Finite Group Databasebeta

← Group #10696564

Character table — Group #10696564

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
χ51111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1
χ922222222222222222-2-2-2-22222000000000000-2-2-2-2002-2-2-20000220000000000
χ1022222222222222222-2-2-2-22222000000000000-2-2-2-200-22220000-2-20000000000
χ112222222-2-22222222-22-22-2-2-2-2-222-2-22222-2-2-2-2-2-2220000000000000000000000
χ122222222-2-22222222-22-22-2-2-2-2-2-2-222-2-2-2-22222-2-2220000000000000000000000
χ132222222-2-22222222-2-22-22-2-2-2-200000000000022-2-22-2000022-2-2000000000000
χ142222222-2-22222222-2-22-22-2-2-2-200000000000022-2-2-220000-2-222000000000000
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
χ17222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-211111111-1-1-1-122-2-211-1-1-1-1110000000000
χ18222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-211111111-1-1-1-1-2-222-1-11111-1-10000000000
χ19222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i31111002-211−i3i3−i3i3-1-10000000000
χ20222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-10000−i3−i3i3i3−i3−i3i3i3111100-22-1-1i3−i3i3−i3110000000000
χ21222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i31111002-211i3−i3i3−i3-1-10000000000
χ22222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-10000i3i3−i3−i3i3i3−i3−i3111100-22-1-1−i3i3−i3i3110000000000
χ23222222-1-2-2-1-1-1-1-1-1-1-22-22-2111122-2-2-1-1-1-1111111-1-10000−i3i3−i3i3i3−i3−i3i30000000000
χ24222222-1-2-2-1-1-1-1-1-1-1-22-22-2111122-2-2-1-1-1-1111111-1-10000i3−i3i3−i3−i3i3i3−i30000000000
χ25222222-1-2-2-1-1-1-1-1-1-1-22-22-21111-2-2221111-1-1-1-111-1-10000−i3i3i3−i3−i3i3−i3i30000000000
χ26222222-1-2-2-1-1-1-1-1-1-1-22-22-21111-2-2221111-1-1-1-111-1-10000i3−i3−i3i3i3−i3i3−i30000000000
χ27222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000−i3−i3i3i3i3i3−i3−i3-1-1112-200i3−i3-1-111−i3i30000000000
χ28222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000−i3−i3i3i3i3i3−i3−i3-1-111-2200−i3i311-1-1i3−i30000000000
χ29222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000i3i3−i3−i3−i3−i3i3i3-1-1112-200−i3i3-1-111i3−i30000000000
χ30222222-1-2-2-1-1-1-1-1-1-1-2-22-2211110000i3i3−i3−i3−i3−i3i3i3-1-111-2200i3−i311-1-1−i3i30000000000
χ312222-2-22222-2-2-2-222-22-2-2222-2-20000000000002-22-200000000000000002-20000
χ322222-2-22222-2-2-2-222-22-2-2222-2-20000000000002-22-20000000000000000-220000
χ332222-2-22222-2-2-2-222-2-222-222-2-2000000000000-22-220000000000000000002-200
χ342222-2-22222-2-2-2-222-2-222-222-2-2000000000000-22-22000000000000000000-2200
χ352222-2-22-2-22-2-2-2-222222-2-2-2-222000000000000-222-2000000000000000000002i−2i
χ362222-2-22-2-22-2-2-2-222222-2-2-2-222000000000000-222-200000000000000000000−2i2i
χ372222-2-22-2-22-2-2-2-2222-2-222-2-2220000000000002-2-2200000000000022-2-2000000
χ382222-2-22-2-22-2-2-2-2222-2-222-2-2220000000000002-2-22000000000000-2-222000000
χ394444-4-4-244-22222-2-2-44-4-44-2-222000000000000-22-220000000000000000000000
χ404444-4-4-244-22222-2-2-4-444-4-2-2220000000000002-22-20000000000000000000000
χ414444-4-4-2-4-4-22222-2-2444-4-422-2-20000000000002-2-220000000000000000000000
χ424444-4-4-2-4-4-22222-2-24-4-44422-2-2000000000000-222-20000000000000000000000
χ4344-4-40044-440000-4-4000004-4002-22-22-22-22-22-200000000000000000000000000
χ4444-4-40044-440000-4-4000004-400-22-22-22-22-22-2200000000000000000000000000
χ4544-4-4004-4440000-4-400000-44002-2-222-22-2-22-2200000000000000000000000000
χ4644-4-4004-4440000-4-400000-4400-222-2-22-222-22-200000000000000000000000000
χ4744-4-400-24-4-2−2i3−2i32i32i32200000-22−2i32i32-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ4844-4-400-24-4-2−2i3−2i32i32i32200000-22−2i32i3-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ4944-4-400-24-4-22i32i3−2i3−2i32200000-222i3−2i32-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ5044-4-400-24-4-22i32i3−2i3−2i32200000-222i3−2i3-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ5144-4-400-2-44-2−2i3−2i32i32i322000002-22i3−2i32-2-22−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ5244-4-400-2-44-2−2i3−2i32i32i322000002-22i3−2i3-222-21+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ5344-4-400-2-44-22i32i3−2i3−2i322000002-2−2i32i32-2-22−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ5444-4-400-2-44-22i32i3−2i3−2i322000002-2−2i32i3-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ554-4-444-4400-44-44-44-400000000000000000000000000000000000002i−2i2i−2i000000
χ564-4-444-4400-44-44-44-40000000000000000000000000000000000000−2i2i−2i2i000000
χ574-4-44-44400-4-44-444-400000000000000000000000000000000000002i−2i−2i2i000000
χ584-4-44-44400-4-44-444-40000000000000000000000000000000000000−2i2i2i−2i000000
χ598-88-800800-80000-8800000000000000000000000000000000000000000000000
χ608-88-800-4004−4i34i34i3−4i34-400000000000000000000000000000000000000000000000
χ618-88-800-40044i3−4i3−4i34i34-400000000000000000000000000000000000000000000000
χ628-8-888-8-4004-44-44-4400000000000000000000000000000000000000000000000
χ638-8-88-88-40044-44-4-4400000000000000000000000000000000000000000000000

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