Finite Group Databasebeta

← Group #13167583

Character table — Group #13167583

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order122222366633666666666666336666666666666666222222222222226666444444446666666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-1111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-1111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111-1-1111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ81111-1-1111111-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ911-1-11-111-1-1111-111-1-111-1-1-1-1111-111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-111-1-1i−ii−ii−ii−i1-111-1-111-1-1ii−i−iii−i−ii−ii−i
χ1011-1-11-111-1-1111-111-1-111-1-1-1-1111-111-1-1-1-11111-1-1-1-111-1-11-111-1-111-1-111-1-1−ii−ii−ii−ii1-111-1-111-1-1−i−iii−i−iii−ii−ii
χ1111-1-11-111-1-1111-111-1-111-1-1-1-1111-111-1-1-1-11111-1-1-1-111-1-11-1-1-111-1-11111-1-1i−ii−i−ii−ii1-1-1-111-1-111−i−iii−i−iiii−ii−i
χ1211-1-11-111-1-1111-111-1-111-1-1-1-1111-111-1-1-1-11111-1-1-1-111-1-11-1-1-111-1-11111-1-1−ii−iii−ii−i1-1-1-111-1-111ii−i−iii−i−i−ii−ii
χ1311-1-1-1111-1-111-1111-1-1-1-111-1-111-1111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-11111-1-1i−i−iii−i−ii-1111-1-1-1-111ii−i−i−i−iiii−i−ii
χ1411-1-1-1111-1-111-1111-1-1-1-111-1-111-1111-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-11111-1-1−iii−i−iii−i-1111-1-1-1-111−i−iiiii−i−i−iii−i
χ1511-1-1-1111-1-111-1111-1-1-1-111-1-111-1111-1-1-1-1-1-1-1-1111111-1-1-11-1-11111-1-111-1-1i−i−ii−iii−i-11-1-11111-1-1−i−iiiii−i−ii−i−ii
χ1611-1-1-1111-1-111-1111-1-1-1-111-1-111-1111-1-1-1-1-1-1-1-1111111-1-1-11-1-11111-1-111-1-1−iii−ii−i−ii-11-1-11111-1-1ii−i−i−i−iii−iii−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-200000000-2-2-2-200000000-2-200000000000000000000
χ18222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000-1-1-1-100002222-1-100000000-1-1-1-1-1-1-1-10000
χ19222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122222200000000-1-1-1-10000-2-2-2-2-1-100000000111111110000
χ20222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-20000000011110000000011000000003−33−33−33−30000
χ21222222-1-1-1-122-1-12222222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2000000001111000000001100000000−33−33−33−330000
χ222222-2-2222222-2-22222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-2000000002200000000000000000000
χ232222-2-2-1-1-1-122112222-2-2-2-222-1-1-2-2-1-1-1-1-1-1111111112222-2-200000000-1-1-1-1000022-2-21100000000-1-1-1-111110000
χ242222-2-2-1-1-1-122112222-2-2-2-222-1-1-2-2-1-1-1-1-1-1111111112222-2-200000000-1-1-1-10000-2-22211000000001111-1-1-1-10000
χ252222-2-2-1-1-1-122112222-2-2-2-222-1-1-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111100000000-1-1000000003−33−3−33−330000
χ262222-2-2-1-1-1-122112222-2-2-2-222-1-1-2-2-1-1-1-1-1-111111111-2-2-2-22200000000111100000000-1-100000000−33−333−33−30000
χ2722-2-22-222-2-2222-222-2-222-2-2-2-2222-222-2-2-2-22222-2-2-2-2-2-222-2200000000-2-22200000000-2200000000000000000000
χ2822-2-22-2-1-11122-1122-2-222-2-2-2-2-1-12-2-1-11111-1-1-1-1111122-2-22-200000000-1-11100002i−2i2i−2i-1100000000−i−iii−i−iii0000
χ2922-2-22-2-1-11122-1122-2-222-2-2-2-2-1-12-2-1-11111-1-1-1-1111122-2-22-200000000-1-1110000−2i2i−2i2i-1100000000ii−i−iii−i−i0000
χ3022-2-22-2-1-11122-1122-2-222-2-2-2-2-1-12-2-1-11111-1-1-1-11111-2-222-220000000011-1-1000000001-100000000−i3i3i3−i3−i3i3i3−i30000
χ3122-2-22-2-1-11122-1122-2-222-2-2-2-2-1-12-2-1-11111-1-1-1-11111-2-222-220000000011-1-1000000001-100000000i3−i3−i3i3i3−i3−i3i30000
