Finite Group Databasebeta

← Group #72270608

Character table — Group #72270608

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222224444444466668888888888888888881616161616161616161616161616161616162424242424242424242424242424243232323232323232324848969696
order12222236662222446622222244444444446666121224666612121212121212121212121222224444444444444812121212242444448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-11111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11-1-1-1-11111-1-11
χ4111111111111111111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-111-1-1-1-111-11111-1-1-1-111-1
χ51111111111111111111111-1-111-1-1-1-111-1-111111111-1-11111-1-111-1-111-1-111-1-1111-1-1-1-111-1-11-1-111-1-1-1-1111-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1111-1-1-1-111-1-1-111-1-11111-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-11-1-111-1-1-1-111-11-1-1-111-1-111-11-1
χ81111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-1-111-1-1-1-1111-1111-1-111-1-11-11
χ9111111111111111111-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ10111111111111111111-1-1-1-1111111111111111111-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1-1-1-111-1-111-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1111111-11111-1-111-1-11
χ13111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-11111-1-111-1-111-1-1-1-111-1-1-11111-1-1111-1-111-1-1-1-1-1-1-111
χ14111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-11111-1-111-111-1-11111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-111-111-1-11111-1-1-11-1-1-111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-111-1-11111-1-11-1111-1-11111-11-1
χ1722222222222-22-2-2-22222220000220000-2-22-22-2-2-20000000022000000-2-22-200-200220000-2-200000000000000
χ1822222222222-22-2-2-22222220000-2-20000222-22-2-2-200000000-2-2000000222-200-200-2-200002200000000000000
χ1922222222222-22-2-2-222-2-2-2-20000220000-2-22-22-2-2-20000000022000000-2-2-2200200-2-200002200000000000000
χ2022222222222-22-2-2-222-2-2-2-20000-2-20000222-22-2-2-200000000-2-200000022-2200200220000-2-200000000000000
χ212222222222-22-22-2-222222200220000-2-200-22-22-2-200000022000000-2-200-2200-2220000-2-20000000000000000
χ222222222222-22-22-2-222222200-2-200002200-22-22-2-2000000-2-20000002200-2200-2-2-20000220000000000000000
χ232222222222-22-22-2-222-2-2-2-200220000-2-200-22-22-2-200000022000000-2-2002-2002-2-20000220000000000000000
χ242222222222-22-22-2-222-2-2-2-200-2-200002200-22-22-2-2000000-2-200000022002-2002220000-2-20000000000000000
χ252222222222-2-2-2-222222222220000-2-20000-2-2-2-222002200000000-2-20000-2-22220000-2-2000000000000000000
χ262222222222-2-2-2-222222222-2-20000220000-2-2-2-22200-2-200000000220000-2-2-2-22000022000000000000000000
χ272222222222-2-2-2-22222-2-2-2-2220000-2-20000-2-2-2-222002200000000-2-2000022-2-2-2000022000000000000000000
χ282222222222-2-2-2-22222-2-2-2-2-2-20000220000-2-2-2-22200-2-2000000002200002222-20000-2-2000000000000000000
χ29222222-1-1-1-1222222-1-10000222222222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000222-1-1-1-1-1-100000
χ30222222-1-1-1-1222222-1-10000222222222222-1-1-1-1-1-1-2-2-1-111-1-1-1-111-1-1-1-1-1-1000000000000000-2-2-211111100000
χ31222222-1-1-1-1222222-1-1000022-2-2-2-222-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-1-1-1-11111000000000000000-2-221111-1-100000
