Finite Group Databasebeta

← Group #13042021

Character table — Group #13042021

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222244444445555888888888888888888101010101010101010101010101010102020202020202020202020202020202020202020202020323232324040404040404040
order12224444888845881010102222224420202020202040404040404040404444444444448888444444444444488888888881010202022444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111-1-1-1-111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-1111111111111111111-1-1-1ii−i−iii−i−i-1-1-1-1-1-1i−ii−iiiii−i−i−i−i-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i
χ61111111111111111111-1-1-1-1111111111111111111-1-1-1−i−iii−i−iii-1-1-1-1-1-1−ii−ii−i−i−i−iiiii-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii
χ71111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1ii−i−iii−i−i-1-1-1-1-1-1i−ii−i−i−i−i−iiiii-1-1iiii−i−i−i−i-1-1-1-11111−i−iii
χ81111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1−i−iii−i−iii-1-1-1-1-1-1−ii−iiiiii−i−i−i−i-1-1−i−i−i−iiiii-1-1-1-11111ii−i−i
χ911111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11-1
χ1011111111-1-1-1-111-1-111111111-11-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-111-1-111-1-1111111111-11-11-11-1-11-11
χ1111111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-11
χ1211111111-1-1-1-111-1-11111111-11-11111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-11-11-11-111-11-1
χ1311111111-1-1-1-111-1-1111-1-1-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-11111-1i−ii−iii−i−i−i−iii11−i−i−i−iiiii1-11-1-11-11i−i−ii
χ1411111111-1-1-1-111-1-1111-1-1-1-11-11-1111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-11111-1−ii−ii−i−iiiii−i−i11iiii−i−i−i−i1-11-1-11-11−iii−i
χ1511111111-1-1-1-111-1-1111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-11111-1i−ii−i−i−iiiii−i−i11−i−i−i−iiiii-11-111-11-1−iii−i
χ1611111111-1-1-1-111-1-1111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-11111-1−ii−iiii−i−i−i−iii11iiii−i−i−i−i-11-111-11-1i−i−ii
χ171111-1-1111111-11-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111
χ181111-1-1111111-11-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111111-111-1-111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1
χ191111-1-1111111-11-1-11111111-1-111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-111111-1-1-11111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1
χ201111-1-1111111-11-1-11111111-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111
χ211111-1-1111111-11-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1ii−i−i−i−iii-1-1-1-1-11−iii−i−i−i−i−iiiii11ii−i−i−i−iii11-1-1-1-111ii−i−i
χ221111-1-1111111-11-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1−i−iiiii−i−i-1-1-1-1-11i−i−iiiiii−i−i−i−i11−i−iiiii−i−i11-1-1-1-111−i−iii
χ231111-1-1111111-11-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1ii−i−i−i−iii-1-1-1-1-11−iii−iiiii−i−i−i−i11ii−i−i−i−iii-1-11111-1-1−i−iii
χ241111-1-1111111-11-1-1111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1−i−iiiii−i−i-1-1-1-1-11i−i−ii−i−i−i−iiiii11−i−iiiii−i−i-1-11111-1-1ii−i−i
χ251111-1-111-1-1-1-1-111111111111-1-11-1-1-1-111-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1111-1-111-1-111-11-1
χ261111-1-111-1-1-1-1-111111111111-1-11-1-1-1-111-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-11-1-111-1-11-11-11
χ271111-1-111-1-1-1-1-11111111111-111-1-1-1-1-111-1-1-1-11111-1-111111-1-1-1-11-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-111-1-111-1-11-11
χ281111-1-111-1-1-1-1-11111111111-111-1-1-1-1-111-1-1-1-11111-1-11-1-1-1-111111-1-1-1-1-111-1-1-1-111-1-1111111-1-111-1-1-111-1-111-11-11-1
χ291111-1-111-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1ii−i−i−i−iii-111111−iii−i−i−iiiii−i−i-1-1−i−iiiii−i−i1-1-11-111-1i−i−ii
χ301111-1-111-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1−i−iiiii−i−i-111111i−i−iiii−i−i−i−iii-1-1ii−i−i−i−iii1-1-11-111-1−iii−i
