Finite Group Databasebeta

← Group #8247

Character table — Group #8247

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1111111111111111222222222222222244444444444444444444444444444444444488888888
order1222444488888888224444448888888844444444448888888888888888888888888824448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i11iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i11iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii11−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii11−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1
χ911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111-1-111-1-1i−iii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ181111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-111-1-111-1-1i−iii−i−iii−i−i-1-111−i−iii-1-111−i−iii-11-11−ii−ii
χ191111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-111-1-111i−i−i−iii−i−iii11-1-1ii−i−i11-1-1ii−i−i-11-11−ii−ii
χ201111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1-1-111-1-111i−i−i−iii−i−iii-1-111−i−iii-1-111−i−iii1-11-1i−ii−i
χ211111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1ii−i−i−i−iiii−i-1-11111-1-1ii−i−i-1-111−i−iii11-1-11-1-11i−i−ii
χ221111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1ii−i−i−i−iiii−i-1-11111-1-1−i−iii11-1-1ii−i−i-1-111-111-1−iii−i
χ231111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1−i−iiiii−i−ii−i11-1-1-1-111ii−i−i-1-111−i−iii11-1-1-111-1−iii−i
χ241111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1−i−iiiii−i−ii−i11-1-1-1-111−i−iii11-1-1ii−i−i-1-1111-1-11i−i−ii
χ251111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111-1-111-1-1−ii−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii
χ261111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-111-1-111-1-1−ii−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i-11-11i−ii−i
χ271111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1-1-111-1-111−iiii−i−iii−i−i11-1-1−i−iii11-1-1−i−iii-11-11i−ii−i
χ281111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1-1-111-1-111−iiii−i−iii−i−i-1-111ii−i−i-1-111ii−i−i1-11-1−ii−ii
χ291111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1ii−i−i−i−iii−ii11-1-1-1-111ii−i−i11-1-1−i−iii-1-1111-1-11−iii−i
χ301111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1ii−i−i−i−iii−ii11-1-1-1-111−i−iii-1-111ii−i−i11-1-1-111-1i−i−ii
χ311111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−i−iiiii−i−i−ii-1-11111-1-1ii−i−i11-1-1−i−iii-1-111-111-1i−i−ii
χ321111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1-1−i−iiiii−i−i−ii-1-11111-1-1−i−iii-1-111ii−i−i11-1-11-1-11−iii−i
χ33222222222222222222-2-222-2-222-2-222-2-2-2-200000000-2-200000000000000000000000000000000
χ342222222222222222-2-222-2-222-2-222-2-222-2-200000000-2-200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-222-2-222-2-2-2-222-2-222-2-2000000002200000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-222-2-2-2-2000000002200000000000000000000000000000000
χ372222-2-2-2-22i2i2i2i−2i−2i−2i−2i22-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2200000000−2i2i00000000000000000000000000000000
χ382222-2-2-2-22i2i2i2i−2i−2i−2i−2i-2-22222-2-2−2i−2i2i2i2i2i−2i−2i-2200000000−2i2i00000000000000000000000000000000
χ392222-2-2-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-2-222−2i−2i2i2i2i2i−2i−2i-22000000002i−2i00000000000000000000000000000000
χ402222-2-2-2-2−2i−2i−2i−2i2i2i2i2i-2-22222-2-22i2i−2i−2i−2i−2i2i2i-22000000002i−2i00000000000000000000000000000000
χ4122-2-222-2-222-2-222-2-2002i−2i002i−2i002i−2i002i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ4222-2-222-2-222-2-222-2-2002i−2i002i−2i002i−2i002i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ4322-2-222-2-222-2-222-2-200−2i2i00−2i2i00−2i2i00−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ4422-2-222-2-222-2-222-2-200−2i2i00−2i2i00−2i2i00−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ4522-2-222-2-2-2-222-2-222002i−2i002i−2i00−2i2i00−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ4622-2-222-2-2-2-222-2-222002i−2i002i−2i00−2i2i00−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ4722