Finite Group Databasebeta

← Group #13150900

Character table — Group #13150900

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12223444466626612121212336666661212121212121212366666666666121212121212121212121212222244442444444466661212121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-11-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-11-1-1-11-1-1-111-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1111111-1-11-1-11-1-11-1111111-1-1-1-1-1-1-1-11111-1-1
χ61111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-111-1-11111-1-11-11-1-1111-1-111-1-11111-1-1-1-1-1-111
χ71111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-111-1-1-1-11111-1-111
χ81111111-1-1111-1-1-111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-1-1-111111111-1-111-1-1
χ911111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-111111111-1-1111-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ1011111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-111111-1-1-1-1-1-1-1-1111111-11-11
χ1111111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-1-1111111-11-11-1-1-11-1-111111111-1-1-1-1-1-1-11-11
χ1211111-1-111111-1-1-1-1-11111111111-1-1-1-111111-1-1-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-1-111-1-1111-11-11-1-1-1-1-11111-1-111-1-1111-11-1
χ1311111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111111-1-111-1-111-1-1-1-11-1-11
χ1411111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11-111-11-111-1-1-1-11111-1-1-1-111-111-1
χ1511111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-111-1
χ1611111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-111-1-111-1-111111-1-11
χ1722222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12200220002000200-1-100-1-1-1-10000-1-1000000
χ1822222222222222222222-122-1-12-12222-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-200-2-2000-2000-20011001111000011000000
χ192222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1002200220020002000-1-10000-1-1-1-100-1-10000
χ202222222222222222222-12-1-122-12-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100-2-200-2-200-2000-2000110000111100110000
χ212222222-2-2222-2-2-222-2-22-122-1-12-122221111-1-2-211-1-11111-1-1-1-2-2-1-1-1-11111220022000-2000-200-1-100-1-111000011000000
χ222222222-2-2222-2-2-222-2-22-122-1-12-122221111-1-2-211-1-11111-1-1-1-2-2-1-1-1-11111-2-200-2-20002000200110011-1-10000-1-1000000
χ232222222-2-2222-2-2-222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-12211-1-1-1-11111002200-2-200-20002000-1-10000111100-1-10000
χ242222222-2-2222-2-2-222-2-2-12-1-122-12-1-1-1-1-2-2-2-2-111-2-2-1-11111-12211-1-1-1-1111100-2-20022002000-2000110000-1-1-1-100110000
χ2522222-2-222222-2-2-2-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-111221111-1-1-1-12200-2-2000-2000200-1-10011110000-1-1000000
χ2622222-2-222222-2-2-2-2-2222-122-1-12-1-2-2-2-2-1-1-1-1-1-2-211-1-11111-111221111-1-1-1-1-2-200220002000-2001100-1-1-1-1000011000000
χ2722222-2-222222-2-2-2-2-222-12-1-122-1211112222-111-2-2-1-11111-1-2-2-1-11111-1-1-1-10022002200-2000-2000-1-10000-1-11100110000
χ2822222-2-222222-2-2-2-2-222-12-1-122-1211112222-111-2-2-1-11111-1-2-2-1-11111-1-1-1-100-2-200-2-2002000200011000011-1-100-1-10000
χ2922222-2-2-2-2222222-2-2-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-111-2-2111111112200-2-20002000-200-1-10011-1-1000011000000
χ3022222-2-2-2-2222222-2-2-2-22-122-1-12-1-2-2-2-21111-122-1-1-1-1-1-1-1-1-111-2-211111111-2-20022000-20002001100-1-1110000-1-1000000
χ3122222-2-2-2-2222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-21111111111002200-2-2002000-2000-1-1000011-1-100110000
χ3222222-2-2-2-2222222-2-2-2-2-12-1-122-121111-2-2-2-2-1-1-122-1-1-1-1-1-1-1-2-2111111111100-2-2002200-20002000110000-1-11100-1-10000
χ3322-2-22002i−2i2-2-2000002i−2i222-22-2-2-200002i2i−2i−2i200002-20000-2002i−2i00002i2i−2i−2i002-2002i−2i00000000002-200002i−2i0000000000
