Finite Group Databasebeta

← Group #72070

Character table — Group #72070

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order12222234444666666688881212121224242424242424244444121212121212121244888888
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111
χ92222222-2-2-2-222222220000-2-2-2-2000000000000000000000000002i−2i
χ102222222-2-2-2-222222220000-2-2-2-200000000000000000000000000−2i2i
χ11222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000
χ12222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000
χ13222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-1111100000000
χ14222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-100000000
χ152222-2-222-2-2222-2-2-2-2222-2-22-2-222222-2-2-2-200000000000000000000
χ162222-2-222-2-2222-2-2-2-22-2-2222-2-22-2-2-2-2222200000000000000000000
χ172222-2-22-222-222-2-2-2-220000-222-2000000000000000000002-2000000
χ182222-2-22-222-222-2-2-2-220000-222-200000000000000000000-22000000
χ192222-2-2-12-2-22-1-11111-122-2-2-111-1-1-1-1-111110000−i3−i3i3i3−i3−i3i3i300000000
χ202222-2-2-12-2-22-1-11111-122-2-2-111-1-1-1-1-111110000i3i3−i3−i3i3i3−i3−i300000000
χ212222-2-2-12-2-22-1-11111-1-2-222-111-11111-1-1-1-10000−i3−i3i3i3i3i3−i3−i300000000
χ222222-2-2-12-2-22-1-11111-1-2-222-111-11111-1-1-1-10000i3i3−i3−i3−i3−i3i3i300000000
χ232-2-222-2222-2-2-2-222-2-22000022-2-20000000000000000000000002i−2i00
χ242-2-222-2222-2-2-2-222-2-22000022-2-2000000000000000000000000−2i2i00
χ252-2-222-22-2-222-2-222-2-220000-2-222000000002-2002-22-2000000000000
χ262-2-222-22-2-222-2-222-2-220000-2-22200000000-2200-22-22000000000000
χ272-2-222-2-1-2-22211-1-111-1000011-1-1−i3−i3i3i3−i3−i3i3i32-200-11-11−i3i3−i3i300000000
χ282-2-222-2-1-2-22211-1-111-1000011-1-1−i3−i3i3i3−i3−i3i3i3-22001-11-1i3−i3i3−i300000000
χ292-2-222-2-1-2-22211-1-111-1000011-1-1i3i3−i3−i3i3i3−i3−i32-200-11-11i3−i3i3−i300000000
χ302-2-222-2-1-2-22211-1-111-1000011-1-1i3i3−i3−i3i3i3−i3−i3-22001-11-1−i3i3−i3i300000000
χ312-2-22-2222-22-2-2-2-2-222200002-22-200000000000000000000002i−2i0000
χ322-2-22-2222-22-2-2-2-2-222200002-22-20000000000000000000000−2i2i0000
χ332-2-22-222-22-22-2-2-2-22220000-22-2200000000002-200002-2-2200000000
χ342-2-22-222-22-22-2-2-2-22220000-22-220000000000-220000-222-200000000
χ352-2-22-22-1-22-221111-1-1-100001-11-1−i3−i3i3i3i3i3−i3−i3002-2−i3i3i3−i3-111-100000000
χ362-2-22-22-1-22-221111-1-1-100001-11-1−i3−i3i3i3i3i3−i3−i300-22i3−i3−i3i31-1-1100000000
χ372-2-22-22-1-22-221111-1-1-100001-11-1i3i3−i3−i3−i3−i3i3i3002-2i3−i3−i3i3-111-100000000
χ382-2-22-22-1-22-221111-1-1-100001-11-1i3i3−i3−i3−i3−i3i3i300-22−i3i3i3−i31-1-1100000000
χ39444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000000000000000000000000000
χ404444-4-4-2-444-4-2-22222-200002-2-220000000000000000000000000000
χ4144-4-400400004-40000-40022−220000000022−2222−2200000000000000000000
χ4244-4-400400004-40000-400−222200000000−2222−222200000000000000000000
χ4344-4-400-20000-22−2i32i3−2i32i320022−220000i6−i6i6−i6−22−2200000000000000000000
χ4444-4-400-20000-22−2i32i3−2i32i3200−22220000−i6i6−i6i62−22−200000000000000000000
χ4544-4-400-20000-222i3−2i32i3−2i320022−220000−i6i6−i6i6−22−2200000000000000000000
χ4644-4-400-20000-222i3−2i32i3−2i3200−22220000i6−i6i6−i62−22−200000000000000000000
χ474-44-40040000-440000-422−2200000022−22−2222000000000000000000000000
χ484-44-40040000-440000-4−2222000000−222222−22000000000000000000000000
χ494-44-400-200002-2−2i32i32i3−2i3222−22000000−222−2i6−i6−i6i600000000000000000000
χ504-44-400-200002-2−2i32i32i3−2i32−22220000002−2−22−i6i6i6−i600000000000000000000
χ514-44-400-200002-22i3−2i3−2i32i3222−22000000−222−2−i6i6i6−i600000000000000000000
χ524-44-400-200002-22i3−2i3−2i32i32−22220000002−2−22i6−i6−i6i600000000000000000000
χ534-4-444-4-244-4-422-2-222-20000-2-2220000000000000000000000000000
χ544-4-44-44-24-44-42222-2-2-20000-22-220000000000000000000000000000

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