Finite Group Databasebeta

← Group #11723556

Character table — Group #11723556

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11222222222223344444444444444444444446666666668888888888888121212121212121212121212121818363636545472108
order123333346666644233336666666666661212121212212121212121212126666666661212121246666121212121212121288224248864
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-111-11111-1-1
χ4111111111111111-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111
χ51111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ61111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11
χ71111111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111111111-111-1-1-11
χ81111111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-11-1-1111-1
χ92222222-2222222202222000000002222-2-2-2-2-2-222222222000000000-2-2-2-20-2-2-2-200000000000000000
χ102222222-222222-2-202222000000002222-2-2-2-2-22-2-2-2-2-2-2-2-2000000000-2-2-2-20222200000000000000000
χ11222222-12-12222002-1-1-1-122222222-1-1-1-12222-1000000000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000222-1-100-10
χ12222222-12-12222002-1-1-1-122222222-1-1-1-12222-1000000000-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000-2-2-2110010
χ13222222-12-1222200-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1000000000111111111-1-1-1-1000000000000022-2-1-10010
χ14222222-12-1222200-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1000000000111111111-1-1-1-10000000000000-2-221100-10
χ15222-1-1-12222-1-1-12222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1-122-1-1-122-1-1-1-1-1-1000000000
χ16222-1-1-12222-1-1-122-22-1-1-1-2-21111112-1-1-12-1-1-12222-1-1-1-1-1-1-2-2-21111112-1-1-1-22-1-1-1-2-2111111000000000
χ17222-1-1-12222-1-1-1-2-222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-12-2-2-2111111222-1-1-1-1-1-12-1-1-1-2-2111-2-2111111000000000
χ18222-1-1-12222-1-1-1-2-2-22-1-1-1-2-21111112-1-1-12-1-1-12-2-2-2111111-2-2-21111112-1-1-12-211122-1-1-1-1-1-1000000000
χ19222-1-1-12-222-1-1-12202-1-1-100−i3−i3−i3i3i3i32-1-1-1-2111-2-222-1-1-1-1-1-1000−i3−i3−i3i3i3i3-21110-211100−i3−i3−i3i3i3i3000000000
χ20222-1-1-12-222-1-1-12202-1-1-100i3i3i3−i3−i3−i32-1-1-1-2111-2-222-1-1-1-1-1-1000i3i3i3−i3−i3−i3-21110-211100i3i3i3−i3−i3−i3000000000
χ21222-1-1-12-222-1-1-1-2-202-1-1-100−i3−i3−i3i3i3i32-1-1-1-2111-22-2-2111111000−i3−i3−i3i3i3i3-211102-1-1-100i3i3i3−i3−i3−i3000000000
χ22222-1-1-12-222-1-1-1-2-202-1-1-100i3i3i3−i3−i3−i32-1-1-1-2111-22-2-2111111000i3i3i3−i3−i3−i3-211102-1-1-100−i3−i3−i3i3i3i3000000000
χ2322-12-1-1222-12-1-1222-12-1-1-1-12-1-12-1-1-12-1-1-12-1-122-1-122-1-1-1-12-1-12-1-12-1-1-12-1-12-12-1-1-1-12-1-12-1-1000000000
χ2422-12-1-1222-12-1-122-2-12-1-111-211-211-12-1-1-12-1-122-1-122-1-1-1-1-211-211-211-12-1-1-2-12-1-111-211-211000000000
χ2522-12-1-1222-12-1-1-2-22-12-1-1-1-12-1-12-1-1-12-1-1-12-1-12-211-2-211112-1-12-1-12-1-1-12-1-1-21-21111-211-211000000000
χ2622-12-1-1222-12-1-1-2-2-2-12-1-111-211-211-12-1-1-12-1-12-211-2-21111-211-211-211-12-1-121-211-1-12-1-12-1-1000000000
χ2722-12-1-12-22-12-1-1220-12-1-1−i3i30−i3i30−i3i3-12-1-11-211-2-2-1-122-1-1-1-10−i3i30−i3i30−i3i31-21101-211−i3i30−i3i30−i3i3000000000