χ3222-2-2-2222-2-222-2222-2-2-2-222-2-222-2222-2-2-2-2-2-2-2-22222-2-2222-200000000-2-222000000002-200000000000000000000
χ3322-2-2-22-1-111221-122-2-2-2-222-2-2-1-1-22-1-111111111-1-1-1-122-2-2-2200000000-1-11100002i−2i−2i2i1-100000000−i−iiiii−i−i0000
χ3422-2-2-22-1-111221-122-2-2-2-222-2-2-1-1-22-1-111111111-1-1-1-122-2-2-2200000000-1-1110000−2i2i2i−2i1-100000000ii−i−i−i−iii0000
χ3522-2-2-22-1-111221-122-2-2-2-222-2-2-1-1-22-1-111111111-1-1-1-1-2-2222-20000000011-1-100000000-1100000000−i3i3i3−i3i3−i3−i3i30000
χ3622-2-2-22-1-111221-122-2-2-2-222-2-2-1-1-22-1-111111111-1-1-1-1-2-2222-20000000011-1-100000000-1100000000i3−i3−i3i3−i3i3i3−i30000
χ372-22-2002-22-22200-2-22-200002-22200-2-222-2-2000000002-22-20000002-22-22-22-2000000000000002-22-2000000000000
χ382-22-2002-22-22200-2-22-200002-22200-2-222-2-2000000002-22-2000000-22-222-22-200000000000000-22-22000000000000
χ392-22-2002-22-22200-2-22-200002-22200-2-222-2-200000000-22-22002-22-20000-22-2200000000002-22-20000000000000000
χ402-22-2002-22-22200-2-22-200002-22200-2-222-2-200000000-22-2200-22-220000-22-220000000000-22-220000000000000000
χ412-2-22002-2-222200-2-2-220000-222200-2-2-2-222000000002-2-220000002-2-222-2-22000000000000002-2-22000000000000
χ422-2-22002-2-222200-2-2-220000-222200-2-2-2-222000000002-2-22000000-222-22-2-2200000000000000-222-2000000000000
χ432-2-22002-2-222200-2-2-220000-222200-2-2-2-22200000000-222-2002-2-220000-222-200000000002-2-220000000000000000
χ442-2-22002-2-222200-2-2-220000-222200-2-2-2-22200000000-222-200-222-20000-222-20000000000-222-20000000000000000
χ4544444444441-2441-2-2-2-2-2-2-2111-2111-21-21-211-2-211-2-200000000000000000022220000000000000000000000-1-1-1-1
χ4644444444441-2441-2-2-2-2-2-2-2111-2111-21-21-211-2-211-2-2000000000000000000-2-2-2-200000000000000000000001111
χ474444444444-2144-21111111-2-2-21-2-2-21-21-21-2-211-2-2110000002222222200000000000000-1-1-1-1-1-1-1-1000000000000
χ484444444444-2144-21111111-2-2-21-2-2-21-21-21-2-211-2-211000000-2-2-2-2-2-2-2-20000000000000011111111000000000000
χ494444-4-444441-2-4-41-2-2-22222111-2-1-11-21-21-2-1-122-1-12200000000000000000022-2-20000000000000000000000-1-111
χ504444-4-444441-2-4-41-2-2-22222111-2-1-11-21-21-2-1-122-1-122000000000000000000-2-222000000000000000000000011-1-1
χ514444-4-44444-21-4-4-2111-1-1-1-1-2-2-2122-21-21-2122-1-122-1-10000002222-2-2-2-200000000000000-1-1-1-11111000000000000
χ524444-4-44444-21-4-4-2111-1-1-1-1-2-2-2122-21-21-2122-1-122-1-1000000-2-2-2-22222000000000000001111-1-1-1-1000000000000
χ5344-4-44-444-4-41-24-41-222-2-222-1-11-21-11-2-12-1211-2-2-1-1220000000000000000002i−2i2i−2i0000000000000000000000−ii−ii
χ5444-4-44-444-4-41-24-41-222-2-222-1-11-21-11-2-12-1211-2-2-1-122000000000000000000−2i2i−2i2i0000000000000000000000i−ii−i
χ5544-4-44-444-4-4-214-4-21-1-111-1-122-21-22-212-12-1-2-21122-1-100000022-2-222-2-200000000000000-1-111-1-111000000000000
χ5644-4-44-444-4-4-214-4-21-1-111-1-122-21-22-212-12-1-2-21122-1-1000000-2-222-2-2220000000000000011-1-111-1-1000000000000
χ5744-4-4-4444-4-41-2-441-22222-2-2-1-11-2-111-2-12-12-1-12211-2-20000000000000000002i−2i−2i2i0000000000000000000000−iii−i
χ5844-4-4-4444-4-41-2-441-22222-2-2-1-11-2-111-2-12-12-1-12211-2-2000000000000000000−2i2i2i−2i0000000000000000000000i−i−ii
χ5944-4-4-4444-4-4-21-44-21-1-1-1-11122-212-2-212-12-122-1-1-2-21100000022-2-2-2-22200000000000000-1-11111-1-1000000000000
χ6044-4-4-4444-4-4-21-44-21-1-1-1-11122-212-2-212-12-122-1-1-2-211000000-2-22222-2-20000000000000011-1-1-1-111000000000000
