Finite Group Databasebeta

← Group #11781596

Character table — Group #11781596

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181836363648484848484872727272
order12224488883366666612121212242424242424242412122424242444448888121212121212121224242424242424244448844121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1-11111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1111-1-1-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11-1-1-111-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1111-1-111-1-1
χ9222222222222222222222222222222222222000000000000000000000000-2-2-2-2-20000000000
χ10222222-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000-2-2-2220000000000
χ112222-2-2000022222222-2-2-2-200000000-2-2000000002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-2-22000000000000
χ122222-2-2000022222222-2-2-2-200000000-2-200000000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-2-22000000000000
χ132222-2-2000022222222-2-2-2-200000000-2-2000022-2-200002222-2-2-2-20000000022-2000000000000
χ142222-2-2000022222222-2-2-2-200000000-2-20000-2-2220000-2-2-2-222220000000022-2000000000000
χ1522-2-2-222i2i−2i−2i22-22-2-2-22-2-2222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000000−i2i22−2
χ1622-2-2-222i2i−2i−2i22-22-2-2-22-2-2222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000000i2−i2−22
χ1722-2-2-22−2i−2i2i2i22-22-2-2-22-2-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000000−i2i2−22
χ1822-2-2-22−2i−2i2i2i22-22-2-2-22-2-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000000i2−i22−2
χ192-22-2002−22−2222-22-2-2-2000022−2−222−2−2002−22−2002i−2i−i2i2−i2i200002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2-2202−20000000000
χ202-22-2002−22−2222-22-2-2-2000022−2−222−2−2002−22−200−2i2ii2−i2i2−i20000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2-2202−20000000000
χ212-22-2002−22−2222-22-2-2-2000022−2−222−2−2002−22−22-2002−2−2222-2-2000022−2−2−2−2222-20−220000000000
χ222-22-2002−22−2222-22-2-2-2000022−2−222−2−2002−22−2-2200−222−2-2-2220000−2−22222−2−22-20−220000000000
χ232-22-200−22−22222-22-2-2-20000−2−222−2−22200−22−22002i−2ii2−i2i2−i200002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2-220−220000000000
χ242-22-200−22−22222-22-2-2-20000−2−222−2−22200−22−2200−2i2i−i2i2−i2i20000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2-220−220000000000
χ252-22-200−22−22222-22-2-2-20000−2−222−2−22200−22−222-200−222−222-2-20000−2−22222−2−22-202−20000000000
χ262-22-200−22−22222-22-2-2-20000−2−222−2−22200−22−22-22002−2−22-2-222000022−2−2−2−2222-202−20000000000
χ2744444444441-21-2-2-211-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000022-1-1-1-10000
χ2844444444441-21-2-2-211-2-2-2-2-2-2-2-2-2-2-2-211111100000000000000000000000000000-2-211110000
χ294444444444-21-2111-2-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ304444444444-21-2111-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000
χ31444444-4-4-4-41-21-2-2-211-2-2-2-22222222211-1-1-1-1000000000000000000000000000002-211-1-10000
χ32444444-4-4-4-41-21-2-2-211-2-2-2-22222222211-1-1-1-100000000000000000000000000000-22-1-1110000
χ33444444-4-4-4-4-21-2111-2-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000
χ34444444-4-4-4-4-21-2111-2-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000
χ354444-4-40000-21-2111-2-2-1-1-1-13i−3i3i−3i3i−3i3i−3i22000022-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000
χ364444-4-40000-21-2111-2-2-1-1-1-13i−3i3i−3i3i−3i3i−3i220000-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000
χ374444-4-40000-21-2111-2-2-1-1-1-1−3i3i−3i3i−3i3i−3i3i22000022-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000
χ384444-4-40000-21-2111-2-2-1-1-1-1−3i3i−3i3i−3i3i−3i3i220000-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000
χ3944-4-44-4000044-44-4-4-4444-4-400000000-440000000000000000000000000000000000000000000
χ4044-4-44-40000-2121-1-12-211-1-13-33-3-33-332-20000000000003−33−33−33−33−33−33−33−3000000000000000
χ4144-4-44-40000-2121-1-12-211-1-13-33-3-33-332-2000000000000−33−33−33−33−33−33−33−33000000000000000
χ4244-4-44-40000-2121-1-12-211-1-1-33-333-33-32-20000000000003−33−33−33−3−33−33−33−33000000000000000
χ4344-4-44-40000-2121-1-12-211-1-1-33-333-33-32-2000000000000−33−33−33−333−33−33−33−3000000000000000
χ4444-4-4-444i4i−4i−4i1-2-1-222-1122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i00000000000000000000000000000003−3−i3i30000
χ4544-4-4-444i4i−4i−4i1-2-1-222-1122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i0000000000000000000000000000000−33i3−i30000
χ4644-4-4-444i4i−4i−4i-2121-1-12-2-1-111iiii−i−i−i−i-22−2i−2i2i2i000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i3000000000000000
χ4744-4-4-444i4i−4i−4i-2121-1-12-2-1-111iiii−i−i−i−i-22−2i−2i2i2i00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i3000000000000000