χ2822-12-1-12-22-12-1-1220-12-1-1i3−i30i3−i30i3−i3-12-1-11-211-2-2-1-122-1-1-1-10i3−i30i3−i30i3−i31-21101-211i3−i30i3−i30i3−i3000000000
χ2922-12-1-12-22-12-1-1-2-20-12-1-1−i3i30−i3i30−i3i3-12-1-11-211-2211-2-211110−i3i30−i3i30−i3i31-2110-12-1-1i3−i30i3−i30i3−i3000000000
χ3022-12-1-12-22-12-1-1-2-20-12-1-1i3−i30i3−i30i3−i3-12-1-11-211-2211-2-211110i3−i30i3−i30i3−i31-2110-12-1-1−i3i30−i3i30−i3i3000000000
χ3122-1-12-1222-1-12-1222-1-12-1-1-1-12-1-1-12-1-12-1-1-12-122-1-1-1-122-1-12-1-1-12-1-1-12-1-12-12-1-12-1-1-1-12-1-1-12000000000
χ3222-1-12-1222-1-12-122-2-1-12-1111-2111-2-1-12-1-1-12-122-1-1-1-122-1-1-2111-2111-2-1-12-1-2-1-12-1111-2111-2000000000
χ3322-1-12-1222-1-12-1-2-22-1-12-1-1-1-12-1-1-12-1-12-1-1-12-12-21111-2-2112-1-1-12-1-1-12-1-12-1-211-21111-2111-2000000000
χ3422-1-12-1222-1-12-1-2-2-2-1-12-1111-2111-2-1-12-1-1-12-12-21111-2-211-2111-2111-2-1-12-1211-21-1-1-12-1-1-12000000000
χ3522-1-12-12-22-1-12-1220-1-12-1−i3i3i30−i3−i3i30-1-12-111-21-2-2-1-1-1-122-1-10−i3i3i30−i3−i3i3011-21011-21−i3i3i30−i3−i3i30000000000
χ3622-1-12-12-22-1-12-1220-1-12-1i3−i3−i30i3i3−i30-1-12-111-21-2-2-1-1-1-122-1-10i3−i3−i30i3i3−i3011-21011-21i3−i3−i30i3i3−i30000000000
χ3722-1-12-12-22-1-12-1-2-20-1-12-1−i3i3i30−i3−i3i30-1-12-111-21-221111-2-2110−i3i3i30−i3−i3i3011-210-1-12-1i3−i3−i30i3i3−i30000000000
χ3822-1-12-12-22-1-12-1-2-20-1-12-1i3−i3−i30i3i3−i30-1-12-111-21-221111-2-2110i3−i3−i30i3i3−i3011-210-1-12-1−i3i3i30−i3−i3i30000000000
χ3922-1-1-12222-1-1-12222-1-1-12-1-1-1-12-12-1-1-1-12-1-1-1222-1-1-1-1-1-1222-1-1-1-12-12-1-1-1-122-1-1-12-1-1-1-12-12-1000000000
χ4022-1-1-12222-1-1-1222-2-1-1-121111-21-21-1-1-12-1-1-1222-1-1-1-1-1-122-21111-21-21-1-1-12-2-1-1-121111-21-21000000000
χ4122-1-1-12222-1-1-12-2-22-1-1-12-1-1-1-12-12-1-1-1-12-1-1-122-2111111-2-22-1-1-1-12-12-1-1-1-12-2111-21111-21-21000000000
χ4222-1-1-12222-1-1-12-2-2-2-1-1-121111-21-21-1-1-12-1-1-122-2111111-2-2-21111-21-21-1-1-122111-2-1-1-1-12-12-1000000000
χ4322-1-1-122-22-1-1-12220-1-1-12−i3i3−i3i30i30−i3-1-1-12111-2-2-2-1-1-1-1-1-1220−i3i3−i3i30i30−i3111-20111-2−i3i3−i3i30i30−i3000000000
χ4422-1-1-122-22-1-1-12220-1-1-12i3−i3i3−i30−i30i3-1-1-12111-2-2-2-1-1-1-1-1-1220i3−i3i3−i30−i30i3111-20111-2i3−i3i3−i30−i30i3000000000
χ4522-1-1-122-22-1-1-12-2-20-1-1-12−i3i3−i3i30i30−i3-1-1-12111-2-22111111-2-20−i3i3−i3i30i30−i3111-20-1-1-12i3−i3i3−i30−i30i3000000000
χ4622-1-1-122-22-1-1-12-2-20-1-1-12i3−i3i3−i30−i30i3-1-1-12111-2-22111111-2-20i3−i3i3−i30−i30i3111-20-1-1-12−i3i3−i3i30i30−i3000000000
χ472-2222220-2-2-2-2-22i−2i0222200000000-2-2-2-20000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002−202−2−i2i200
χ482-2222220-2-2-2-2-22i−2i0222200000000-2-2-2-20000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−220−22i2−i200
χ492-2222220-2-2-2-2-2−2i2i0222200000000-2-2-2-2000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002−202−2i2−i200
χ502-2222220-2-2-2-2-2−2i2i0222200000000-2-2-2-2000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−220−22−i2i200
χ51444444-2-4-24444000-2-2-2-200000000-2-2-2-2-4-4-4-4200000000000000000022220000000000000000000000
χ52444-2-2-2-24-24-2-2-2004-211144-2-2-2-2-2-2-21114-2-2-2-2000000000-2-2-2111111-21110000000000000000000000
χ53444-2-2-2-24-24-2-2-200-4-2111-4-4222222-21114-2-2-2-2000000000222-1-1-1-1-1-1-21110000000000000000000000