χ311111-1-111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1ii−i−i−i−iii-111111−iii−iii−i−i−i−iii-1-1−i−iiiii−i−i-111-11-1-11−iii−i
χ321111-1-111-1-1-1-1-1111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1−i−iiiii−i−i-111111i−i−ii−i−iiiii−i−i-1-1ii−i−i−i−iii-111-11-1-11i−i−ii
χ33222222-2-20000-22002222222000022-2-2-2-20000000022-222222222-20000-2-2-2-2-2000000000000000000000000000000
χ34222222-2-20000-22002222222000022-2-2-2-20000000022-2-2-2-2-2-2-2-2-2-20000-22222000000000000000000000000000000
χ35222222-2-20000-2200222-2-2-2-2000022-2-2-2-200000000-2-222i2i−2i−2i2i2i−2i−2i200002−2i2i−2i2i000000000000000000000000000000
χ36222222-2-20000-2200222-2-2-2-2000022-2-2-2-200000000-2-22−2i−2i2i2i−2i−2i2i2i2000022i−2i2i−2i000000000000000000000000000000
χ372222-2-2-2-20000220022222220000-2-222-2-200000000-2-2-22222-2-2-2-2-20000222-2-2000000000000000000000000000000
χ382222-2-2-2-20000220022222220000-2-222-2-200000000-2-2-2-2-2-2-22222-200002-2-222000000000000000000000000000000
χ392222-2-2-2-200002200222-2-2-2-20000-2-222-2-2000000002222i2i−2i−2i−2i−2i2i2i20000-22i−2i−2i2i000000000000000000000000000000
χ402222-2-2-2-200002200222-2-2-2-20000-2-222-2-200000000222−2i−2i2i2i2i2i−2i−2i20000-2−2i2i2i−2i000000000000000000000000000000
χ4122-2-22i−2i0022−2−202i2−i22-2-22-2-2200002i−2i000022−2−2i2i2−i2−i22i−2i02i−2i2i−2i2-22-2022−2−20000000000000i2−i2i2−i22−2i2−i22−2000000000000
χ4222-2-22i−2i0022−2−202i2−i22-2-22-2-2200002i−2i000022−2−2i2i2−i2−i22i−2i0−2i2i−2i2i-22-22022−2−20000000000000i2−i2−i2i2−22−i2i2−22000000000000
χ4322-2-22i−2i0022−2−202i2−i22-2-2-222-200002i−2i000022−2−2i2i2−i2−i2−2i2i02-2-22−2i2i2i−2i0−2−2220000000000000−i2i22−2−i2i2−22i2−i2000000000000
χ4422-2-22i−2i0022−2−202i2−i22-2-2-222-200002i−2i000022−2−2i2i2−i2−i2−2i2i0-222-22i−2i−2i2i0−2−2220000000000000−i2i2−22i2−i22−2−i2i2000000000000
χ4522-2-22i−2i00−2−22202−i2i22-2-22-2-2200002i−2i0000−2−222−i2−i2i2i22i−2i02i−2i2i−2i2-22-20−2−2220000000000000−i2i2−i2i2−22−i2i2−22000000000000
χ4622-2-22i−2i00−2−22202−i2i22-2-22-2-2200002i−2i0000−2−222−i2−i2i2i22i−2i0−2i2i−2i2i-22-220−2−2220000000000000−i2i2i2−i22−2i2−i22−2000000000000
χ4722-2-22i−2i00−2−22202−i2i22-2-2-222-200002i−2i0000−2−222−i2−i2i2i2−2i2i02-2-22−2i2i2i−2i022−2−20000000000000i2−i2−22i2−i22−2−i2i2000000000000
χ4822-2-22i−2i00−2−22202−i2i22-2-2-222-200002i−2i0000−2−222−i2−i2i2i2−2i2i0-222-22i−2i−2i2i022−2−20000000000000i2−i22−2−i2i2−22i2−i2000000000000
χ4922-2-2−2i2i0022−2−202−i2i22-2-22-2-220000−2i2i000022−2−2−i2−i2i2i2−2i2i02i−2i2i−2i-22-22022−2−20000000000000−i2i2i2−i2−22i2−i2−22000000000000
χ5022-2-2−2i2i0022−2−202−i2i22-2-22-2-220000−2i2i000022−2−2−i2−i2i2i2−2i2i0−2i2i−2i2i2-22-2022−2−20000000000000−i2i2−i2i22−2−i2i22−2000000000000
χ5122-2-2−2i2i0022−2−202−i2i22-2-2-222-20000−2i2i000022−2−2−i2−i2i2i22i−2i02-2-222i−2i−2i2i0−2−2220000000000000i2−i22−2i2−i2−22−i2i2000000000000
χ5222-2-2−2i2i0022−2−202−i2i22-2-2-222-20000−2i2i000022−2−2−i2−i2i2i22i−2i0-222-2−2i2i2i−2i0−2−2220000000000000i2−i2−22−i2i22−2i2−i2000000000000
χ5322-2-2−2i2i00−2−22202i2−i22-2-22-2-220000−2i2i0000−2−222i2i2−i2−i2−2i2i02i−2i2i−2i-22-220−2−2220000000000000i2−i2−i2i22−2−i2i22−2000000000000
χ5422-2-2−2i2i00−2−22202i2−i22-2-22-2-220000−2i2i0000−2−222i2i2−i2−i2−2i2i0−2i2i−2i2i2-22-20−2−2220000000000000i2−i2i2−i2−22i2−i2−22000000000000
χ5522-2-2−2i2i00−2−22202i2−i22-2-2-222-20000−2i2i0000−2−222i2i2−i2−i22i−2i02-2-222i−2i−2i2i022−2−20000000000000−i2i2−22−i2i22−2i2−i2000000000000
χ5622-2-2−2i2i00−2−22202i2−i22-2-2-222-20000−2i2i0000−2−222i2i2−i2−i22i−2i0-222-2−2i2i2i−2i022−2−20000000000000−i2i22−2i2−i2−22−i2i2000000000000
χ572-2-22002-22-22-20200-2-222-22-2000000002-22-22-2000000200000000-22-22-2000002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ582-2-22002-22-22-20200-2-222-22-2000000002-22-22-2000000200000000-22-22-200000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ592-2-22002-22-22-20200-2-22-22-22000000002-22-22-2000000-2000000002-22-22000002-22-2-22-220000000000000000000000
