Finite Group Databasebeta

← Group #72271440

Character table — Group #72271440

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size11111111222288888888121212121212242424484848484848484848486464646464646464646464646464646496969696969696969696128128128128128128128128128128128128128128128128128128128128128128128128192192
order122222222222222244444444444444444444444336666666666666622444488886666666666666666121212121212121288
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i321111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211
χ3111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i321111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211
χ4111111111111-1-1-1-1-1-1-1-1111111111-1-111-1-111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111-1-1-1-1-1-1-1-1111111111-1-111-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32111111-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1
χ6111111111111-1-1-1-1-1-1-1-1111111111-1-111-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32111111-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1
χ733333333333333333333333333333333333-1-1-1-10000000000000000-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1
χ8333333333333333333333-1-1333-1-1-1-1-1-1-1-1-133-1-10000000000000000-1-13-1-1-133-1-1000000000000000000000000-1-1
χ9333333333333333333333-1-1333-1-1-1-1-1-1-1-1-1-1-1330000000000000000-1-1-13-1-1-1-133000000000000000000000000-1-1
χ10333333333333333333333-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000003-1-1-13-1-1-1-1-10000000000000000000000003-1
χ11333333333333333333333-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-13-1-1-13-1-1-1-1000000000000000000000000-13
χ12333333333333-3-3-3-3-3-3-3-3333333333-3-333-3-3-1-1-1-10000000000000000-1-1-1-1-1-1111100000000000000000000000011
χ13333333333333-3-3-3-3-3-3-3-33-1-1333-1-1-111-1-11133-1-10000000000000000-1-13-1-1-1-3-31100000000000000000000000011
χ14333333333333-3-3-3-3-3-3-3-33-1-1333-1-1-111-1-111-1-1330000000000000000-1-1-13-1-111-3-300000000000000000000000011
χ15333333333333-3-3-3-3-3-3-3-33-1-1333-1-1-111-1-111-1-1-1-100000000000000003-1-1-13-11111000000000000000000000000-31
χ16333333333333-3-3-3-3-3-3-3-33-1-1333-1-1-111-1-111-1-1-1-10000000000000000-13-1-1-1311110000000000000000000000001-3
χ1744444444-4-4-4-42222-2-2-2-2044000-4002200-2-2000011111111111111110000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111100
χ1844444444-4-4-4-42222-2-2-2-2044000-4002200-2-20000−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3200000000001+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200
χ1944444444-4-4-4-42222-2-2-2-2044000-4002200-2-20000−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3200000000001−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200
χ2044444444-4-4-4-4-2-2-2-22222044000-400-2-20022000011111111111111110000000000-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-100
χ2144444444-4-4-4-4-2-2-2-22222044000-400-2-200220000−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i3200000000001+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3200
χ2244444444-4-4-4-4-2-2-2-22222044000-400-2-200220000−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i3200000000001−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3200
χ2344-444-4-4-4-44-4444-4-444-4-4-4004-4400000000000001111-1-1-1-111-1-1-1-111000000000011-1-111-1-111-1-111-1-111-1-111-1-100
χ2444-444-4-4-4-44-4444-4-444-4-4-4004-440000000000000−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i320000000000−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200
χ2544-444-4-4-4-44-4444-4-444-4-4-4004-440000000000000−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i320000000000−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200
χ2644-444-4-4-4-44-44-4-444-4-444-4004-4400000000000001111-1-1-1-111-1-1-1-111000000000011-1-1-1-11111-1-1-1-111-1-111-1-11100
χ2744-444-4-4-4-44-44-4-444-4-444-4004-440000000000000−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i320000000000−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200
χ2844-444-4-4-4-44-44-4-444-4-444-4004-440000000000000−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i320000000000−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200
χ294-444-44-4-4-4-4444-44-44-44-4-400-444000000000000011-1-111-1-1-1-111-1-11100000000001-11-11-11-11-11-11-11-11-11-11-11-100
χ304-444-44-4-4-4-4444-44-44-44-4-400-4440000000000000−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i320000000000−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i3200
χ314-444-44-4-4-4-4444-44-44-44-4-400-4440000000000000−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i320000000000−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i3200
χ324-444-44-4-4-4-444-44-44-44-44-400-444000000000000011-1-111-1-1-1-111-1-11100000000001-11-1-11-111-11-1-11-11-11-11-11-1100
