Finite Group Databasebeta

← Group #13156615

Character table — Group #13156615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444488888888888888181818181818181818181818242424242424242424242424242424242424242424242424242424363636363636363636363636216
order12223334466666666633366666666612121212121236661212121212121212121244448888888824466666666121212121212121212121212121212121212121224242424242424242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11-1111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000022-2-2000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000000-2-222000000000
χ11222222-12222222-1-1-122-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-122-1-1-1-1-1-122220000000022022-1-1-1-1-1-1-1-1002200-1-1-1-10000-1-1-1-1000000000
χ12222222-12222222-1-1-122-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222200000000-2-20-2-21111111100-2-20011110000-1-1-1-1000000000
χ13222222-12222222-1-1-122-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2000000002-2022-1-1-1-1-1-11100-2-200111100001111000000000
χ14222222-12222222-1-1-122-1-122-1-1-1-1-12-12-1-1222-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200000000-220-2-2111111-1-1002200-1-1-1-100001111000000000
χ15222222-1-2-222222-1-1-122-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-2-211111122-2-20000000000000−i3i3−i3−i3i3i3−i3i3000000−i3−i3i3i30000-1-111000000000
χ16222222-1-2-222222-1-1-122-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-2-211111122-2-20000000000000i3−i3i3i3−i3−i3i3−i3000000i3i3−i3−i30000-1-111000000000
χ17222222-1-2-222222-1-1-122-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-2-2111111-2-2220000000000000−i3i3−i3−i3i3i3i3−i3000000i3i3−i3−i3000011-1-1000000000
χ18222222-1-2-222222-1-1-122-1-122-1-1-1-1-12-1-211-2-2-2-1-1-1-111-2-2111111-2-2220000000000000i3−i3i3i3−i3−i3−i3i3000000−i3−i3i3i3000011-1-1000000000
χ1922222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1000022220000202-1-122-1-1-1-100-1-100220000-1-1-1-10000-1-1-1-100000
χ2022222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1000022220000-20-211-2-21111001100-2-2000011110000-1-1-1-100000
χ2122222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-2000020-2-1-122-1-1-1-1001100-2-2000011110000111100000
χ2222222-122222-1-1-12222-12-1-1-122-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000-20211-2-2111100-1-100220000-1-1-1-10000111100000
χ232222-12222-1-1222222-1-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-1000000002222022000000002222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-10
χ242222-12222-1-1222222-1-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-10000000022220-2-200000000-2-2-2-211111111111100000000-1-1-1-10
χ252222-12222-1-1222222-1-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-202-20000000022-2-2-1-111-1-1-1-111110000000011110
χ262222-12222-1-1222222-1-1-12-1-1-1-1222-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20-2200000000-2-22211-1-11111-1-1-1-10000000011110
χ2722-2-2222002-22-2-2-22-2-22222-22-22-2-2-2-200000022-2-20000000000002i−2i−i2−i2i2i222−2−2000000000000000000000000000002i−2i−i2−i2i2i222−2−20
χ2822-2-2222002-22-2-2-22-2-22222-22-22-2-2-2-200000022-2-20000000000002i−2ii2i2−i2−i2−2−222000000000000000000000000000002i−2ii2i2−i2−i2−2−2220
χ2922-2-2222002-22-2-2-22-2-22222-22-22-2-2-2-200000022-2-2000000000000−2i2i−i2−i2i2i2−2−22200000000000000000000000000000−2i2i−i2−i2i2i2−2−2220
χ3022-2-2222002-22-2-2-22-2-22222-22-22-2-2-2-200000022-2-2000000000000−2i2ii2i2−i2−i222−2−200000000000000000000000000000−2i2ii2i2−i2−i222−2−20
χ312-22-222200-22-22-2-2-22-2222-22-22-22-2-2-20000002-22-200000000002i−2i00−i2i2−i2i22−22−20000000000000000000000000002i−2i00−i2i2−i2i22−22−20
χ322-22-222200-22-22-2-2-22-2222-22-22-22-2-2-20000002-22-200000000002i−2i00i2−i2i2−i2−22−220000000000000000000000000002i−2i00i2−i2i2−i2−22−220
χ332-22-222200-22-22-2-2-22-2222-22-22-22-2-2-20000002-22-20000000000−2i2i00−i2i2−i2i2−22−22000000000000000000000000000−2i2i00−i2i2−i2i2−22−220
χ342-22-222200-22-22-2-2-22-2222-22-22-22-2-2-20000002-22-20000000000−2i2i00i2−i2i2−i22−22−2000000000000000000000000000−2i2i00i2−i2i2−i22−22−20