-2-222-2-2-2-222-2-22200−2i2i00−2i2i002i−2i002i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ4822-2-222-2-2-2-222-2-22200−2i2i00−2i2i002i−2i002i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ4922-2-2-2-2222i2i−2i−2i−2i−2i2i2i002i−2i00−2i2i00-22002-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ5022-2-2-2-2222i2i−2i−2i−2i−2i2i2i002i−2i00−2i2i00-22002-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ5122-2-2-2-2222i2i−2i−2i−2i−2i2i2i00−2i2i002i−2i002-200-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ5222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00−2i2i002i−2i002-200-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ5322-2-2-2-222−2i−2i2i2i2i2i−2i−2i002i−2i00−2i2i002-200-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ5422-2-2-2-222−2i−2i2i2i2i2i−2i−2i002i−2i00−2i2i002-200-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ5522-2-2-2-222−2i−2i2i2i2i2i−2i−2i00−2i2i002i−2i00-22002-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ5622-2-2-2-222−2i−2i2i2i2i2i−2i−2i00−2i2i002i−2i00-22002-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ572-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-2002i−2i002ζ−2ζ002ζ3−2ζ300000000000000000000002−2i2−i21+i−1−i1−i−1+i2−2i2−i21+i−1−i1−i−1+i00000000
χ582-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-2002i−2i002ζ−2ζ002ζ3−2ζ30000000000000000000000−22−i2i2−1−i1+i−1+i1−i−22−i2i2−1−i1+i−1+i1−i00000000
χ592-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-2200−2i2i00−2ζ2ζ00−2ζ32ζ30000000000000000000000i2−i2−22−1+i1−i1+i−1−i−i2i22−21−i−1+i−1−i1+i00000000
χ602-22-22i−2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-2200−2i2i00−2ζ2ζ00−2ζ32ζ30000000000000000000000−i2i22−21−i−1+i−1−i1+ii2−i2−22−1+i1−i1+i−1−i00000000
χ612-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32-2002i−2i00−2ζ2ζ00−2ζ32ζ300000000000000000000002−2i2−i2−1−i1+i−1+i1−i2−2i2−i2−1−i1+i−1+i1−i00000000
χ622-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32-2002i−2i00−2ζ2ζ00−2ζ32ζ30000000000000000000000−22−i2i21+i−1−i1−i−1+i−22−i2i21+i−1−i1−i−1+i00000000
χ632-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3-2200−2i2i002ζ−2ζ002ζ3−2ζ30000000000000000000000i2−i2−221−i−1+i−1−i1+i−i2i22−2−1+i1−i1+i−1−i00000000
χ642-22-22i−2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3-2200−2i2i002ζ−2ζ002ζ3−2ζ30000000000000000000000−i2i22−2−1+i1−i1+i−1−ii2−i2−221−i−1+i−1−i1+i00000000
χ652-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-200−2i2i002ζ3−2ζ3002ζ−2ζ00000000000000000000002−2−i2i2−1+i1−i−1−i1+i2−2−i2i2−1+i1−i−1−i1+i00000000
χ662-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-200−2i2i002ζ3−2ζ3002ζ−2ζ0000000000000000000000−22i2−i21−i−1+i1+i−1−i−22i2−i21−i−1+i1+i−1−i00000000
χ672-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-22002i−2i00−2ζ32ζ300−2ζ2ζ0000000000000000000000i2−i22−2−1−i1+i1−i−1+i−i2i2−221+i−1−i−1+i1−i00000000
χ682-22-2−2i2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-22002i−2i00−2ζ32ζ300−2ζ2ζ0000000000000000000000−i2i2−221+i−1−i−1+i1−ii2−i22−2−1−i1+i1−i−1+i00000000
χ692-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-200−2i2i00−2ζ32ζ300−2ζ2ζ00000000000000000000002−2−i2i21−i−1+i1+i−1−i2−2−i2i21−i−1+i1+i−1−i00000000
χ702-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-200−2i2i00−2ζ32ζ300−2ζ2ζ0000000000000000000000−22i2−i2−1+i1−i−1−i1+i−22i2−i2−1+i1−i−1−i1+i00000000
χ712-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-22002i−2i002ζ3−2ζ3002ζ−2ζ0000000000000000000000i2−i22−21+i−1−i−1+i1−i−i2i2−22−1−i1+i1−i−1+i00000000
χ722-22-2−2i2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-22002i−2i002ζ3−2ζ3002ζ−2ζ0000000000000000000000−i2i2−22−1−i1+i1−i−1+ii2−i22−21+i−1−i−1+i1−i00000000
χ734-4-444i−4i−4i4i4ζ−4ζ−4ζ4ζ4ζ3−4ζ3−4ζ34ζ3000000000000000000000000000000000000000000000000000000000000
χ744-4-444i−4i−4i4i−4ζ4ζ4ζ−4ζ−4ζ34ζ34ζ3−4ζ3000000000000000000000000000000000000000000000000000000000000
χ754-4-44−4i4i4i−4i4ζ3−4ζ3−4ζ34ζ34ζ−4ζ−4ζ4ζ000000000000000000000000000000000000000000000000000000000000
χ764-4-44−4i4i4i−4i−4ζ34ζ34ζ3−4ζ3−4ζ4ζ4ζ−4ζ000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.