χ3422-2-22002i−2i2-2-2000002i−2i222-22-2-2-200002i2i−2i−2i200002-20000-2002i−2i00002i2i−2i−2i00-2200−2i2i0000000000-220000−2i2i0000000000
χ3522-2-22002i−2i2-2-2000002i−2i-12-112-21-233−3−32i2i−2i−2i-1−i3i300-11−i3−i3i3i3100−ii33−3−3−i−iii002-2002i−2i0000000000-110000−ii−i3i3003−30000
χ3622-2-22002i−2i2-2-2000002i−2i-12-112-21-233−3−32i2i−2i−2i-1−i3i300-11−i3−i3i3i3100−ii33−3−3−i−iii00-2200−2i2i00000000001-10000i−ii3−i300−330000
χ3722-2-22002i−2i2-2-2000002i−2i-12-112-21-2−3−3332i2i−2i−2i-1i3−i300-11i3i3−i3−i3100−ii−3−333−i−iii002-2002i−2i0000000000-110000−iii3−i300−330000
χ3822-2-22002i−2i2-2-2000002i−2i-12-112-21-2−3−3332i2i−2i−2i-1i3−i300-11i3i3−i3−i3100−ii−3−333−i−iii00-2200−2i2i00000000001-10000i−i−i3i3003−30000
χ3922-2-2200−2i2i2-2-200000−2i2i222-22-2-2-20000−2i−2i2i2i200002-20000-200−2i2i0000−2i−2i2i2i002-200−2i2i00000000002-20000−2i2i0000000000
χ4022-2-2200−2i2i2-2-200000−2i2i222-22-2-2-20000−2i−2i2i2i200002-20000-200−2i2i0000−2i−2i2i2i00-22002i−2i0000000000-2200002i−2i0000000000
χ4122-2-2200−2i2i2-2-200000−2i2i-12-112-21-233−3−3−2i−2i2i2i-1i3−i300-11i3i3−i3−i3100i−i33−3−3ii−i−i002-200−2i2i0000000000-110000i−ii3−i3003−30000
χ4222-2-2200−2i2i2-2-200000−2i2i-12-112-21-233−3−3−2i−2i2i2i-1i3−i300-11i3i3−i3−i3100i−i33−3−3ii−i−i00-22002i−2i00000000001-10000−ii−i3i300−330000
χ4322-2-2200−2i2i2-2-200000−2i2i-12-112-21-2−3−333−2i−2i2i2i-1−i3i300-11−i3−i3i3i3100i−i−3−333ii−i−i002-200−2i2i0000000000-110000i−i−i3i300−330000
χ4422-2-2200−2i2i2-2-200000−2i2i-12-112-21-2−3−333−2i−2i2i2i-1−i3i300-11−i3−i3i3i3100i−i−3−333ii−i−i00-22002i−2i00000000001-10000−iii3−i3003−30000
χ452-22-222i−2i00-22-20002i−2i0022-22-22-2-22i−2i2i−2i000020000-220000-22i−2i002i−2i2i−2i00002-2002i−2i00000000002-2002i−2i00000000000000
χ462-22-222i−2i00-22-20002i−2i0022-22-22-2-22i−2i2i−2i000020000-220000-22i−2i002i−2i2i−2i0000-2200−2i2i0000000000-2200−2i2i00000000000000
χ472-22-222i−2i00-22-20002i−2i002-1-221-1-212i−2i2i−2i3−33−3-100−i3i31-1−i3i3−i3i31−ii00−ii−ii3−33−32-2002i−2i0000000000-1100−ii−i3i300003−3000000
χ482-22-222i−2i00-22-20002i−2i002-1-221-1-212i−2i2i−2i3−33−3-100−i3i31-1−i3i3−i3i31−ii00−ii−ii3−33−3-2200−2i2i00000000001-100i−ii3−i30000−33000000
χ492-22-222i−2i00-22-20002i−2i002-1-221-1-212i−2i2i−2i−33−33-100i3−i31-1i3−i3i3−i31−ii00−ii−ii−33−332-2002i−2i0000000000-1100−iii3−i30000−33000000
χ502-22-222i−2i00-22-20002i−2i002-1-221-1-212i−2i2i−2i−33−33-100i3−i31-1i3−i3i3−i31−ii00−ii−ii−33−33-2200−2i2i00000000001-100i−i−i3i300003−3000000
χ512-22-22−2i2i00-22-2000−2i2i0022-22-22-2-2−2i2i−2i2i000020000-220000-2−2i2i00−2i2i−2i2i00002-200−2i2i00000000002-200−2i2i00000000000000
χ522-22-22−2i2i00-22-2000−2i2i0022-22-22-2-2−2i2i−2i2i000020000-220000-2−2i2i00−2i2i−2i2i0000-22002i−2i0000000000-22002i−2i00000000000000
χ532-22-22−2i2i00-22-2000−2i2i002-1-221-1-21−2i2i−2i2i3−33−3-100i3−i31-1i3−i3i3−i31i−i00i−ii−i3−33−32-200−2i2i0000000000-1100i−ii3−i300003−3000000
χ542-22-22−2i2i00-22-2000−2i2i002-1-221-1-21−2i2i−2i2i3−33−3-100i3−i31-1i3−i3i3−i31i−i00i−ii−i3−33−3-22002i−2i00000000001-100−ii−i3i30000−33000000
χ552-22-22−2i2i00-22-2000−2i2i002-1-221-1-21−2i2i−2i2i−33−33-100−i3i31-1−i3i3−i3i31i−i00i−ii−i−33−332-200−2i2i0000000000-1100i−i−i3i30000−33000000
χ562-22-22−2i2i00-22-2000−2i2i002-1-221-1-21−2i2i−2i2i−33−33-100−i3i31-1−i3i3−i3i31i−i00i−ii−i−33−33-22002i−2i00000000001-100−iii3−i300003−3000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221222211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ5944444-4-444444-4-4-4-4-444-2-2-2-2-2-2-2-22222-2-2-2-21222211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ6044444-4-4-4-4444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ6144-4-44004i−4i4-4-4000004i−4i4-24-4-22-420000−2i−2i2i2i-20000-2200002004i−4i0000−2i−2i2i2i000000000000000000000000000000000000
χ6244-4-44004i−4i4-4-4000004i−4i-2-2-22-22222323−23−23−2i−2i2i2i1−2i32i3001-1i3i3−i3−i3-100−2i2i−3−333ii−i−i000000000000000000000000000000000000