χ352-2-222222-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2-2-222-2-222-22-22-222-2-2000000002-2-22000000000000000000000000000000000002-2-220
χ362-2-222222-2-2-2-2-222-2-22222-2-2-2-2-2-222222-2-2-222-2-222-22-22-222-2-200000000-222-200000000000000000000000000000000000-222-20
χ372-2-22222-22-2-2-2-222-2-22222-2-2-2-2-2-2222-2-2222-22-2-22-22-22-22-2-22200002-2-22000000000000000000000000000000000002-2-2200000
χ382-2-22222-22-2-2-2-222-2-22222-2-2-2-2-2-2222-2-2222-22-2-22-22-22-22-2-2220000-222-200000000000000000000000000000000000-222-200000
χ392-2-222-12-22-2-211-12-2-22-12-111-2-211-1-121-222-1-2-111-11-11-1-2211-1-100002-2-220000000−i3i300−i3i3−i3i300−i3i300000000−i3−i3i3i30000-111-100000
χ402-2-222-12-22-2-211-12-2-22-12-111-2-211-1-121-222-1-2-111-11-11-1-2211-1-100002-2-220000000i3−i300i3−i3i3−i300i3−i300000000i3i3−i3−i30000-111-100000
χ412-2-222-12-22-2-211-12-2-22-12-111-2-211-1-121-222-1-2-111-11-11-1-2211-1-10000-222-20000000−i3i300−i3i3−i3i300i3−i300000000i3i3−i3−i300001-1-1100000
χ422-2-222-12-22-2-211-12-2-22-12-111-2-211-1-121-222-1-2-111-11-11-1-2211-1-10000-222-20000000i3−i300i3−i3i3−i300−i3i300000000−i3−i3i3i300001-1-1100000
χ432-2-22-1222-211-2-222-2-2-1-1-121111-2-22-1-122-21-2-1-111-12-2-11-11-1-111000000002-2-22000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000-111-10
χ442-2-22-1222-211-2-222-2-2-1-1-121111-2-22-1-122-21-2-1-111-12-2-11-11-1-111000000002-2-22000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000-111-10
χ452-2-22-1222-211-2-222-2-2-1-1-121111-2-22-1-122-21-2-1-111-12-2-11-11-1-11100000000-222-2000000000000000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i3000000001-1-110
χ462-2-22-1222-211-2-222-2-2-1-1-121111-2-22-1-122-21-2-1-111-12-2-11-11-1-11100000000-222-2000000000000000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i3000000001-1-110
χ4744444-24-4-444-2-2-24444-24-2-2-244-2-2-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000000
χ4844444-2-24444-2-2-2-2-2-24-2-21-2-2-2-2111-2-2-2-2-24-24111111-2-2-2-21111000000000000400-2-2-2-2111100000000000000000000000000000
χ4944444-2-24444-2-2-2-2-2-24-2-21-2-2-2-2111-2-2-2-2-24-24111111-2-2-2-21111000000000000-4002222-1-1-1-100000000000000000000000000000
χ5044444-2-2-4-444-2-2-2-2-2-24-2-21-2-2-2-2111-2-2222-42-41111-1-12222-1-1-1-100000000000000000−2i32i3i3i3−i3−i300000000000000000000000000000
χ5144444-2-2-4-444-2-2-2-2-2-24-2-21-2-2-2-2111-2-2222-42-41111-1-12222-1-1-1-1000000000000000002i3−2i3−i3−i3i3i300000000000000000000000000000
χ524444-244-4-4-2-2444444-2-2-24-2-2-2-2444-2-2-4-4-42-42-2-2-2-2-4-4222222220000000000000000000000000000000000000000000000000000
χ534444-24-244-2-2444-2-2-2-2-21-2-2-211-2-2-2-214-2-2-24-21111-2-2-2-211111100000000000004000000000-2-200-2-200111100000000000000000
χ544444-24-244-2-2444-2-2-2-2-21-2-2-211-2-2-2-214-2-2-24-21111-2-2-2-21111110000000000000-400000000022002200-1-1-1-100000000000000000
χ554444-24-2-4-4-2-2444-2-2-2-2-21-2-2-211-2-2-2-21-4222-4211112222-1-1-1-1-1-100000000000000000000000−2i32i3000000i3i3−i3−i300000000000000000
χ564444-24-2-4-4-2-2444-2-2-2-2-21-2-2-211-2-2-2-21-4222-4211112222-1-1-1-1-1-1000000000000000000000002i3−2i3000000−i3−i3i3i300000000000000000
χ574444-2-2444-2-2-2-2-2444-21-2-211-2-2-2-2-21-2-244-2-2-21111-2-211-2-211110000000000000040000000000-2-200-2-2000011110000000000000
χ584444-2-2444-2-2-2-2-2444-21-2-211-2-2-2-2-21-2-244-2-2-21111-2-211-2-2111100000000000000-400000000002200220000-1-1-1-10000000000000
χ594444-2-24-4-4-2-2-2-2-2444-21-2-211-2-2-2-2-21-22-4-4222111122-1-122-1-1-1-1000000000000000000000000000000000003-3-330000000000000
χ604444-2-24-4-4-2-2-2-2-2444-21-2-211-2-2-2-2-21-22-4-4222111122-1-122-1-1-1-100000000000000000000000000000000000-333-30000000000000
χ6144-4-444-2004-44-4-42-22-44-2-24-4-22-222-42000000-2-2220000000000004i−4i0000000000000000000000000000000000000−2i2i000000000
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χ6344-4-44-24004-4-222-44-4-4-24-2-224-4-2222-4000000-2-22200000000000000−2i2−2i22i22i200000000000000000000000000000000000i2i2−i2−i200000
