Finite Group Databasebeta

← Group #72226615

Character table — Group #72226615

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size1111333344446666666612121212121212121212121212121212121212121212121212121212121212121212121296969696969696969696969696969696256256256256256256256256256256256256256256256256
order1222222222222222222222222222222222222222222222222222222244444444444444443366666666666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1
χ511111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ611111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ722-2-222-2-222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000-1-111-111-1-111-111-1-1
χ822-2-222-2-222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-200000000000000001+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32
χ922-2-222-2-222-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-200000000000000001−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ1022-2-222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222220000000000000000-1-111-1-1-11111-1-1-111
χ1122-2-222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222200000000000000001+i321−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ1222-2-222-2-2-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222200000000000000001−i321+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ1333333333333333333333333333333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1433333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-133-1-1-1-1-1-10000000000000000
χ1533333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-133-1-1-1-10000000000000000
χ1633333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-133-1-10000000000000000
χ1733333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1330000000000000000
χ1833333333-3-3-3-3333333333333333333333333-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-1111111110000000000000000
χ1933333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-311111111-3-31111111133-1-1-1-1-1-1-3-31111110000000000000000
χ2033333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-311111111-3-311111111-1-133-1-1-1-111-3-311110000000000000000
χ2133333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-311111111-3-311111111-1-1-1-133-1-11111-3-3110000000000000000
χ2233333333-3-3-3-333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-311111111-3-311111111-1-1-1-1-1-133111111-3-30000000000000000
χ234-44-44-44-42-22-2000000000000004-40000004-42-22222-2-2-2-22-22222-2-2-2-20000000000000000111-1-11-11-11-1-11-11-1
χ244-44-44-44-42-22-2000000000000004-40000004-42-22222-2-2-2-22-22222-2-2-2-20000000000000000−1−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32
χ254-44-44-44-42-22-2000000000000004-40000004-42-22222-2-2-2-22-22222-2-2-2-20000000000000000−1+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ264-44-44-44-4-22-22000000000000004-40000004-4-22-2-2-2-22222-22-2-2-2-222220000000000000000111-1-1-11-111-1-1-11-11
χ274-44-44-44-4-22-22000000000000004-40000004-4-22-2-2-2-22222-22-2-2-2-222220000000000000000−1−i32−1+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32
χ284-44-44-44-4-22-22000000000000004-40000004-4-22-2-2-2-22222-22-2-2-2-222220000000000000000−1+i32−1−i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ294-4-444-4-442-2-22000000000000004-4000000-442-22222-2-2-2-2-22-2-2-2-22222000000000000000011-11-1-111-1-11-1-111-1
χ304-4-444-4-442-2-22000000000000004-4000000-442-22222-2-2-2-2-22-2-2-2-222220000000000000000−1−i32−1+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32
χ314-4-444-4-442-2-22000000000000004-4000000-442-22222-2-2-2-2-22-2-2-2-222220000000000000000−1+i32−1−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32
χ324-4-444-4-44-222-2000000000000004-4000000-44-22-2-2-2-222222-22222-2-2-2-2000000000000000011-11-11-1-11-11-11-1-11
χ334-4-444-4-44-222-2000000000000004-4000000-44-22-2-2-2-222222-22222-2-2-2-20000000000000000−1−i32−1+i321+i32−1−i321+i32−1−i321+i321+i32−1−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32
χ344-4-444-4-44-222-2000000000000004-4000000-44-22-2-2-2-222222-22222-2-2-2-20000000000000000−1+i32−1−i321−i32−1+i321−i32−1+i321−i321−i32−1+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32
χ35666666660000-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-2-2-2-2-2000000000000000000002-22-2-22-22000000000000000000000000
χ36666666660000-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-2-2-2-2-200000000000000000000-22-222-22-2000000000000000000000000
χ37666666660000-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-2-2-2000000000000000000002-2-222-2-22000000000000000000000000
χ38666666660000-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-2-2-200000000000000000000-222-2-222-2000000000000000000000000
χ39666666660000-2-2-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-2000000000000000000002-2-22-222-2000000000000000000000000
χ40666666660000-2-2-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-266-2-200000000000000000000-222-22-2-22000000000000000000000000
χ41666666660000-2-2-2-2-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-266000000000000000000002-22-22-22-2000000000000000000000000
χ42666666660000-2-2-2-2-2-2-2-2-2-2-2-2-2-266-2-2-2-2-2-26600000000000000000000-22-22-22-22000000000000000000000000