χ6344-4-44004i−4i4-4-4000004i−4i-2-2-22-2222−23−232323−2i−2i2i2i12i3−2i3001-1−i3−i3i3i3-100−2i2i33−3−3ii−i−i000000000000000000000000000000000000
χ6444-4-4400−4i4i4-4-400000−4i4i4-24-4-22-4200002i2i−2i−2i-20000-220000200−4i4i00002i2i−2i−2i000000000000000000000000000000000000
χ6544-4-4400−4i4i4-4-400000−4i4i-2-2-22-22222323−23−232i2i−2i−2i12i3−2i3001-1−i3−i3i3i3-1002i−2i−3−333−i−iii000000000000000000000000000000000000
χ6644-4-4400−4i4i4-4-400000−4i4i-2-2-22-2222−23−2323232i2i−2i−2i1−2i32i3001-1i3i3−i3−i3-1002i−2i33−3−3−i−iii000000000000000000000000000000000000
χ674-44-444i−4i00-44-40004i−4i00-242-2-442-4−2i2i−2i2i0000-200002-2000024i−4i00−2i2i−2i2i0000000000000000000000000000000000000000
χ684-44-444i−4i00-44-40004i−4i00-2-22-22-222−2i2i−2i2i23−2323−23100−2i32i3-11i3−i3i3−i3-1−2i2i00i−ii−i−33−33000000000000000000000000000000000000
χ694-44-444i−4i00-44-40004i−4i00-2-22-22-222−2i2i−2i2i−2323−23231002i3−2i3-11−i3i3−i3i3-1−2i2i00i−ii−i3−33−3000000000000000000000000000000000000
χ704-44-44−4i4i00-44-4000−4i4i00-242-2-442-42i−2i2i−2i0000-200002-200002−4i4i002i−2i2i−2i0000000000000000000000000000000000000000
χ714-44-44−4i4i00-44-4000−4i4i00-2-22-22-2222i−2i2i−2i23−2323−231002i3−2i3-11−i3i3−i3i3-12i−2i00−ii−ii−33−33000000000000000000000000000000000000
χ724-44-44−4i4i00-44-4000−4i4i00-2-22-22-2222i−2i2i−2i−2323−2323100−2i32i3-11i3−i3i3−i3-12i−2i00−ii−ii3−33−3000000000000000000000000000000000000
χ734-4-4440000-4-44000000044-4-4-4-4440000000040000-4-400004000000000000000000000000000000000000000000000000
χ744-4-4440000-4-4400000004-2-4-4224-20000−2i32i32i3−2i3-20000220000-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ754-4-4440000-4-4400000004-2-4-4224-200002i3−2i3−2i32i3-20000220000-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ764-4-4440000-4-440000000-2422-4-4-24−2i32i32i3−2i30000-20000220000-20000−2i32i32i3−2i30000000000000000000000000000000000000000
χ774-4-4440000-4-440000000-2422-4-4-242i3−2i3−2i32i30000-20000220000-200002i3−2i3−2i32i30000000000000000000000000000000000000000
χ784-4-4440000-4-440000000-2-22222-2-2−2i32i32i3−2i3−2i32i32i3−2i310000-1-1-333-310000i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000000000
χ794-4-4440000-4-440000000-2-22222-2-2−2i32i32i3−2i32i3−2i3−2i32i310000-1-13-3-3310000i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ804-4-4440000-4-440000000-2-22222-2-22i3−2i3−2i32i3−2i32i32i3−2i310000-1-13-3-3310000−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ814-4-4440000-4-440000000-2-22222-2-22i3−2i3−2i32i32i3−2i3−2i32i310000-1-1-333-310000−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000000000
χ826666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000200220020000000000000000-1-1-1-1
χ836666-36666-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000-200-2-200-200000000000000001111
χ846666-366-6-6-3-3-3-633-3-3330000000000000000000000000000000000000000000000002002-200-20000000000000000-1-111
χ856666-366-6-6-3-3-3-633-3-333000000000000000000000000000000000000000000000000-200-22002000000000000000011-1-1
χ866666-3-6-666-3-3-3-63333-3-3000000000000000000000000000000000000000000000000200-2200-20000000000000000-11-11
χ876666-3-6-666-3-3-3-63333-3-3000000000000000000000000000000000000000000000000-2002-200200000000000000001-11-1
χ886666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000200-2-20020000000000000000-111-1
χ896666-3-6-6-6-6-3-3-36-3-33333000000000000000000000000000000000000000000000000-2002200-200000000000000001-1-11
χ901212-12-12-60012i−12i-66600000−6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-600−12i12i-666000006i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-612i−12i006-66000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6−12i12i006-660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-60−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-606i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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