Finite Group Databasebeta

← Group #13156614

Character table — Group #13156614

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222244444444444444444488888888888888181818181818181818181818242424242424242424242424242424242424242424242424242424363636363636363636363636216
order122233344666666666333666666666121212121212366612121212121212121212444488888888224666666666666666612121212121212121212121224242424242424244
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
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11
χ511111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1
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
χ11222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000222200002202222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-100000
χ12222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-1000022220000-2-20-2-2-2-2111111111111000000000000-1-1-1-100000
χ13222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-200002-2022-2-2-1-111-1-1-1-11111000000000000111100000
χ14222222-12222-1-1-122222-1-122-1-1-1-1-1-12-1222-12-1-1-1-1-1-1-1-122-1-1-1-10000-2-2-2-20000-220-2-22211-1-11111-1-1-1-1000000000000111100000
χ1522222-1222222222-1-1-1-12-1-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1222200000000202-1-1002200-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1000000000
χ1622222-1222222222-1-1-1-12-1-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1222200000000-20-21100-2-20011110000-2-2111111-1-1-1-1000000000
χ1722222-1222222222-1-1-1-12-1-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000020-2-1-1002200-1-1-1-10000-2-21111111111000000000
χ1822222-1222222222-1-1-1-12-1-1-122-1-12-1-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-2021100-2-2001111000022-1-1-1-1-1-11111000000000
χ1922222-12-2-2222222-1-1-1-12-1-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111122-2-200000000000−i3i3000000−i3−i3i3i3000000−i3i3−i3−i3i3i3-1-111000000000
χ2022222-12-2-2222222-1-1-1-12-1-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-21111111122-2-200000000000i3−i3000000i3i3−i3−i3000000i3−i3i3i3−i3−i3-1-111000000000
χ2122222-12-2-2222222-1-1-1-12-1-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-211111111-2-22200000000000−i3i3000000−i3−i3i3i3000000i3−i3i3i3−i3−i311-1-1000000000
χ2222222-12-2-2222222-1-1-1-12-1-1-122-1-12-1-1-2-211-2-2-1-1-1-1-2-211111111-2-22200000000000i3−i3000000i3i3−i3−i3000000−i3i3−i3−i3i3i311-1-1000000000
χ232222-12222-1-1222-1222-1-12-1-1-1-122-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100000000222202200-1-100220000-1-1-1-1-1-122-1-1-1-100000000-1-1-1-10
χ242222-12222-1-1222-1222-1-12-1-1-1-122-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-10000000022220-2-2001100-2-20000111111-2-2111100000000-1-1-1-10
χ252222-12222-1-1222-1222-1-12-1-1-1-122-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-202-200-1-100220000-1-1-1-111-2-211110000000011110
χ262222-12222-1-1222-1222-1-12-1-1-1-122-12-12-1222-1-1-1-1-1-1-122-1-1-1-1-1-100000000-2-2-2-20-22001100-2-200001111-1-122-1-1-1-10000000011110
χ2722-2-2222002-22-2-2-2-22-22222-22-22-2-2-2-200000022-2-20000000000002i−2i22−2−2−i2−i2i2i2000000000000000000000000000002i−2i22−2−2−i2−i2i2i20