χ602-2-22002-22-22-20200-2-22-22-22000000002-22-22-2000000-2000000002-22-2200000-22-222-22-20000000000000000000000
χ612-2-22002-2-22-220200-2-222-22-2000000002-2-22-22000000200000000-2-22-22000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ622-2-22002-2-22-220200-2-222-22-2000000002-2-22-22000000200000000-2-22-2200000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ632-2-22002-2-22-220200-2-22-22-22000000002-2-22-22000000-20000000022-22-2000002-2-22-222-20000000000000000000000
χ642-2-22002-2-22-220200-2-22-22-22000000002-2-22-22000000-20000000022-22-200000-222-22-2-220000000000000000000000
χ654444444444444-144-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000-1-1-1-100000000
χ664444444444444-144-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000000111100000000
χ6744444444-4-4-4-44-1-4-4-1-1-100004-44-4-1-1-1-1-1-111111111000000000000000000000000000000000000000-11-1100000000
χ6844444444-4-4-4-44-1-4-4-1-1-10000-44-44-1-1-1-1-1-1111111110000000000000000000000000000000000000001-11-100000000
χ694444-4-4444444-4-1-4-4-1-1-1000044-4-41111-1-1-1-1-1-11111000000000000000000000000000000000000000-1-11100000000
χ704444-4-4444444-4-1-4-4-1-1-10000-4-4441111-1-1-1-1-1-1111100000000000000000000000000000000000000011-1-100000000
χ714444-4-444-4-4-4-4-4-144-1-1-100004-4-441111-1-11111-1-1-1-1000000000000000000000000000000000000000-111-100000000
χ724444-4-444-4-4-4-4-4-144-1-1-10000-444-41111-1-11111-1-1-1-10000000000000000000000000000000000000001-1-1100000000
χ734-44-4000022−22−22220400-44-444-4-4000000000022−22−2222000000000000000022−22−222200000000000000000000000000000000000
χ744-44-4000022−22−22220400-44-4-4-444000000000022−22−22220000000000000000−222222−2200000000000000000000000000000000000
χ754-44-40000−222222−220400-44-444-4-40000000000−222222−220000000000000000−222222−2200000000000000000000000000000000000
χ764-44-40000−222222−220400-44-4-4-4440000000000−222222−22000000000000000022−22−222200000000000000000000000000000000000
χ774-4-4400-4400000400-4-444-44-400000000-440000000000-4000000004000000000000000000000000000000000000000
χ784-4-4400-4400000400-4-44-44-4400000000-440000000000400000000-4000000000000000000000000000000000000000
χ79888888-8-80000-8-200-2-2-200000000-2-2222200000000000000000000000000000000000000000000000000000000000
χ808888-8-8-8-800008-200-2-2-20000000022-2-22200000000000000000000000000000000000000000000000000000000000
χ8188-8-88i−8i004242−42−420-24i2−4i2-22200000000−2i2i0000−2−222−i2−i2i2i2000000000000000000000000000000000000000000000000000
χ8288-8-88i−8i00−42−4242420-2−4i24i2-22200000000−2i2i000022−2−2i2i2−i2−i2000000000000000000000000000000000000000000000000000
χ8388-8-8−8i8i004242−42−420-2−4i24i2-222000000002i−2i0000−2−222i2i2−i2−i2000000000000000000000000000000000000000000000000000
χ8488-8-8−8i8i00−42−4242420-24i2−4i2-222000000002i−2i000022−2−2−i2−i2i2i2000000000000000000000000000000000000000000000000000
χ858-88-8000042−42−42420-2002-2200000000002i5−2i500−222−2i10−i10i10−i10000000000000000000000000000000000000000000000000000
χ868-88-8000042−42−42420-2002-220000000000−2i52i500−222−2−i10i10−i10i10000000000000000000000000000000000000000000000000000
χ878-88-80000−424242−420-2002-2200000000002i5−2i5002−2−22−i10i10−i10i10000000000000000000000000000000000000000000000000000
χ888-88-80000−424242−420-2002-220000000000−2i52i5002−2−22i10−i10i10−i10000000000000000000000000000000000000000000000000000
χ898-8-88008-88-88-80-20022-2000000000000-22-22-220000000000000000000000000000000000000000000000000000000
χ908-8-88008-8-88-880-20022-2000000000000-222-22-20000000000000000000000000000000000000000000000000000000
χ918-8-8800-8800000-20022-20000000000002-2000025−25−2525000000000000000000000000000000000000000000000000000
χ928-8-8800-8800000-20022-20000000000002-20000−252525−25000000000000000000000000000000000000000000000000000

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