Finite Group Databasebeta

← Group #78770

Character table — Group #78770

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11112222222222333344444444446666668888121212121111222222222233334444444444666666888812121212
order12223446668888444444441212242424244488881212121222442222644666888844444444121224242424448888121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111-1-1111111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111-1-111
χ61111111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1
χ71111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1
χ81111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111
χ911-1-11-11-1-11ii−i−iii−i−i1-1i−i1-1ii−i−ii−i11-1-1i−i1-11-1i−i11-1-11-11-1-11ii−i−iii−i−i1-1i−i1-1ii−i−ii−i11-1-1i−i1-11-1i−i
χ1011-1-11-11-1-11ii−i−iii−i−i-11−ii1-1ii−i−ii−i11-1-1−ii-11-11−ii11-1-11-11-1-11ii−i−iii−i−i-11−ii1-1ii−i−ii−i11-1-1−ii-11-11−ii
χ1111-1-11-11-1-11ii−i−i−i−iii1-1i−i1-1ii−i−i−ii-1-111i−i1-1-11−ii11-1-11-11-1-11ii−i−i−i−iii1-1i−i1-1ii−i−i−ii-1-111i−i1-1-11−ii
χ1211-1-11-11-1-11ii−i−i−i−iii-11−ii1-1ii−i−i−ii-1-111−ii-111-1i−i11-1-11-11-1-11ii−i−i−i−iii-11−ii1-1ii−i−i−ii-1-111−ii-111-1i−i
χ1311-1-11-11-1-11−i−iiiii−i−i1-1−ii1-1−i−iiii−i-1-111−ii1-1-11i−i11-1-11-11-1-11−i−iiiii−i−i1-1−ii1-1−i−iiii−i-1-111−ii1-1-11i−i
χ1411-1-11-11-1-11−i−iiiii−i−i-11i−i1-1−i−iiii−i-1-111i−i-111-1−ii11-1-11-11-1-11−i−iiiii−i−i-11i−i1-1−i−iiii−i-1-111i−i-111-1−ii
χ1511-1-11-11-1-11−i−iii−i−iii1-1−ii1-1−i−iii−ii11-1-1−ii1-11-1−ii11-1-11-11-1-11−i−iii−i−iii1-1−ii1-1−i−iii−ii11-1-1−ii1-11-1−ii
χ1611-1-11-11-1-11−i−iii−i−iii-11i−i1-1−i−iii−ii11-1-1i−i-11-11i−i11-1-11-11-1-11−i−iii−i−iii-11i−i1-1−i−iii−ii11-1-1i−i-11-11i−i
χ1722222-2-2222000022220000-2-20000-2-200000000000022222-2-2222000022220000-2-20000-2-2000000000000
χ1822222-2-22220000-2-2-2-20000-2-200002200000000000022222-2-22220000-2-2-2-20000-2-2000022000000000000
χ192222-122-1-1-1222200002222-1-1-1-1-1-1000000-1-1-1-100002222-122-1-1-1222200002222-1-1-1-1-1-1000000-1-1-1-10000
χ202222-122-1-1-122220000-2-2-2-2-1-1-1-1-1-1000000111100002222-122-1-1-122220000-2-2-2-2-1-1-1-1-1-100000011110000
χ212222-122-1-1-1-2-2-2-2000022-2-2-1-1111100000011-1-100002222-122-1-1-1-2-2-2-2000022-2-2-1-1111100000011-1-10000
χ222222-122-1-1-1-2-2-2-20000-2-222-1-11111000000-1-11100002222-122-1-1-1-2-2-2-20000-2-222-1-11111000000-1-1110000
χ2322-2-222-2-2-2200002i2i−2i−2i0000-220000−2i2i00000000000022-2-222-2-2-2200002i2i−2i−2i0000-220000−2i2i000000000000
χ2422-2-222-2-2-220000−2i−2i2i2i0000-2200002i−2i00000000000022-2-222-2-2-220000−2i−2i2i2i0000-2200002i−2i000000000000
χ2522-2-2-1-2211-12i2i−2i−2i00002-22i−2i-11−i−iii000000−ii-11000022-2-2-1-2211-12i2i−2i−2i00002-22i−2i-11−i−iii000000−ii-110000
χ2622-2-2-1-2211-12i2i−2i−2i0000-22−2i2i-11−i−iii000000i−i1-1000022-2-2-1-2211-12i2i−2i−2i0000-22−2i2i-11−i−iii000000i−i1-10000
χ2722-2-2-1-2211-1−2i−2i2i2i00002-2−2i2i-11ii−i−i000000i−i-11000022-2-2-1-2211-1−2i−2i2i2i00002-2−2i2i-11ii−i−i000000i−i-110000
χ2822-2-2-1-2211-1−2i−2i2i2i0000-222i−2i-11ii−i−i000000−ii1-1000022-2-2-1-2211-1−2i−2i2i2i0000-222i−2i-11ii−i−i000000−ii1-10000
χ292-22-2200-22-2i2−i2i2−i22-22-2000000i2−i2i2−i200i2−i2i2−i2000000002-22-2200-22-2i2−i2i2−i22-22-2000000i2−i2i2−i200i2−i2i2−i200000000