χ2822-2-2222002-22-2-2-2-22-22222-22-22-2-2-2-200000022-2-20000000000002i−2i−2−222i2i2−i2−i2000000000000000000000000000002i−2i−2−222i2i2−i2−i20
χ2922-2-2222002-22-2-2-2-22-22222-22-22-2-2-2-200000022-2-2000000000000−2i2i22−2−2i2i2−i2−i200000000000000000000000000000−2i2i22−2−2i2i2−i2−i20
χ3022-2-2222002-22-2-2-2-22-22222-22-22-2-2-2-200000022-2-2000000000000−2i2i−2−222−i2−i2i2i200000000000000000000000000000−2i2i−2−222−i2−i2i2i20
χ312-22-222200-22-22-2-2-2-22222-22-22-22-2-2-20000002-22-200000000002i−2i002−22−2−i2i2−i2i20000000000000000000000000002i−2i002−22−2−i2i2−i2i20
χ322-22-222200-22-22-2-2-2-22222-22-22-22-2-2-20000002-22-200000000002i−2i00−22−22i2−i2i2−i20000000000000000000000000002i−2i00−22−22i2−i2i2−i20
χ332-22-222200-22-22-2-2-2-22222-22-22-22-2-2-20000002-22-20000000000−2i2i002−22−2i2−i2i2−i2000000000000000000000000000−2i2i002−22−2i2−i2i2−i20
χ342-22-222200-22-22-2-2-2-22222-22-22-22-2-2-20000002-22-20000000000−2i2i00−22−22−i2i2−i2i2000000000000000000000000000−2i2i00−22−22−i2i2−i2i20
χ352-2-222222-2-2-2-2-2222-2-2222-2-2-2-2-2-22222-22-2-222-2-222-22-22-222-2-2000000002-2-22000000000000000000000000000000000002-2-220
χ362-2-222222-2-2-2-2-2222-2-2222-2-2-2-2-2-22222-22-2-222-2-222-22-22-222-2-200000000-222-200000000000000000000000000000000000-222-20
χ372-2-22222-22-2-2-2-2222-2-2222-2-2-2-2-2-2222-22-222-22-2-22-22-22-22-2-22200002-2-22000000000000000000000000000000000002-2-2200000
χ382-2-22222-22-2-2-2-2222-2-2222-2-2-2-2-2-2222-22-222-22-2-22-22-22-22-2-2220000-222-200000000000000000000000000000000000-222-200000
χ392-2-2222-1-22-2-211-122-2-22-1-1-2-21111-1-1212-22-1-2-111-11-11-1-2211-1-100002-2-2200000000000−i3i3−i3i3−i3i3−i3i3−i3−i3i3i3000000000000-111-100000
χ402-2-2222-1-22-2-211-122-2-22-1-1-2-21111-1-1212-22-1-2-111-11-11-1-2211-1-100002-2-2200000000000i3−i3i3−i3i3−i3i3−i3i3i3−i3−i3000000000000-111-100000
χ412-2-2222-1-22-2-211-122-2-22-1-1-2-21111-1-1212-22-1-2-111-11-11-1-2211-1-10000-222-200000000000−i3i3i3−i3−i3i3−i3i3i3i3−i3−i30000000000001-1-1100000
χ422-2-2222-1-22-2-211-122-2-22-1-1-2-21111-1-1212-22-1-2-111-11-11-1-2211-1-10000-222-200000000000i3−i3−i3i3i3−i3i3−i3−i3−i3i3i30000000000001-1-1100000
χ432-2-22-1222-211-2-22-12-2-2-1-121111-2-2-12-1212-2-2-1-111-1-112-2-11-1-111000000002-2-2200000−i3i300000000−i3i3−i3i3−i3i300−i3i3−i3i300000000-111-10
χ442-2-22-1222-211-2-22-12-2-2-1-121111-2-2-12-1212-2-2-1-111-1-112-2-11-1-111000000002-2-2200000i3−i300000000i3−i3i3−i3i3−i300i3−i3i3−i300000000-111-10
χ452-2-22-1222-211-2-22-12-2-2-1-121111-2-2-12-1212-2-2-1-111-1-112-2-11-1-11100000000-222-200000−i3i300000000−i3i3−i3i3i3−i300i3−i3i3−i3000000001-1-110
χ462-2-22-1222-211-2-22-12-2-2-1-121111-2-2-12-1212-2-2-1-111-1-112-2-11-1-11100000000-222-200000i3−i300000000i3−i3i3−i3−i3i300−i3i3−i3i3000000001-1-110
χ47444444-2-4-444-2-2-244444-2-244-2-2-2-2-2-242-4-4-42-4-2-2-2-22222-4-422220000000000000000000000000000000000000000000000000000
χ4844444-2-24444-2-2-24-2-2-2-2-21-2-2-2-211-21-2-24-2-2-241111-2-211-2-21111000000000000400-2-200-2-20011110000000000000000000000000
χ4944444-2-24444-2-2-24-2-2-2-2-21-2-2-2-211-21-2-24-2-2-241111-2-211-2-21111000000000000-40022002200-1-1-1-10000000000000000000000000
