Finite Group Databasebeta

← Group #11781504

Character table — Group #11781504

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222244444444444444444444888888121212121212121212121212121212121212121212121212181836363648484848484872727272
order122244888833666666121212122424242424242424121224242424444488881212121212121212242424242424242444488246612128888
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
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-111-1-111-1-1
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-1-111-1-111
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11-111-1-1-1-111
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-11-1-11111-1-1
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−2i22-222-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000000−i2i22−2
χ1622-2-2-222i2i−2i−2i22-222-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i2-22i2i−2i−2i00000000000000000000000000000000000i2−i2−22
χ1722-2-2-22−2i−2i2i2i22-222-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000000−i2i2−22
χ1822-2-2-22−2i−2i2i2i22-222-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2-2−2i−2i2i2i00000000000000000000000000000000000i2−i22−2
χ192-2-22002−22−222-2-2-22-22000022−2−222−2−2002−22−2002-22−22−2000022-2-222−2−222−2−2-2202−20000000000
χ202-2-22002−22−222-2-2-22-22000022−2−222−2−2002−22−200-22−22−220000-2-222−2−222−2−222-2202−20000000000
χ212-2-22002−22−222-2-2-22-22000022−2−222−2−2002−22−22i−2i00−i2i2i2−i22i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i22-20−220000000000
χ222-2-22002−22−222-2-2-22-22000022−2−222−2−2002−22−2−2i2i00i2−i2−i2i2−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i22-20−220000000000
χ232-2-2200−22−2222-2-2-22-220000−2−222−2−22200−22−22002-2−22−22000022-2-2−2−222−2−222-220−220000000000
χ242-2-2200−22−2222-2-2-22-220000−2−222−2−22200−22−2200-222−22−20000-2-22222−2−222−2−2-220−220000000000
χ252-2-2200−22−2222-2-2-22-220000−2−222−2−22200−22−222i−2i00i2−i2−i2i22i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i22-202−20000000000
χ262-2-2200−22−2222-2-2-22-220000−2−222−2−22200−22−22−2i2i00−i2i2i2−i2−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i22-202−20000000000
χ2744444444441-2-21-211-2111111111111-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ2844444444441-2-21-211-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111111111000000000000000
χ294444444444-211-21-2-21-2-2-2-2-2-2-2-2-2-2-2-21111110000000000000000000000000000022-1-1-1-10000
χ304444444444-211-21-2-21-2-2-2-2-2-2-2-2-2-2-2-211111100000000000000000000000000000-2-211110000
χ31444444-4-4-4-41-2-21-211-21111-1-1-1-1-1-1-1-1-2-222222222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000
χ32444444-4-4-4-41-2-21-211-21111-1-1-1-1-1-1-1-1-2-22222-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000
χ33444444-4-4-4-4-211-21-2-21-2-2-2-22222222211-1-1-1-1000000000000000000000000000002-2-1-1110000
χ34444444-4-4-4-4-211-21-2-21-2-2-2-22222222211-1-1-1-100000000000000000000000000000-2211-1-10000
χ354444-4-400001-2-21-211-2-1-1-1-13i−3i3i−3i3i−3i3i−3i22000022-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000
χ364444-4-400001-2-21-211-2-1-1-1-13i−3i3i−3i3i−3i3i−3i220000-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000
χ374444-4-400001-2-21-211-2-1-1-1-1−3i3i−3i3i−3i3i−3i3i22000022-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000
χ384444-4-400001-2-21-211-2-1-1-1-1−3i3i−3i3i−3i3i−3i3i220000-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000
χ3944-4-44-400001-221-2-1-1211-1-13-33-3-33-332-20000000000003−33−33−33−33−33−33−33−3000000000000000
χ4044-4-44-400001-221-2-1-1211-1-13-33-3-33-332-2000000000000−33−33−33−33−33−33−33−33000000000000000
χ4144-4-44-400001-221-2-1-1211-1-1-33-333-33-32-20000000000003−33−33−33−3−33−33−33−33000000000000000
χ4244-4-44-400001-221-2-1-1211-1-1-33-333-33-32-2000000000000−33−33−33−333−33−33−33−3000000000000000
χ4344-4-44-4000044-444-4-4-444-4-400000000-440000000000000000000000000000000000000000000
χ4444-4-4-444i4i−4i−4i1-221-2-1-12-1-111iiii−i−i−i−i-22−2i−2i2i2i000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i3000000000000000
χ4544-4-4-444i4i−4i−4i1-221-2-1-12-1-111iiii−i−i−i−i-22−2i−2i2i2i00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i3000000000000000
χ4644-4-4-444i4i−4i−4i-21-1-2122-122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i0000000000000000000000000000000−i3i33−30000
χ4744-4-4-444i4i−4i−4i-21-1-2122-122-2-2−2i−2i−2i−2i2i2i2i2i1-1ii−i−i0000000000000000000000000000000i3−i3−330000
χ4844-4-4-44−4i−4i4i4i1-221-2-1-12-1-111−i−i−i−iiiii-222i2i−2i−2i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i3000000000000000