χ6444-4-44-24004-4-222-44-4-4-24-2-224-4-2222-4000000-2-222000000000000002i22i2−2i2−2i200000000000000000000000000000000000−i2−i2i2i200000
χ6544-4-4-24400-224-4-4-44-42-2-24-22-224-4-422000000-2-2220000000000000000002222−22−2200000000000000000000000000000000000−2−2220
χ6644-4-4-24400-224-4-4-44-42-2-24-22-224-4-422000000-2-222000000000000000000−22−2222220000000000000000000000000000000000022−2−20
χ674-44-444-200-44-44-422-2-44-2-2-442-22-22-42000000-22-2200000000004i−4i0000000000000000000000000000000000000−2i2i00000000000
χ684-44-444-200-44-44-422-2-44-2-2-442-22-22-42000000-22-220000000000−4i4i00000000000000000000000000000000000002i−2i00000000000
χ694-44-44-2400-442-22-4-44-4-24-22-2-442-222-4000000-22-2200000000000000−2i22i2−2i22i200000000000000000000000000000000000i2−i2i2−i200000
χ704-44-44-2400-442-22-4-44-4-24-22-2-442-222-4000000-22-22000000000000002i2−2i22i2−2i200000000000000000000000000000000000−i2i2−i2i200000
χ714-44-4-244002-2-44-4-4-442-2-242-22-2-44-422000000-22-2200000000000000000022−2222−2200000000000000000000000000000000000−22−220
χ724-44-4-244002-2-44-4-4-442-2-242-22-2-44-422000000-22-22000000000000000000−2222−2222000000000000000000000000000000000002−22−20
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χ764-4-444-2-24-4-4-422-2-2224-2-212222-1-11-2-2-2-22-4241-1-111-1-22-2211-1-100000000000000000003-3-3300000000000000000000000000000
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χ804-4-44-244-4422-4-444-4-4-2-2-242222-4-44-2-2-4-44-242-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000000
χ814-4-44-24-24-422-4-44-222-2-21-222-1-122-2-214-222-4-21-1-11-22-221-111-1-1000000000000000000000000000−2i32i300i3−i3i3−i300000000000000000
χ824-4-44-24-24-422-4-44-222-2-21-222-1-122-2-214-222-4-21-1-11-22-221-111-1-10000000000000000000000000002i3−2i300−i3i3−i3i300000000000000000
χ834-4-44-24-2-4422-4-44-222-2-21-222-1-122-2-21-42-2-2421-1-112-22-2-11-1-11100000000000000000000000000000003-3-3300000000000000000
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χ854-4-44-2-244-42222-24-4-4-21-2-2-1-12222-21-2-24-422-21-1-11-221-1-2211-1-100000000000000000000000000000−2i32i30000i3−i3i3−i30000000000000
χ864-4-44-2-244-42222-24-4-4-21-2-2-1-12222-21-2-24-422-21-1-11-221-1-2211-1-1000000000000000000000000000002i3−2i30000−i3i3−i3i30000000000000
χ874-4-44-2-24-442222-24-4-4-21-2-2-1-12222-21-22-44-2-221-1-112-2-112-2-1-1110000000000000000000000000−2i32i300000000i3i3−i3−i30000000000000
χ884-4-44-2-24-442222-24-4-4-21-2-2-1-12222-21-22-44-2-221-1-112-2-112-2-1-11100000000000000000000000002i3−2i300000000−i3−i3i3i30000000000000
χ898888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-4-1-1-1-1222222-1-1-1-10000000000000000000000000000000000000000000000000000
χ908888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-1-1-1-1-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4008-8-4444-44-8-4-42-44-442-2-24400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-400-448-8-84-444-42-4-442-2-4444-200000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4800-44-444-88-842-4-42-2-44-444-2400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-400-44-4444-4442222-22-22-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-400-44-4444-4442222-22-22-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000
χ968-88-88-4-400-884-4444-4-8-4-424-44-4-22-2440000002-22-200000000000000000000000000000000000000000000000000000000000000
χ978-88-8-48-4004-4-88-844-44-42-44-4-224-444-20000002-22-200000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-48004-44-44-8-8842-4-4-224-44-44-240000002-22-200000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4004-44-4444-44222-22-22-22-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4004-44-4444-44222-22-22-22-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-48-84444-4-444-4222-2-2-2-2-2-2222-4-4444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-884444-4-444-4222-2-2-2-2-2-222244-4-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000

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