χ5044444-2-2-4-444-2-2-24-2-2-2-2-21-2-2-2-211-21-22-4222-4111122-1-122-1-1-1-1000000000000000−2i32i3000000i3i3−i3−i30000000000000000000000000
χ5144444-2-2-4-444-2-2-24-2-2-2-2-21-2-2-2-211-21-22-4222-4111122-1-122-1-1-1-10000000000000002i3−2i3000000−i3−i3i3i30000000000000000000000000
χ524444-244-4-4-2-2444-2444-2-24-2-2-2-244-24-2-42-4-4-42-2-2-2-222-4-42222220000000000000000000000000000000000000000000000000000
χ534444-24-244-2-2-2-2-2-2444-21-2-2-211-2-21-2-2-2-244-2-2111111-2-2-2-2111100000000000004000-2-200-2-200001111000000000000000000000
χ544444-24-244-2-2-2-2-2-2444-21-2-2-211-2-21-2-2-2-244-2-2111111-2-2-2-211110000000000000-40002200220000-1-1-1-1000000000000000000000
χ554444-24-2-4-4-2-2-2-2-2-2444-21-2-2-211-2-21-2-222-4-4221111-1-12222-1-1-1-10000000000000000000000000003-3-33000000000000000000000
χ564444-24-2-4-4-2-2-2-2-2-2444-21-2-2-211-2-21-2-222-4-4221111-1-12222-1-1-1-1000000000000000000000000000-333-3000000000000000000000
χ574444-2-2444-2-2444-2-2-2-21-2-211-2-2-2-2-2-214-2-2-24-21111-2-2-2-21111110000000000000040000000000000000-2-2-2-211110000000000000
χ584444-2-2444-2-2444-2-2-2-21-2-211-2-2-2-2-2-214-2-2-24-21111-2-2-2-211111100000000000000-400000000000000002222-1-1-1-10000000000000
χ594444-2-24-4-4-2-2444-2-2-2-21-2-211-2-2-2-2-2-21-4222-4211112222-1-1-1-1-1-1000000000000000000000000000000000−2i32i3i3i3−i3−i30000000000000
χ604444-2-24-4-4-2-2444-2-2-2-21-2-211-2-2-2-2-2-21-4222-4211112222-1-1-1-1-1-10000000000000000000000000000000002i3−2i3−i3−i3i3i30000000000000
χ6144-4-444-2004-4-222-4-44-44-2-24-4-22-2222-4000000-2-222000000000000002222−22−2200000000000000000000000000000000000−2−22200000
χ6244-4-444-2004-4-222-4-44-44-2-24-4-22-2222-4000000-2-22200000000000000−22−2222220000000000000000000000000000000000022−2−200000
χ6344-4-44-24004-44-4-4-42-22-24-2-224-4-22-422000000-2-2220000000000004i−4i0000000000000000000000000000000000000−2i2i000000000
χ6444-4-44-24004-44-4-4-42-22-24-2-224-4-22-422000000-2-222000000000000−4i4i00000000000000000000000000000000000002i−2i000000000
χ6544-4-4-24400-224-4-42-44-4-2-24-22-224-42-42000000-2-222000000000000000000−2i2−2i22i22i200000000000000000000000000000000000i2i2−i2−i20
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χ674-44-444-200-442-22-4-4-444-2-2-442-22-222-4000000-22-220000000000000022−2222−2200000000000000000000000000000000000−22−2200000
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χ694-44-44-2400-44-44-4-422-2-24-22-2-442-2-422000000-22-2200000000004i−4i0000000000000000000000000000000000000−2i2i00000000000
χ704-44-44-2400-44-44-4-422-2-24-22-2-442-2-422000000-22-220000000000−4i4i00000000000000000000000000000000000002i−2i00000000000
χ714-44-4-244002-2-44-42-4-44-2-242-22-2-442-42000000-22-22000000000000000000−2i22i2−2i22i200000000000000000000000000000000000i2−i2i2−i20
χ724-44-4-244002-2-44-42-4-44-2-242-22-2-442-42000000-22-220000000000000000002i2−2i22i2−2i200000000000000000000000000000000000−i2i2−i2i20
χ734-4-4444-24-4-4-422-244-4-44-2-2-4-42222-2-24-2-44-424-222-2-22-224-4-2-2220000000000000000000000000000000000000000000000000000
χ744-4-444-244-4-4-4-4-444-222-24-222-4-4224-2-24-4-22-44-222-24-4-22-22-2-2220000000000000000000000000000000000000000000000000000