χ4844-4-4-44−4i−4i4i4i1-2-1-222-1122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii00000000000000000000000000000003−3i3−i30000
χ4944-4-4-44−4i−4i4i4i1-2-1-222-1122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii0000000000000000000000000000000−33−i3i30000
χ5044-4-4-44−4i−4i4i4i-2121-1-12-2-1-111−i−i−i−iiiii-222i2i−2i−2i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i3000000000000000
χ5144-4-4-44−4i−4i4i4i-2121-1-12-2-1-111−i−i−i−iiiii-222i2i−2i−2i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i3000000000000000
χ524-44-40022−2222−22-21-2-11-1223i−3i3i−3i−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300−22−222-22i−2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23-1-111−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000
χ534-44-40022−2222−22-21-2-11-1223i−3i3i−3i−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300−22−22-22−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ2311-1-1ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000
χ544-44-40022−2222−22-21-2-11-122−3i3i−3i3iζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2300−22−222-2−2i2i2ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13-1-111ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000
χ554-44-40022−2222−22-21-2-11-122−3i3i−3i3iζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2300−22−22-222i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ1311-1-1−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000
χ564-44-400−2222−2222-21-2-11-1223i−3i3i−3i2ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23002−22−22-22i−2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23-1-111−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000
χ574-44-400−2222−2222-21-2-11-1223i−3i3i−3i2ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23002−22−2-22−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ2311-1-1ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000
χ584-44-400−2222−2222-21-2-11-122−3i3i−3i3i−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23002−22−22-2−2i2i−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13-1-111ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000
χ594-44-400−2222−2222-21-2-11-122−3i3i−3i3i−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23002−22−2-222i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ1311-1-1−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000
χ604-4-4400−2i22i22i2−2i244-4-4-444-40000−2i2−2i22i22i22i22i2−2i2−2i200−2i22i22i2−2i2000000000000000000000000000000000000000
χ614-4-4400−2i22i22i2−2i2-212-1-11-223i−3i−3i3i−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300i2−i2−i2i2000000003−3−33i3−i3−i3i3−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ624-4-4400−2i22i22i2−2i2-212-1-11-223i−3i−3i3i−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300i2−i2−i2i200000000−333−3−i3i3i3−i3ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ634-4-4400−2i22i22i2−2i2-212-1-11-22−3i3i3i−3iζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ2300i2−i2−i2i2000000003−3−33−i3i3i3−i3−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ644-4-4400−2i22i22i2−2i2-212-1-11-22−3i3i3i−3iζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ2300i2−i2−i2i200000000−333−3i3−i3−i3i3ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ654-4-44002i2−2i2−2i22i244-4-4-444-400002i22i2−2i2−2i2−2i2−2i22i22i2002i2−2i2−2i22i2000000000000000000000000000000000000000
χ664-4-44002i2−2i2−2i22i2-212-1-11-223i−3i−3i3i2ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300−i2i2i2−i2000000003−3−33i3−i3−i3i3ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ674-4-44002i2−2i2−2i22i2-212-1-11-223i−3i−3i3i2ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300−i2i2i2−i200000000−333−3−i3i3i3−i3−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ684-4-44002i2−2i2−2i22i2-212-1-11-22−3i3i3i−3i−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ2300−i2i2i2−i2000000003−3−33−i3i3i3−i3ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ694-4-44002i2−2i2−2i22i2-212-1-11-22−3i3i3i−3i−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ2300−i2i2i2−i200000000−333−3i3−i3−i3i3−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ708888-8-800002-42-4-4-422444400000000-2-20000000000000000000000000000000000000000000
χ7188-8-88-800002-4-2-444-22-4-44400000000-220000000000000000000000000000000000000000000
χ728-88-80042−4242−422-424-44-2-20000−22−222222−22−222222002−22−2000000000000000000000000000000000000000
χ738-88-800−4242−42422-424-44-2-200002222−22−222222−22−2200−22−22000000000000000000000000000000000000000
χ748-8-8800−4i24i24i2−4i22-4-244-42-200002i22i2−2i2−2i2−2i2−2i22i22i200−i2i2i2−i2000000000000000000000000000000000000000
χ758-8-88004i2−4i2−4i24i22-4-244-42-20000−2i2−2i22i22i22i22i2−2i2−2i200i2−i2−i2i2000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.