Finite Group Databasebeta

← Group #10696639

Character table — Group #10696639

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222222222444444444488881616161616161616161616161616161616162424242424242424242424244848
order12223444444666244412121212121261212122244666688121212122424242488888888888822
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-11-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111111111111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-2-2222-2-2-22222-2-22-2-22-220-20220000-2-200000000000000000000
χ10222222222-2-2222-2-2-22222-2-22-2-22-2-2020-2-200002200000000000000000000
χ11222222-2-2222222-22-2-22-2-2222-2-2-22020-200220000-2-2000000000000000000
χ12222222-2-2222222-22-2-22-2-2222-2-2-220-20200-2-2000022000000000000000000
χ13222222-2-22-2-22222-22-22-2-2-2-2222-2-2000000002-2000022-2-200000000000000
χ14222222-2-22-2-22222-22-22-2-2-2-2222-2-200000000-220000-2-22200000000000000
χ1522222-222-222222-2-22-2-22222-2-22-2-200000000000000000022-2-20000000000
χ1622222-222-222222-2-22-2-22222-2-22-2-2000000000000000000-2-2220000000000
χ1722222-222-2-2-222222-2-2-222-2-2-22-2-2200000000000000000000002i2i−2i−2i000000
χ1822222-222-2-2-222222-2-2-222-2-2-22-2-220000000000000000000000−2i−2i2i2i000000
χ1922222-2-2-2-2222222-2-22-2-2-222-22-22-20000000000000000000000000000002-2
χ2022222-2-2-2-2222222-2-22-2-2-222-22-22-2000000000000000000000000000000-22
χ2122222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-22220000000000000000000000000022-2-200
χ2222222-2-2-2-2-2-2222-2222-2-2-2-2-2-2-222200000000000000000000000000-2-22200
χ232222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-100000000000000
χ242222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12-22-2-1-111-2-2-1-111111100000000000000
χ252222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-22-2211-1-1-2-211-1-1111100000000000000
χ262222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111221111-1-1-1-100000000000000
χ272222-12222-2-2-1-1-1-2-2-22-1-1-111-111-1120-20-1-1−i3i30011−i3i3−i3i3−i3i300000000000000
χ282222-12222-2-2-1-1-1-2-2-22-1-1-111-111-1120-20-1-1i3−i30011i3−i3i3−i3i3−i300000000000000
χ292222-12222-2-2-1-1-1-2-2-22-1-1-111-111-11-202011−i3i300-1-1−i3i3i3−i3i3−i300000000000000
χ302222-12222-2-2-1-1-1-2-2-22-1-1-111-111-11-202011i3−i300-1-1i3−i3−i3i3−i3i300000000000000
χ312222-12-2-2222-1-1-1-22-2-2-111-1-1-1111-1020-2−i3i3-1-100−i3i311−i3i3i3−i300000000000000
χ322222-12-2-2222-1-1-1-22-2-2-111-1-1-1111-1020-2i3−i3-1-100i3−i311i3−i3−i3i300000000000000
χ332222-12-2-2222-1-1-1-22-2-2-111-1-1-1111-10-202−i3i31100−i3i3-1-1i3−i3−i3i300000000000000
χ342222-12-2-2222-1-1-1-22-2-2-111-1-1-1111-10-202i3−i31100i3−i3-1-1−i3i3i3−i300000000000000
χ352222-12-2-22-2-2-1-1-12-22-2-11111-1-1-1110000−i3i3−i3i32-2i3−i3i3−i3-1-11100000000000000
χ362222-12-2-22-2-2-1-1-12-22-2-11111-1-1-1110000−i3i3i3−i3-22i3−i3−i3i311-1-100000000000000
χ372222-12-2-22-2-2-1-1-12-22-2-11111-1-1-1110000i3−i3−i3i3-22−i3i3i3−i311-1-100000000000000
χ382222-12-2-22-2-2-1-1-12-22-2-11111-1-1-1110000i3−i3i3−i32-2−i3i3−i3i3-1-11100000000000000
χ394444-2-444-444-2-2-2-4-44-42-2-2-2-222-22200000000000000000000000000000000
χ404444-2-444-4-4-4-2-2-244-4-42-2-2222-222-200000000000000000000000000000000
χ414444-2-4-4-4-444-2-2-24-4-44222-2-22-22-2200000000000000000000000000000000
χ424444-2-4-4-4-4-4-4-2-2-2-44442222222-2-2-200000000000000000000000000000000
χ4344-4-44400-4004-4-4000040000-4000000000000000000000000002i−2i2i−2i000000
χ4444-4-44400-4004-4-4000040000-400000000000000000000000000−2i2i−2i2i000000
χ4544-4-44-4004004-4-40000-400004000000000000000000000000002-2-22000000
χ4644-4-44-4004004-4-40000-40000400000000000000000000000000-222-2000000
χ474-44-4400004-4-44-400000004-400000000000000000000000000000002-22-200
χ484-44-4400004-4-44-400000004-40000000000000000000000000000000-22-2200
χ494-44-440000-44-44-40000000-4400000000000000000000000000000002-2-2200
χ504-44-440000-44-44-40000000-440000000000000000000000000000000-222-200
χ514-4-44404-4000-4-44000004-400000000000000000000000000022−220000000000
χ524-4-44404-4000-4-44000004-4000000000000000000000000000−22220000000000
χ534-4-4440-44000-4-4400000-44000000000000000000000000022−22000000000000
χ544-4-4440-44000-4-4400000-440000000000000000000000000−2222000000000000
χ5588-8-8-4800-800-4440000-400004000000000000000000000000000000000000
χ5688-8-8-4-800800-444000040000-4000000000000000000000000000000000000
χ578-88-8-400008-84-440000000-440000000000000000000000000000000000000
χ588-88-8-40000-884-4400000004-40000000000000000000000000000000000000
χ598-8-88-408-800044-400000-44000000000000000000000000000000000000000
χ608-8-88-40-8800044-4000004-4000000000000000000000000000000000000000

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