χ754-4-444-24-44-4-4-4-444-222-24-222-4-4224-2-2-442-24-4-222-2-442-22-222-2-20000000000000000000000000000000000000000000000000000
χ764-4-444-2-24-4-4-422-24-222-2-212222-1-1-21-2-2-4-22241-1-11-221-1-2211-1-1000000000000000000000003-3-330000000000000000000000000
χ774-4-444-2-24-4-4-422-24-222-2-212222-1-1-21-2-2-4-22241-1-11-221-1-2211-1-100000000000000000000000-333-30000000000000000000000000
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χ794-4-444-2-2-44-4-422-24-222-2-212222-1-1-21-2242-2-2-41-1-112-2-112-2-1-11100000000000000000002i3−2i300−i3i3−i3i30000000000000000000000000
χ804-4-44-244-4422-4-44-24-4-4-2-242222-4-4-24-2-4-2-4442-222-22-2-442-222-2-20000000000000000000000000000000000000000000000000000
χ814-4-44-24-24-42222-2-24-4-4-21-222-1-1221-2-2-224-42-21-1-111-1-22-2211-1-100000000000000000−2i32i300000000i3−i3i3−i3000000000000000000000
χ824-4-44-24-24-42222-2-24-4-4-21-222-1-1221-2-2-224-42-21-1-111-1-22-2211-1-1000000000000000002i3−2i300000000−i3i3−i3i3000000000000000000000
χ834-4-44-24-2-442222-2-24-4-4-21-222-1-1221-2-22-2-44-221-1-11-112-22-2-1-111000000000000000000000−2i32i30000i3i3−i3−i3000000000000000000000
χ844-4-44-24-2-442222-2-24-4-4-21-222-1-1221-2-22-2-44-221-1-11-112-22-2-1-1110000000000000000000002i3−2i30000−i3−i3i3i3000000000000000000000
χ854-4-44-2-244-422-4-44-2-2221-2-2-1-12222-2-2142-22-4-21-1-11-22-221-111-1-10000000000000000000000000000000−2i32i300i3−i3i3−i30000000000000
χ864-4-44-2-244-422-4-44-2-2221-2-2-1-12222-2-2142-22-4-21-1-11-22-221-111-1-100000000000000000000000000000002i3−2i300−i3i3−i3i30000000000000
χ874-4-44-2-24-4422-4-44-2-2221-2-2-1-12222-2-21-4-22-2421-1-112-22-2-11-1-111000000000000000000000000000000000003-3-330000000000000
χ884-4-44-2-24-4422-4-44-2-2221-2-2-1-12222-2-21-4-22-2421-1-112-22-2-11-1-11100000000000000000000000000000000000-333-30000000000000
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
χ9188-8-88-4-4008-8-444-84-44-4-42-44-442-24-2400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-400-44-4444-88-8-42-4-442-2-44-24400000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4800-448-8-844-442-4-42-2-44-4444-200000022-2-200000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-400-44-44444-442222-22-22-2-2-2-2000000-1-11100000033−3333−330000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-400-44-44444-442222-22-22-2-2-2-2000000-1-111000000−3333−33330000000000000000000000000000000000000000000000000000
χ968-88-88-4-400-884-44-844-4-4-424-44-4-224-240000002-22-200000000000000000000000000000000000000000000000000000000000000
χ978-88-8-48-4004-44-444-8-88-42-44-4-224-4-2440000002-22-200000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-48004-4-88-8444-42-4-4-224-44-444-20000002-22-200000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4004-44-44444-4222-22-22-22-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4004-44-44444-4222-22-22-22-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-48-84444-4-4-444222-2-2-2-2-2-2222-44-444-4-111-12-22-22-2-1-1110000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-884444-4-4-444222-2-2-2-2-2-22224-44-4-44-111-1-22-22-2211-1-10000000000000000000000000000000000000000000000000000

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