χ4944-4-4-44−4i−4i4i4i1-221-2-1-12-1-111−i−i−i−iiiii-222i2i−2i−2i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i3000000000000000
χ5044-4-4-44−4i−4i4i4i-21-1-2122-122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii0000000000000000000000000000000−i3i3−330000
χ5144-4-4-44−4i−4i4i4i-21-1-2122-122-2-22i2i2i2i−2i−2i−2i−2i1-1−i−iii0000000000000000000000000000000i3−i33−30000
χ524-44-400−2i22i22i2−2i21-2-2-12-1123i−3i3i−3i−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−i3i3i3−i33−3−33ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ534-44-400−2i22i22i2−2i21-2-2-12-1123i−3i3i−3i−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−i2i200000000i3−i3−i3i3−333−3−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ544-44-400−2i22i22i2−2i21-2-2-12-112−3i3i−3i3iζ5−2ζ7+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−i3i3i3−i3−333−3−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ554-44-400−2i22i22i2−2i21-2-2-12-112−3i3i−3i3iζ5−2ζ7+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−i2i200000000i3−i3−i3i33−3−33ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ564-44-400−2i22i22i2−2i2444-4-4-44-40000−2i2−2i22i22i22i22i2−2i2−2i200−2i22i22i2−2i2000000000000000000000000000000000000000
χ574-44-4002i2−2i2−2i22i21-2-2-12-1123i−3i3i−3i2ζ5−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−i3i3i3−i33−3−33−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000
χ584-44-4002i2−2i2−2i22i21-2-2-12-1123i−3i3i−3i2ζ5−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−i200000000i3−i3−i3i3−333−3ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000
χ594-44-4002i2−2i2−2i22i21-2-2-12-112−3i3i−3i3i−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−i3i3i3−i3−333−3ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000
χ604-44-4002i2−2i2−2i22i21-2-2-12-112−3i3i−3i3i−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−i200000000i3−i3−i3i33−3−33−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000
χ614-44-4002i2−2i2−2i22i2444-4-4-44-400002i22i2−2i2−2i2−2i2−2i22i22i2002i2−2i2−2i22i2000000000000000000000000000000000000000
χ624-4-440022−2222−221-22-121-1-23i−3i−3i3i−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−ζ13−2ζ2300−22−222i−2i-22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−i−iii11-1-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000
χ634-4-440022−2222−221-22-121-1-23i−3i−3i3i−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−ζ13−2ζ2300−22−22−2i2i2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ii−i−i-1-111−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000
χ644-4-440022−2222−221-22-121-1-2−3i3i3i−3iζ5+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+ζ2300−22−222i−2i2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−i−iii-1-111ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000
χ654-4-440022−2222−221-22-121-1-2−3i3i3i−3iζ5+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+ζ2300−22−22−2i2i-222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23ii−i−i11-1-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000
χ664-4-4400−2222−22221-22-121-1-23i−3i−3i3i2ζ5+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+2ζ23002−22−22i−2i-222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−i−iii11-1-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000000
χ674-4-4400−2222−22221-22-121-1-23i−3i−3i3i2ζ5+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+2ζ23002−22−2−2i2i2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ii−i−i-1-111ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13000000000000000
χ684-4-4400−2222−22221-22-121-1-2−3i3i3i−3i−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−ζ23002−22−22i−2i2-22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−i−iii-1-111−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23000000000000000
χ694-4-4400−2222−22221-22-121-1-2−3i3i3i−3i−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−ζ23002−22−2−2i2i-22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23ii−i−i11-1-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23000000000000000
χ708888-8-80000-422-42-4-42444400000000-2-20000000000000000000000000000000000000000000
χ7188-8-88-80000-42-2-4244-2-4-44400000000-220000000000000000000000000000000000000000000
χ728-88-800−4i24i24i2−4i2-4224-24-4-200002i22i2−2i2−2i2−2i2−2i22i22i200−i2i2i2−i2000000000000000000000000000000000000000
χ738-88-8004i2−4i2−4i24i2-4224-24-4-20000−2i2−2i22i22i22i22i2−2i2−2i200i2−i2−i2i2000000000000000000000000000000000000000
χ748-8-880042−4242−42-42-24-2-4420000−22−222222−22−222222002−22−2000000000000000000000000000000000000000
χ758-8-8800−4242−4242-42-24-2-44200002222−22−222222−22−2200−22−22000000000000000000000000000000000000000

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