χ4366-6-666-6-60000-2-2-2-2222266-2-2-2-2-2-2-6-622222200000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4466-6-666-6-60000-2-2-2-2222266-2-2-2-2-2-2-6-62222220000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4566-6-666-6-60000-2-2-2-22222-2-266-2-2-2-222-6-6222200000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ4666-6-666-6-60000-2-2-2-22222-2-266-2-2-2-222-6-622220000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ4766-6-666-6-60000-2-2-2-22222-2-2-2-266-2-22222-6-62200000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ4866-6-666-6-60000-2-2-2-22222-2-2-2-266-2-22222-6-6220000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ4966-6-666-6-60000-2-2-2-22222-2-2-2-2-2-266222222-6-600000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5066-6-666-6-60000-2-2-2-22222-2-2-2-2-2-266222222-6-60000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ5166-6-666-6-666-6-66666-6-6-6-6-2-2-2-2-2-2-2-22222222266-2-2-2-2-2-2-2-2-6-62222222200000000000000000000000000000000
χ5266-6-666-6-6-6-6666666-6-6-6-6-2-2-2-2-2-2-2-222222222-6-62222222266-2-2-2-2-2-2-2-200000000000000000000000000000000
χ5312121212-4-4-4-4000012-4-4-412-4-4-400000000000000000044-4-444-4-40044-4-444-4-400000000000000000000000000000000
χ5412121212-4-4-4-4000012-4-4-412-4-4-4000000000000000000-4-444-4-44400-4-444-4-44400000000000000000000000000000000
χ5512121212-4-4-4-40000-412-4-4-412-4-40000000000000000004-44-44-44-4004-44-44-44-400000000000000000000000000000000
χ5612121212-4-4-4-40000-412-4-4-412-4-4000000000000000000-44-44-44-4400-44-44-44-4400000000000000000000000000000000
χ5712121212-4-4-4-40000-4-412-4-4-412-40000000000000000004-4-444-4-44004-4-444-4-4400000000000000000000000000000000
χ5812121212-4-4-4-40000-4-412-4-4-412-4000000000000000000-444-4-444-400-444-4-444-400000000000000000000000000000000
χ5912121212-4-4-4-412121212-4-4-412-4-4-4120000000000000000-4-400000000-4-40000000000000000000000000000000000000000
χ6012121212-4-4-4-4-12-12-12-12-4-4-412-4-4-41200000000000000004400000000440000000000000000000000000000000000000000
χ611212-12-12-4-444000012-4-4-4-1244400000000000000000044-4-444-4-400-4-444-4-44400000000000000000000000000000000
χ621212-12-12-4-444000012-4-4-4-12444000000000000000000-4-444-4-4440044-4-444-4-400000000000000000000000000000000
χ631212-12-12-4-4440000-412-4-44-12440000000000000000004-44-44-44-400-44-44-44-4400000000000000000000000000000000
χ641212-12-12-4-4440000-412-4-44-1244000000000000000000-44-44-44-44004-44-44-44-400000000000000000000000000000000
χ651212-12-12-4-4440000-4-412-444-1240000000000000000004-4-444-4-4400-444-4-444-400000000000000000000000000000000
χ661212-12-12-4-4440000-4-412-444-124000000000000000000-444-4-444-4004-4-444-4-4400000000000000000000000000000000
χ671212-12-12-4-4441212-12-12-4-4-412444-120000000000000000-4-400000000440000000000000000000000000000000000000000
χ681212-12-12-4-444-12-121212-4-4-412444-1200000000000000004400000000-4-40000000000000000000000000000000000000000
χ6912-1212-1212-1212-126-66-600000000000000-44000000-446-6-2-2-2-222226-6-2-2-2-2222200000000000000000000000000000000
χ7012-1212-1212-1212-12-66-6600000000000000-44000000-44-662222-2-2-2-2-662222-2-2-2-200000000000000000000000000000000
χ7112-1212-12-44-446-66-6000000004-44-44-4004-44-44-400-22222-6-2-2-26-22222-6-2-2-2600000000000000000000000000000000
χ7212-1212-12-44-446-66-6000000004-4-44-44004-4-44-4400-2222-62-2-26-2-2222-62-2-26-200000000000000000000000000000000
χ7312-1212-12-44-446-66-600000000-444-4-4400-444-4-4400-222-622-26-2-2-222-622-26-2-200000000000000000000000000000000
χ7412-1212-12-44-446-66-600000000-44-444-400-44-444-400-22-62226-2-2-2-22-62226-2-2-200000000000000000000000000000000
χ7512-1212-12-44-44-66-66000000004-44-44-4004-44-44-4002-2-2-2-26222-62-2-2-2-26222-600000000000000000000000000000000
χ7612-1212-12-44-44-66-66000000004-4-44-44004-4-44-44002-2-2-26-222-622-2-2-26-222-6200000000000000000000000000000000
χ7712-1212-12-44-44-66-6600000000-444-4-4400-444-4-44002-2-26-2-22-6222-2-26-2-22-62200000000000000000000000000000000
χ7812-1212-12-44-44-66-6600000000-44-444-400-44-444-4002-26-2-2-2-62222-26-2-2-2-622200000000000000000000000000000000
χ7912-12-121212-12-12126-6-6600000000000000-440000004-46-6-2-2-2-22222-662222-2-2-2-200000000000000000000000000000000
χ8012-12-121212-12-1212-666-600000000000000-440000004-4-662222-2-2-2-26-6-2-2-2-2222200000000000000000000000000000000
χ8112-12-1212-444-46-6-66000000004-44-44-400-44-44-4400-22222-6-2-2-262-2-2-2-26222-600000000000000000000000000000000
χ8212-12-1212-444-46-6-66000000004-4-44-4400-444-44-400-2222-62-2-26-22-2-2-26-222-6200000000000000000000000000000000
χ8312-12-1212-444-46-6-6600000000-444-4-44004-4-444-400-222-622-26-2-22-2-26-2-22-62200000000000000000000000000000000
χ8412-12-1212-444-46-6-6600000000-44-444-4004-44-4-4400-22-62226-2-2-22-26-2-2-2-622200000000000000000000000000000000
χ8512-12-1212-444-4-666-6000000004-44-44-400-44-44-44002-2-2-2-26222-6-22222-6-2-2-2600000000000000000000000000000000
χ8612-12-1212-444-4-666-6000000004-4-44-4400-444-44-4002-2-2-26-222-62-2222-62-2-26-200000000000000000000000000000000
χ8712-12-1212-444-4-666-600000000-444-4-44004-4-444-4002-2-26-2-22-622-222-622-26-2-200000000000000000000000000000000
χ8812-12-1212-444-4-666-600000000-44-444-4004-44-4-44002-26-2-2-2-6222-22-62226-2-2-200000000000000000000000000000000

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