χ302-22-2200-22-2i2−i2i2−i2-22-22000000i2−i2i2−i200−i2i2−i2i2000000002-22-2200-22-2i2−i2i2−i2-22-22000000i2−i2i2−i200−i2i2−i2i200000000
χ312-22-2200-22-2−i2i2−i2i22-22-2000000−i2i2−i2i200−i2i2−i2i2000000002-22-2200-22-2−i2i2−i2i22-22-2000000−i2i2−i2i200−i2i2−i2i200000000
χ322-22-2200-22-2−i2i2−i2i2-22-22000000−i2i2−i2i200i2−i2i2−i2000000002-22-2200-22-2−i2i2−i2i2-22-22000000−i2i2−i2i200i2−i2i2−i200000000
χ332-2-222002-2-22−2−222i−2i−2i2i0000002−2−2200−i2i2i2−i2000000002-2-222002-2-22−2−222i−2i−2i2i0000002−2−2200−i2i2i2−i200000000
χ342-2-222002-2-22−2−22−2i2i2i−2i0000002−2−2200i2−i2−i2i2000000002-2-222002-2-22−2−22−2i2i2i−2i0000002−2−2200i2−i2−i2i200000000
χ352-2-222002-2-2−222−22i−2i−2i2i000000−222−200i2−i2−i2i2000000002-2-222002-2-2−222−22i−2i−2i2i000000−222−200i2−i2−i2i200000000
χ362-2-222002-2-2−222−2−2i2i2i−2i000000−222−200−i2i2i2−i2000000002-2-222002-2-2−222−2−2i2i2i−2i000000−222−200−i2i2i2−i200000000
χ374444-2-4-4-2-2-2000000000000220000000000000000004444-2-4-4-2-2-200000000000022000000000000000000
χ3844-4-4-24-422-20000000000002-200000000000000000044-4-4-24-422-20000000000002-2000000000000000000
χ394-44-4-2002-222i2−2i22i2−2i20000000000−i2i2−i2i2000000000000004-44-4-2002-222i2−2i22i2−2i20000000000−i2i2−i2i200000000000000
χ404-44-4-2002-22−2i22i2−2i22i20000000000i2−i2i2−i2000000000000004-44-4-2002-22−2i22i2−2i22i20000000000i2−i2i2−i200000000000000
χ414-4-44-200-22222−22−22220000000000−222−2000000000000004-4-44-200-22222−22−22220000000000−222−200000000000000
χ424-4-44-200-222−222222−2200000000002−2−22000000000000004-4-44-200-222−222222−2200000000002−2−2200000000000000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ44111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ4511111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ4611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1
χ471111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1111111-1-111-1-1
χ481111111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-111
χ491111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-111-1-1-1-111
χ501111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ5111-1-11-11-1-11ii−i−iii−i−i1-1i−i1-1ii−i−ii−i11-1-1i−i1-11-1i−i-1-111-11-111-1−i−iii−i−iii-11−ii-11−i−iii−ii-1-111−ii-11-11−ii
χ5211-1-11-11-1-11ii−i−iii−i−i-11−ii1-1ii−i−ii−i11-1-1−ii-11-11−ii-1-111-11-111-1−i−iii−i−iii1-1i−i-11−i−iii−ii-1-111i−i1-11-1i−i
χ5311-1-11-11-1-11ii−i−i−i−iii1-1i−i1-1ii−i−i−ii-1-111i−i1-1-11−ii-1-111-11-111-1−i−iiiii−i−i-11−ii-11−i−iiii−i11-1-1−ii-111-1i−i
χ5411-1-11-11-1-11ii−i−i−i−iii-11−ii1-1ii−i−i−ii-1-111−ii-111-1i−i-1-111-11-111-1−i−iiiii−i−i1-1i−i-11−i−iiii−i11-1-1i−i1-1-11−ii
χ5511-1-11-11-1-11−i−iiiii−i−i1-1−ii1-1−i−iiii−i-1-111−ii1-1-11i−i-1-111-11-111-1ii−i−i−i−iii-11i−i-11ii−i−i−ii11-1-1i−i-111-1−ii
χ5611-1-11-11-1-11−i−iiiii−i−i-11i−i1-1−i−iiii−i-1-111i−i-111-1−ii-1-111-11-111-1ii−i−i−i−iii1-1−ii-11ii−i−i−ii11-1-1−ii1-1-11i−i
χ5711-1-11-11-1-11−i−iii−i−iii1-1−ii1-1−i−iii−ii11-1-1−ii1-11-1−ii-1-111-11-111-1ii−i−iii−i−i-11i−i-11ii−i−ii−i-1-111i−i-11-11i−i
χ5811-1-11-11-1-11−i−iii−i−iii-11i−i1-1−i−iii−ii11-1-1i−i-11-11i−i-1-111-11-111-1ii−i−iii−i−i1-1−ii-11ii−i−ii−i-1-111−ii1-11-1−ii