χ614-44-4004-44-4-21002-11-13-33-3-22-21002-1-212-1003-3003-30000002-22-22-22-200000000000000-11-11-11-11000000000000
χ624-44-4004-44-4-21002-11-13-33-3-22-21002-1-212-1003-3003-3000000-22-22-22-22000000000000001-11-11-11-1000000000000
χ634-44-4004-44-4-21002-11-1-33-33-22-21002-1-212-100-3300-330000002-22-2-22-2200000000000000-11-111-11-1000000000000
χ644-44-4004-44-4-21002-11-1-33-33-22-21002-1-212-100-3300-33000000-22-222-22-2000000000000001-11-1-11-11000000000000
χ654-44-400-22-224400-4-44-400004-4-2-20022-2-222000000004-44-40000000000-22-22000000000000000000000000000000
χ664-44-400-22-224400-4-44-400004-4-2-20022-2-22200000000-44-4400000000002-22-2000000000000000000000000000000
χ674-4-44004-4-44-21002-1-113-3-332-2-21002-12-1-21003-300-330000002-2-222-2-2200000000000000-111-1-111-1000000000000
χ684-4-44004-4-44-21002-1-113-3-332-2-21002-12-1-21003-300-33000000-222-2-222-2000000000000001-1-111-1-11000000000000
χ694-4-44004-4-44-21002-1-11-333-32-2-21002-12-1-2100-33003-30000002-2-22-222-200000000000000-111-11-1-11000000000000
χ704-4-44004-4-44-21002-1-11-333-32-2-21002-12-1-2100-33003-3000000-222-22-2-22000000000000001-1-11-111-1000000000000
χ714-4-4400-222-24400-4-4-440000-44-2-2002222-2-2000000004-4-440000000000-222-2000000000000000000000000000000
χ724-4-4400-222-24400-4-4-440000-44-2-2002222-2-200000000-444-400000000002-2-22000000000000000000000000000000
χ73888888-4-4-4-42-4-4-42-4-4-4-4-4-4-422-1222-12-12-12-1-122-1-122000000000000000000000000000000000000000000000000
χ74888888-4-4-4-4-42-4-4-42222222-4-42-1-4-42-12-12-122-1-122-1-1000000000000000000000000000000000000000000000000
χ758888-8-8-4-4-4-42-4442-4-4-4444422-12-2-2-12-12-1211-2-211-2-2000000000000000000000000000000000000000000000000
χ768888-8-8-4-4-4-4-4244-4222-2-2-2-2-4-42-1442-12-12-1-2-211-2-211000000000000000000000000000000000000000000000000
χ7788-8-88-8-4-4442-4-442-444-4-444-2-2-122-2-121-21-2-1-12211-2-2000000000000000000000000000000000000000000000000
χ7888-8-88-8-4-444-42-44-42-2-222-2-2442-1-442-1-21-2122-1-1-2-211000000000000000000000000000000000000000000000000
χ7988-8-8-88-4-4442-44-42-44444-4-4-2-2-12-22-121-21-211-2-2-1-122000000000000000000000000000000000000000000000000
χ8088-8-8-88-4-444-424-4-42-2-2-2-222442-14-42-1-21-21-2-21122-1-1000000000000000000000000000000000000000000000000
χ818-88-8008-88-82-400-24-4400002-22-400-242-4-2400000000000000000000000000000000000000000000000000000000
χ828-88-800-44-442-400-24-4400002-2-12001-2-121-2−3i33i300−3i33i300000000000000000000000000000000000000000000000000
χ838-88-800-44-442-400-24-4400002-2-12001-2-121-23i3−3i3003i3−3i300000000000000000000000000000000000000000000000000
χ848-88-800-44-44-42004-22-26-66-6-442-100-212-1-2100-3300-33000000000000000000000000000000000000000000000000
χ858-88-800-44-44-42004-22-2-66-66-442-100-212-1-21003-3003-3000000000000000000000000000000000000000000000000
χ868-8-88008-8-882-400-244-40000-222-400-24-242-400000000000000000000000000000000000000000000000000000000
χ878-8-8800-444-42-400-244-40000-22-12001-21-2-12−3i33i3003i3−3i300000000000000000000000000000000000000000000000000
χ888-8-8800-444-42-400-244-40000-22-12001-21-2-123i3−3i300−3i33i300000000000000000000000000000000000000000000000000
χ898-8-8800-444-4-42004-2-226-6-664-42-100-21-212-100-33003-3000000000000000000000000000000000000000000000000
χ908-8-8800-444-4-42004-2-22-666-64-42-100-21-212-1003-300-33000000000000000000000000000000000000000000000000

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