χ54444-2-2-2-2-4-24-2-2-2000-211100−2i3−2i3−2i32i32i32i3-2111-42222000000000000i3i3i3−i3−i3−i32-1-1-10000000000000000000000
χ55444-2-2-2-2-4-24-2-2-2000-2111002i32i32i3−2i3−2i3−2i3-2111-42222000000000000−i3−i3−i3i3i3i32-1-1-10000000000000000000000
χ5644-24-2-2-24-2-24-2-20041-211-2-24-2-24-2-21-211-24-2-2-2000000000-211-211-2111-2110000000000000000000000
χ5744-24-2-2-24-2-24-2-200-41-21122-422-4221-211-24-2-2-20000000002-1-12-1-12-1-11-2110000000000000000000000
χ5844-24-2-2-2-4-2-24-2-20001-211−2i32i30−2i32i30−2i32i31-2112-42220000000000i3−i30i3−i30i3−i3-12-1-10000000000000000000000
χ5944-24-2-2-2-4-2-24-2-20001-2112i3−2i302i3−2i302i3−2i31-2112-42220000000000−i3i30−i3i30−i3i3-12-1-10000000000000000000000
χ6044-2-24-2-24-2-2-24-200411-21-2-2-24-2-2-2411-21-2-24-2-2000000000-2111-2111-211-210000000000000000000000
χ6144-2-24-2-24-2-2-24-200-411-21222-4222-411-21-2-24-2-20000000002-1-1-12-1-1-1211-210000000000000000000000
χ6244-2-24-2-2-4-2-2-24-200011-21−2i32i32i30−2i3−2i32i3011-2122-4220000000000i3−i3−i30i3i3−i30-1-12-10000000000000000000000
χ6344-2-24-2-2-4-2-2-24-200011-212i3−2i3−2i302i32i3−2i3011-2122-4220000000000−i3i3i30−i3−i3i30-1-12-10000000000000000000000
χ6444-2-2-24-24-2-2-2-24004111-2-2-2-2-24-24-2111-2-2-2-24-2000000000-21111-21-21111-20000000000000000000000
χ6544-2-2-24-24-2-2-2-2400-4111-22222-42-42111-2-2-2-24-20000000002-1-1-1-12-12-1111-20000000000000000000000
χ6644-2-2-24-2-4-2-2-2-24000111-2−2i32i3−2i32i302i30−2i3111-2222-420000000000i3−i3i3−i30−i30i3-1-1-120000000000000000000000
χ6744-2-2-24-2-4-2-2-2-24000111-22i3−2i32i3−2i30−2i302i3111-2222-420000000000−i3i3−i3i30i30−i3-1-1-120000000000000000000000
χ684-44444-202-4-4-4-4000-2-2-2-2000000002222000000000000000000000000000000000000000022−220−220000
χ694-44444-202-4-4-4-4000-2-2-2-20000000022220000000000000000000000000000000000000000−222202−20000
χ704-44-2-2-240-4-42224i−4i04-2-2-200000000-42220000004i−4i−2i2i−2i2i−2i2i00000000000000000000000000000000000
χ714-44-2-2-240-4-4222−4i4i04-2-2-200000000-4222000000−4i4i2i−2i2i−2i2i−2i00000000000000000000000000000000000
χ724-4-24-2-240-42-4224i−4i0-24-2-2000000002-422000000−2i2i4i−4i−2i2i−2i2i00000000000000000000000000000000000
χ734-4-24-2-240-42-422−4i4i0-24-2-2000000002-4220000002i−2i−4i4i2i−2i2i−2i00000000000000000000000000000000000
χ744-4-2-24-240-422-424i−4i0-2-24-20000000022-42000000−2i2i−2i2i4i−4i−2i2i00000000000000000000000000000000000
χ754-4-2-24-240-422-42−4i4i0-2-24-20000000022-420000002i−2i2i−2i−4i4i2i−2i00000000000000000000000000000000000
χ764-4-2-2-2440-4222-44i−4i0-2-2-2400000000222-4000000−2i2i−2i2i−2i2i4i−4i00000000000000000000000000000000000
χ774-4-2-2-2440-4222-4−4i4i0-2-2-2400000000222-40000002i−2i2i−2i2i−2i−4i4i00000000000000000000000000000000000
χ788-88-4-4-4-404-8444000-4222000000004-2-2-20000000000000000000000000000000000000000000000000
χ798-8-48-4-4-4044-8440002-42200000000-24-2-20000000000000000000000000000000000000000000000000
χ808-8-4-48-4-40444-8400022-4200000000-2-24-20000000000000000000000000000000000000000000000000
χ818-8-4-4-48-404444-8000222-400000000-2-2-240000000000000000000000000000000000000000000000000

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