χ334-444-44-4-4-4-444-44-44-44-44-400-4440000000000000−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i320000000000−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i3200
χ344-444-44-4-4-4-444-44-44-44-44-400-4440000000000000−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i320000000000−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i3200
χ354-4-44-4-4444-4-444-4-444-4-44400-4-44000000000000011-1-1-1-111-1-1-1-1111100000000001-1-111-1-111-1-111-1-111-1-111-1-1100
χ364-4-44-4-4444-4-444-4-444-4-44400-4-440000000000000−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i320000000000−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i3200
χ374-4-44-4-4444-4-444-4-444-4-44400-4-440000000000000−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i320000000000−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i3200
χ384-4-44-4-4444-4-44-444-4-444-4400-4-44000000000000011-1-1-1-111-1-1-1-1111100000000001-1-11-111-11-1-11-111-1-111-1-111-100
χ394-4-44-4-4444-4-44-444-4-444-4400-4-440000000000000−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i320000000000−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i3200
χ404-4-44-4-4444-4-44-444-4-444-4400-4-440000000000000−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i320000000000−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i3200
χ414-4-44-4-444-444-42-2-22-222-200000004-42-2002-2000011-1-1-1-111-1-1-1-111110000000000-111-1-111-1-111-1-111-11-1-111-1-1100
χ424-4-44-4-444-444-42-2-22-222-200000004-42-2002-20000−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i3200000000001+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i3200
χ434-4-44-4-444-444-42-2-22-222-200000004-42-2002-20000−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i3200000000001−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i3200
χ444-4-44-4-444-444-4-222-22-2-2200000004-4-2200-22000011-1-1-1-111-1-1-1-111110000000000-111-11-1-11-111-11-1-11-111-1-111-100
χ454-4-44-4-444-444-4-222-22-2-2200000004-4-2200-220000−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+i3200000000001+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i3200
χ464-4-44-4-444-444-4-222-22-2-2200000004-4-2200-220000−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−i3200000000001−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i3200
χ4766666666666600000000-266-2-2-26-2-200-2-20022220000000000000000-2-2-2-222000000000000000000000000000000
χ4866666666666600000000-266-2-2-26-2-200-2-200-2-2-2-200000000000000002222-2-2000000000000000000000000000000
χ4966666666666600000000-2-2-2-2-2-2-26600-2-2002222000000000000000022-2-2-2-2000000000000000000000000000000
χ5066666666666600000000-2-2-2-2-2-2-26600-2-200-2-2-2-20000000000000000-2-22222000000000000000000000000000000
χ5166666666666600000000-2-2-2-2-2-2-2-2-2006-20022-2-200000000000000002-2-22-22000000000000000000000000000000
χ5266666666666600000000-2-2-2-2-2-2-2-2-2006-200-2-2220000000000000000-222-22-2000000000000000000000000000000
χ5366666666666600000000-2-2-2-2-2-2-2-2-200-260022-2-20000000000000000-22-222-2000000000000000000000000000000
χ5466666666666600000000-2-2-2-2-2-2-2-2-200-2600-2-22200000000000000002-22-2-22000000000000000000000000000000
χ5588-888-8-8-88-88-844-4-4-4-4440000000000000000000-1-1-1-11111-1-11111-1-1000000000011-1-111-1-111-1-111-1-1-1-111-1-11100
χ5688-888-8-8-88-88-844-4-4-4-44400000000000000000001+i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321−i320000000000−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3200
χ5788-888-8-8-88-88-844-4-4-4-44400000000000000000001−i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321+i320000000000−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3200
χ5888-888-8-8-88-88-8-4-44444-4-40000000000000000000-1-1-1-11111-1-11111-1-1000000000011-1-1-1-11111-1-1-1-11111-1-111-1-100
χ5988-888-8-8-88-88-8-4-44444-4-400000000000000000001+i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321−i320000000000−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3200
χ6088-888-8-8-88-88-8-4-44444-4-400000000000000000001−i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321+i320000000000−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3200
χ6188-8-8-88-880000000000000000000000000004-400222-22-22-22-22-22-2-2-2000000000000000000000000000000000000
χ6288-8-8-88-880000000000000000000000000004-400−1−i3−1+i3−1−i31+i3−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i3−1+i31−i31+i31−i3000000000000000000000000000000000000
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χ648-888-88-8-888-8-84-44-4-44-440000000000000000000-1-111-1-11111-1-111-1-100000000001-11-11-11-11-11-11-11-1-11-11-11-1100
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χ9024-2424-2424-24-242400000000000000000000000000000-440000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).