000004-44-40000-440000000-44002-2-2200002-2-222-2-220000000000000000000000000000
χ544-44-40000004-44-40000-440000000-4400-222-20000-222-2-222-20000000000000000000000000000
χ554-44-4000000-24-42−2i32i3−2i32i32-20000000-22−2i32i32-22-20000−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i30000000000000000000000000000
χ564-44-4000000-24-42−2i32i3−2i32i32-20000000-22−2i32i3-22-2200001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i30000000000000000000000000000
χ574-44-4000000-24-422i3−2i32i3−2i32-20000000-222i3−2i32-22-20000−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i30000000000000000000000000000
χ584-44-4000000-24-422i3−2i32i3−2i32-20000000-222i3−2i3-22-2200001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i30000000000000000000000000000
χ594-44-4000000-2-442−2i32i3−2i32i32-200000002-22i3−2i32-2-220000−1−i31+i31−i3−1+i3−1+i31−i31+i3−1−i30000000000000000000000000000
χ604-44-4000000-2-442−2i32i3−2i32i32-200000002-22i3−2i3-222-200001+i3−1−i3−1+i31−i31−i3−1+i3−1−i31+i30000000000000000000000000000
χ614-44-4000000-2-4422i3−2i32i3−2i32-200000002-2−2i32i32-2-220000−1+i31−i31+i3−1−i3−1−i31+i31−i3−1+i30000000000000000000000000000
χ624-44-4000000-2-4422i3−2i32i3−2i32-200000002-2−2i32i3-222-200001−i3−1+i3−1−i31+i31+i3−1−i3−1+i31−i30000000000000000000000000000
χ634-4-444-444-4-4-200-2-2-22222000-22-2200000000004i−4i000000000000−2i2i−2i2i00000000000000000000
χ644-4-444-444-4-4-200-2-2-22222000-22-220000000000−4i4i0000000000002i−2i2i−2i00000000000000000000
χ654-4-444-4-4-4444004-4-444-4-40004-4-44000000000000000000000000000000000000000000000000
χ664-4-444-4-4-444-200-222-2-222000-222-20000000000000000000023−23−2323000000000000000000000000
χ674-4-444-4-4-444-200-222-2-222000-222-200000000000000000000−232323−23000000000000000000000000
χ684-4-44-444-44-4-200-222-2-2220002-2-22000000004i−4i0000000000−2i2i−2i2i000000000000000000000000
χ694-4-44-444-44-4-200-222-2-2220002-2-2200000000−4i4i00000000002i−2i2i−2i000000000000000000000000
χ704-4-44-44-44-44400444-4-4-4-4000-44-44000000000000000000000000000000000000000000000000
χ714-4-44-44-44-44-200-2-2-222220002-22-200000000000000000000000023−23−232300000000000000000000
χ724-4-44-44-44-44-200-2-2-222220002-22-2000000000000000000000000−232323−2300000000000000000000
χ7388-8-8000000800-800008-80000000000000000000000000000000000000000000000000000000
χ7488-8-8000000-4004−4i34i34i3−4i3-440000000000000000000000000000000000000000000000000000000
χ7588-8-8000000-40044i3−4i3−4i34i3-440000000000000000000000000000000000000000000000000000000

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