χ32222222-1-1-1-1222222-1-1000022-2-2-2-222-2-2-2-2-1-1-1-1-1-1-2-2-1-111111111-1-1111100000000000000022-2-1-1-1-11100000
χ33222222-1-1-1-1222222-1-10000-2-222-2-2-2-222-2-2-1-1-1-1-1-12211-1-1-1-111-1-111-1-1110000000000000002-2-2-1-1111100000
χ34222222-1-1-1-1222222-1-10000-2-222-2-2-2-222-2-2-1-1-1-1-1-1-2-21111-1-1111111-1-111000000000000000-22211-1-1-1-100000
χ35222222-1-1-1-1222222-1-10000-2-2-2-222-2-2-2-222-1-1-1-1-1-12211-1-111-1-1-1-11111-1-1000000000000000-22-211-1-11100000
χ36222222-1-1-1-1222222-1-10000-2-2-2-222-2-2-2-222-1-1-1-1-1-1-2-2111111-1-1111111-1-10000000000000002-22-1-111-1-100000
χ3722-2-22-22-2-2222-2-22-22-200002-200002-20000-2-222-22002-2000000002-20000000002i−2i2i−2i002i−2i2i−2i00000000000000
χ3822-2-22-22-2-2222-2-22-22-200002-200002-20000-2-222-22002-2000000002-2000000000−2i2i−2i2i00−2i2i−2i2i00000000000000
χ3922-2-22-22-2-2222-2-22-22-20000-220000-220000-2-222-2200-2200000000-220000000002i−2i−2i2i002i−2i−2i2i00000000000000
χ4022-2-22-22-2-2222-2-22-22-20000-220000-220000-2-222-2200-2200000000-22000000000−2i2i2i−2i00−2i2i2i−2i00000000000000
χ4122-2-22-22-2-222-2-22-222-20000002i−2i00002i−2i00-222-22-20000002i−2i0000002i−2i00002-20002i−2i2-200−2i2i00000000000000
χ4222-2-22-22-2-222-2-22-222-20000002i−2i00002i−2i00-222-22-20000002i−2i0000002i−2i0000-22000−2i2i-22002i−2i00000000000000
χ4322-2-22-22-2-222-2-22-222-2000000−2i2i0000−2i2i00-222-22-2000000−2i2i000000−2i2i00002-2000−2i2i2-2002i−2i00000000000000
χ4422-2-22-22-2-222-2-22-222-2000000−2i2i0000−2i2i00-222-22-2000000−2i2i000000−2i2i0000-220002i−2i-2200−2i2i00000000000000
χ4522-2-22-22-2-22-222-2-222-2000000002i−2i00002i−2i2-2-222-2000000002i−2i0000002i−2i002-202i−2i00-22−2i2i0000000000000000
χ4622-2-22-22-2-22-222-2-222-2000000002i−2i00002i−2i2-2-222-2000000002i−2i0000002i−2i00-220−2i2i002-22i−2i0000000000000000
χ4722-2-22-22-2-22-222-2-222-200000000−2i2i0000−2i2i2-2-222-200000000−2i2i000000−2i2i002-20−2i2i00-222i−2i0000000000000000
χ4822-2-22-22-2-22-222-2-222-200000000−2i2i0000−2i2i2-2-222-200000000−2i2i000000−2i2i00-2202i−2i002-2−2i2i0000000000000000
χ4922-2-22-22-2-22-2-2222-22-200002-22i−2i2i−2i-22−2i2i−2i2i22-2-2-22002-2002i−2i2i−2i00-22−2i2i−2i2i00000000000000000000000000000
χ5022-2-22-22-2-22-2-2222-22-200002-2−2i2i−2i2i-222i−2i2i−2i22-2-2-22002-200−2i2i−2i2i00-222i−2i2i−2i00000000000000000000000000000
χ5122-2-22-22-2-22-2-2222-22-20000-222i−2i−2i2i2-2−2i2i2i−2i22-2-2-2200-22002i−2i−2i2i002-2−2i2i2i−2i00000000000000000000000000000
χ5222-2-22-22-2-22-2-2222-22-20000-22−2i2i2i−2i2-22i−2i−2i2i22-2-2-2200-2200−2i2i2i−2i002-22i−2i−2i2i00000000000000000000000000000
χ5322-2-22-2-111-1-2-2222-2-1100002-22i−2i2i−2i-22−2i2i−2i2i-1-1111-100-11−i3i3−ii−ii−i3i31-1i−ii−i0000000000000000003−33−3−i3i300000
χ5422-2-22-2-111-1-2-2222-2-1100002-22i−2i2i−2i-22−2i2i−2i2i-1-1111-100-11i3−i3−ii−iii3−i31-1i−ii−i000000000000000000−33−33i3−i300000
χ5522-2-22-2-111-1-2-2222-2-1100002-2−2i2i−2i2i-222i−2i2i−2i-1-1111-100-11−i3i3i−ii−i−i3i31-1−ii−ii000000000000000000−33−33−i3i300000
χ5622-2-22-2-111-1-2-2222-2-1100002-2−2i2i−2i2i-222i−2i2i−2i-1-1111-100-11i3−i3i−ii−ii3−i31-1−ii−ii0000000000000000003−33−3i3−i300000
χ5722-2-22-2-111-1-2-2222-2-110000-222i−2i−2i2i2-2−2i2i2i−2i-1-1111-1001-1−i3i3−iii−i−i3i3-11i−i−ii0000000000000000003−3−33i3−i300000
