Finite Group Databasebeta

← Group #11723708

Character table — Group #11723708

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122222224444444444444444888888888888888889918181818181818363636363636363636367272
order12333466633333466666121212121212121212121212121212121212121212122246688882241212122424242466
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-111-1-11-1-1-1-1-111-1-11-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-111-11-1-1-1-1-1-111-11
χ511111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-1-11111-1-1
χ611111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11-1-1-1-1-1-111
χ711111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-11
χ811111111111111-1111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-111-1-1111-1
χ922222-222222222022222-200-2-200-2-2-2-2-2000000000022-2220000000-200000000
χ1022222-222222222022222-200-2-200-2-2-2-2-20000000000-2-22-2-20000000200000000
χ112222-122-122-1-1-1-122-1-1-1-12222-12-12-1-1-1-122-1-1-1-1-1-1-1-100000002202000000-1-10-1
χ122222-122-122-1-1-1-122-1-1-1-12222-12-12-1-1-1-122-1-1-1-1-1-1-1-10000000-2-20-20000001101
χ132222-122-122-1-1-1-1-22-1-1-1-12-2-22-1-212-1-1-1-1-2-2111111110000000220-2000000-1-101
χ142222-122-122-1-1-1-1-22-1-1-1-12-2-22-1-212-1-1-1-1-2-2111111110000000-2-202000000110-1
χ15222-122-122-12-1-1-12-12-1-1-1222-12-12-12-1-1-1-1-122-1-1-1-1-1-1000002200200000-1-100-10
χ16222-122-122-12-1-1-12-12-1-1-1222-12-12-12-1-1-1-1-122-1-1-1-1-1-100000-2-200-200000110010
χ17222-122-122-12-1-1-1-2-12-1-1-12-2-2-121-2-12-1-1-111-2-2111111000002200-200000-1-10010
χ18222-122-122-12-1-1-1-2-12-1-1-12-2-2-121-2-12-1-1-111-2-211111100000-2-2002000001100-10
χ1922-122222-1-1-12-1-12-1-12-1-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1222-1-10000002-1-1-1000000
χ2022-122222-1-1-12-1-12-1-12-1-1-1-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-2-2-211000000-2111000000
χ2122-122222-1-1-12-1-1-2-1-12-1-1-11122-2-2-1-12-1-11111-2-21111222-1-1000000-2-111000000
χ2222-122222-1-1-12-1-1-2-1-12-1-1-11122-2-2-1-12-1-11111-2-21111-2-2-21100000021-1-1000000
χ2322-122-222-1-1-12-1-10-1-12-1-11−i3i3-2-20011-211−i3i3−i3i300−i3−i3i3i322-2-1-100000001−i3i3000000
χ2422-122-222-1-1-12-1-10-1-12-1-11−i3i3-2-20011-211−i3i3−i3i300−i3−i3i3i3-2-22110000000-1i3−i3000000
χ2522-122-222-1-1-12-1-10-1-12-1-11i3−i3-2-20011-211i3−i3i3−i300i3i3−i3−i322-2-1-100000001i3−i3000000
χ2622-122-222-1-1-12-1-10-1-12-1-11i3−i3-2-20011-211i3−i3i3−i300i3i3−i3−i3-2-22110000000-1−i3i3000000
χ272-22220-2-2-2222220-2-2-2-2-200000000000000000000002-202-2−i2i2−i2i2000000−i2i2−i2i200
χ282-22220-2-2-2222220-2-2-2-2-200000000000000000000002-202-2i2−i2i2−i2000000i2−i2i2−i200
χ292-22220-2-2-2222220-2-2-2-2-20000000000000000000000-220-22−i2i2i2−i2000000−i2i2i2−i200
χ302-22220-2-2-2222220-2-2-2-2-20000000000000000000000-220-22i2−i2−i2i2000000i2−i2−i2i200
χ314444-2-44-244-2-2-2-204-2-2-2-2-400-4200-422220000000000000000000000000000000
χ32444-24-4-244-24-2-2-20-24-2-2-2-4002-4002-42220000000000000000000000000000000