χ5922222-2-2222000022220000-2-20000-2-2000000000000-2-2-2-2-222-2-2-20000-2-2-2-2000022000022000000000000
χ6022222-2-22220000-2-2-2-20000-2-2000022000000000000-2-2-2-2-222-2-2-2000022220000220000-2-2000000000000
χ612222-122-1-1-1222200002222-1-1-1-1-1-1000000-1-1-1-10000-2-2-2-21-2-2111-2-2-2-20000-2-2-2-211111100000011110000
χ622222-122-1-1-122220000-2-2-2-2-1-1-1-1-1-100000011110000-2-2-2-21-2-2111-2-2-2-200002222111111000000-1-1-1-10000
χ632222-122-1-1-1-2-2-2-2000022-2-2-1-1111100000011-1-10000-2-2-2-21-2-211122220000-2-22211-1-1-1-1000000-1-1110000
χ642222-122-1-1-1-2-2-2-20000-2-222-1-11111000000-1-1110000-2-2-2-21-2-21112222000022-2-211-1-1-1-100000011-1-10000
χ6522-2-222-2-2-2200002i2i−2i−2i0000-220000−2i2i000000000000-2-222-2-2222-20000−2i−2i2i2i00002-200002i−2i000000000000
χ6622-2-222-2-2-220000−2i−2i2i2i0000-2200002i−2i000000000000-2-222-2-2222-200002i2i−2i−2i00002-20000−2i2i000000000000
χ6722-2-2-1-2211-12i2i−2i−2i00002-22i−2i-11−i−iii000000−ii-110000-2-22212-2-1-11−2i−2i2i2i0000-22−2i2i1-1ii−i−i000000i−i1-10000
χ6822-2-2-1-2211-12i2i−2i−2i0000-22−2i2i-11−i−iii000000i−i1-10000-2-22212-2-1-11−2i−2i2i2i00002-22i−2i1-1ii−i−i000000−ii-110000
χ6922-2-2-1-2211-1−2i−2i2i2i00002-2−2i2i-11ii−i−i000000i−i-110000-2-22212-2-1-112i2i−2i−2i0000-222i−2i1-1−i−iii000000−ii1-10000
χ7022-2-2-1-2211-1−2i−2i2i2i0000-222i−2i-11ii−i−i000000−ii1-10000-2-22212-2-1-112i2i−2i−2i00002-2−2i2i1-1−i−iii000000i−i-110000
χ712-22-2200-22-2i2−i2i2−i22-22-2000000i2−i2i2−i200i2−i2i2−i200000000-22-22-2002-22−i2i2−i2i2-22-22000000−i2i2−i2i200−i2i2−i2i200000000
χ722-22-2200-22-2i2−i2i2−i2-22-22000000i2−i2i2−i200−i2i2−i2i200000000-22-22-2002-22−i2i2−i2i22-22-2000000−i2i2−i2i200i2−i2i2−i200000000
χ732-22-2200-22-2−i2i2−i2i22-22-2000000−i2i2−i2i200−i2i2−i2i200000000-22-22-2002-22i2−i2i2−i2-22-22000000i2−i2i2−i200i2−i2i2−i200000000
χ742-22-2200-22-2−i2i2−i2i2-22-22000000−i2i2−i2i200i2−i2i2−i200000000-22-22-2002-22i2−i2i2−i22-22-2000000i2−i2i2−i200−i2i2−i2i200000000
χ752-2-222002-2-22−2−222i−2i−2i2i0000002−2−2200−i2i2i2−i200000000-222-2-200-222−222−2−2i2i2i−2i000000−222−200i2−i2−i2i200000000
χ762-2-222002-2-22−2−22−2i2i2i−2i0000002−2−2200i2−i2−i2i200000000-222-2-200-222−222−22i−2i−2i2i000000−222−200−i2i2i2−i200000000
χ772-2-222002-2-2−222−22i−2i−2i2i000000−222−200i2−i2−i2i200000000-222-2-200-2222−2−22−2i2i2i−2i0000002−2−2200−i2i2i2−i200000000
χ782-2-222002-2-2−222−2−2i2i2i−2i000000−222−200−i2i2i2−i200000000-222-2-200-2222−2−222i−2i−2i2i0000002−2−2200i2−i2−i2i200000000
χ794444-2-4-4-2-2-200000000000022000000000000000000-4-4-4-4244222000000000000-2-2000000000000000000
χ8044-4-4-24-422-20000000000002-2000000000000000000-4-4442-44-2-22000000000000-22000000000000000000
χ814-44-4-2002-222i2−2i22i2−2i20000000000−i2i2−i2i200000000000000-44-44200-22-2−2i22i2−2i22i20000000000i2−i2i2−i200000000000000
χ824-44-4-2002-22−2i22i2−2i22i20000000000i2−i2i2−i200000000000000-44-44200-22-22i2−2i22i2−2i20000000000−i2i2−i2i200000000000000
χ834-4-44-200-22222−22−22220000000000−222−200000000000000-444-42002-2-2−222222−2200000000002−2−2200000000000000
χ844-4-44-200-222−222222−2200000000002−2−2200000000000000-444-42002-2-222−22−22220000000000−222−200000000000000

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