χ5822-2-22-2-111-1-2-2222-2-110000-222i−2i−2i2i2-2−2i2i2i−2i-1-1111-1001-1i3−i3−iii−ii3−i3-11i−i−ii000000000000000000−333−3−i3i300000
χ5922-2-22-2-111-1-2-2222-2-110000-22−2i2i2i−2i2-22i−2i−2i2i-1-1111-1001-1−i3i3i−i−ii−i3i3-11−iii−i000000000000000000−333−3i3−i300000
χ6022-2-22-2-111-1-2-2222-2-110000-22−2i2i2i−2i2-22i−2i−2i2i-1-1111-1001-1i3−i3i−i−iii3−i3-11−iii−i0000000000000000003−3−33−i3i300000
χ61444444-2-2-2-24-44-4-4-4-2-200000000440000-4-4-22-222200000000-2-20000002200000000000000000000000000000
χ62444444-2-2-2-24-44-4-4-4-2-200000000-4-4000044-22-22220000000022000000-2-200000000000000000000000000000
χ63444444-2-2-2-2-44-44-4-4-2-2000000440000-4-4002-22-222000000-2-2000000220000000000000000000000000000000
χ64444444-2-2-2-2-44-44-4-4-2-2000000-4-4000044002-22-22200000022000000-2-20000000000000000000000000000000
χ65444444-2-2-2-2-4-4-4-444-2-20000440000-4-400002222-2-200-2-20000000022000000000000000000000000000000000
χ66444444-2-2-2-2-4-4-4-444-2-20000-4-400004400002222-2-2002200000000-2-2000000000000000000000000000000000
χ674444-4-44444000000-4-444-4-40000000000000000002-200220000-2-20000000000000000000000000000002-2000
χ684444-4-44444000000-4-444-4-4000000000000000000-2200-2-2000022000000000000000000000000000000-22000
χ694444-4-44444000000-4-4-4-4440000000000000000002-200220000-2-2000000000000000000000000000000-22000
χ704444-4-44444000000-4-4-4-444000000000000000000-2200-2-20000220000000000000000000000000000002-2000
χ7144-4-44-4-222-244-4-44-4-2200004-400004-4000022-2-22-200-2200000000-22000000000000000000000000000000000
χ7244-4-44-4-222-244-4-44-4-220000-440000-44000022-2-22-2002-2000000002-2000000000000000000000000000000000
χ7344-4-44-4-222-24-4-44-44-220000004i−4i00004i−4i002-2-22-22000000−2i2i000000−2i2i0000000000000000000000000000000
χ7444-4-44-4-222-24-4-44-44-22000000−4i4i0000−4i4i002-2-22-220000002i−2i0000002i−2i0000000000000000000000000000000
χ7544-4-44-4-222-2-444-4-44-22000000004i−4i00004i−4i-222-2-2200000000−2i2i000000−2i2i00000000000000000000000000000
χ7644-4-44-4-222-2-444-4-44-2200000000−4i4i0000−4i4i-222-2-22000000002i−2i0000002i−2i00000000000000000000000000000
χ778888-8-8-4-4-4-40000004400000000000000000000004-400-2-200002200000000000000000000000000000000000
χ788888-8-8-4-4-4-4000000440000000000000000000000-4400220000-2-200000000000000000000000000000000000
χ7988-8-8-888-8-88000000-88000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-8-88-444-40000004-400000000000000000000000000−2i32i300002i3−2i300000000000000000000000000000000000
χ8188-8-8-88-444-40000004-4000000000000000000000000002i3−2i30000−2i32i300000000000000000000000000000000000
χ828-88-80088-8-800000000008-800000000000000000000000000000000000000000000000000000000000000000
χ838-88-80088-8-80000000000-8800000000000000000000000000000000000000000000000000000000000000000
χ848-8-88008-88-8000000008-80000000000000000000000000000000000000000000000000000000000000000000
χ858-8-88008-88-800000000-880000000000000000000000000000000000000000000000000000000000000000000
χ8616-1616-1600-8-88800000000000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16-161600-88-8800000000000000000000000000000000000000000000000000000000000000000000000000000

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