χ33444-2-24-2-24-2-21114-2-2111444-2-2-2-2-2-2111-2-2-2-2111111000000000000000000000
χ34444-2-24-2-24-2-2111-4-2-21114-4-4-2-222-2-21112222-1-1-1-1-1-1000000000000000000000
χ35444-2-2-4-2-24-2-21110-2-2111-400220022-1-1-100003-33-33-3000000000000000000000
χ36444-2-2-4-2-24-2-21110-2-2111-400220022-1-1-10000-33-33-33000000000000000000000
χ3744-24-244-2-2-21-2114-21-211-2-2-24-24-2-21-211-2-211-2-21111000000000000000000000
χ3844-24-244-2-2-21-211-4-21-211-2224-2-42-21-21122-1-122-1-1-1-1000000000000000000000
χ3944-24-2-44-2-2-21-2110-21-2112−2i32i3-42002-12-1-1−2i32i3i3−i300i3i3−i3−i3000000000000000000000
χ4044-24-2-44-2-2-21-2110-21-21122i3−2i3-42002-12-1-12i3−2i3−i3i300−i3−i3i3i3000000000000000000000
χ4144-2-244-24-21-2-21141-2-211-2-2-2-24-241-2-21111-2-2-2-21111000000000000000000000
χ4244-2-244-24-21-2-211-41-2-211-222-242-41-2-211-1-12222-1-1-1-1000000000000000000000
χ4344-2-24-4-24-21-2-21101-2-2112−2i32i32-400-122-1-1i3−i3−2i32i300i3i3−i3−i3000000000000000000000
χ4444-2-24-4-24-21-2-21101-2-21122i3−2i32-400-122-1-1−i3i32i3−2i300−i3−i3i3i3000000000000000000000
χ4544-2-2-24-2-2-2111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000
χ4644-2-2-24-2-2-2111−1−3i32−1+3i32-4111−1−3i32−1+3i32-222-2-222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321−3i321+3i32000000000000000000000
χ4744-2-2-24-2-2-2111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000
χ4844-2-2-24-2-2-2111−1+3i32−1−3i32-4111−1+3i32−1−3i32-222-2-222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321+3i321−3i32000000000000000000000
χ4944-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i322−2i32i32200-1-1-11+3i321−3i32i3−i3i3−i33-3−3−i323−i32−3+i323+i32000000000000000000000
χ5044-2-2-2-4-2-2-2111−1−3i32−1+3i320111−1−3i32−1+3i3222i3−2i32200-1-1-11+3i321−3i32−i3i3−i3i3-333+i32−3+i323−i32−3−i32000000000000000000000
χ5144-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i322−2i32i32200-1-1-11−3i321+3i32i3−i3i3−i3-333−i32−3−i323+i32−3+i32000000000000000000000
χ5244-2-2-2-4-2-2-2111−1+3i32−1−3i320111−1+3i32−1−3i3222i3−2i32200-1-1-11−3i321+3i32−i3i3−i3i33-3−3+i323+i32−3−i323−i32000000000000000000000
χ534-444-20-42-44-2-2-2-20-4222200000000000000000000000000000−2i22i200000000i2−i200
χ544-444-20-42-44-2-2-2-20-42222000000000000000000000000000002i2−2i200000000−i2i200
χ554-44-2402-4-4-24-2-2-202-4222000000000000000000000000000−2i22i200000000i2−i20000
χ564-44-2402-4-4-24-2-2-202-42220000000000000000000000000002i2−2i200000000−i2i20000
χ574-4-2440-4-42-2-24-2-2022-42200000000000000000000004-40-220000000000000000
χ584-4-2440-4-42-2-24-2-2022-4220000000000000000000000-4402-20000000000000000
χ598-88-4-4044-8-4-4222044-2-2-20000000000000000000000000000000000000000000
χ608-8-48-40-844-42-42204-24-2-20000000000000000000000000000000000000000000
χ618-8-4-4804-842-4-4220-244-2-20000000000000000000000000000000000000000000
χ628-8-4-4-40444222−1−3i3−1+3i30-2-2-21+3i31−3i30000000000000000000000000000000000000000000
χ638-8-4-4-40444222−1+3i3−1−3i30-2-2-21−3i31+3i30000000000000000000000000000000000000000000

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