Finite Group Databasebeta

← Group #11712708

Character table — Group #11712708

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11112233334466888812121212121212121212161616161616242424241111223333446688881212121212121212121216161616161624242424
order124424224488243612124444444488612242424242444224424224488246612124444444488612242424242444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ31111111111-1-111111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-111111111111111-1-111-1-1-1-1-1-1-1-1
χ41111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511-1-1-1111-1-1i−i-1111-1-1ii−i−iii−i−ii−i-11ii−i−i1-11-111-1-1-1111-1-1i−i-1111-1-1ii−i−iii−i−ii−i-11ii−i−i1-11-1
χ611-1-1-1111-1-1i−i-1111-1-1−i−iii−i−iiii−i-11ii−i−i-11-1111-1-1-1111-1-1i−i-1111-1-1−i−iii−i−iiii−i-11ii−i−i-11-11
χ711-1-1-1111-1-1−ii-1111-1-1ii−i−iii−i−i−ii-11−i−iii-11-1111-1-1-1111-1-1−ii-1111-1-1ii−i−iii−i−i−ii-11−i−iii-11-11
χ811-1-1-1111-1-1−ii-1111-1-1−i−iii−i−iii−ii-11−i−iii1-11-111-1-1-1111-1-1−ii-1111-1-1−i−iii−i−iii−ii-11−i−iii1-11-1
χ922222222222222-1-1-1-10000000022-1-1-1-1-1-1000022222222222222-1-1-1-10000000022-1-1-1-1-1-10000
χ102222222222-2-222-1-1-1-100000000-2-2-1-1111100002222222222-2-222-1-1-1-100000000-2-2-1-111110000
χ112222-2-2222200-2-222220000000000-2-2000000002222-2-2222200-2-222220000000000-2-200000000
χ122222-2-2222200-2-2-1-1-1-1000000000011−i3i3−i3i300002222-2-2222200-2-2-1-1-1-1000000000011−i3i3−i3i30000
χ132222-2-2222200-2-2-1-1-1-1000000000011i3−i3i3−i300002222-2-2222200-2-2-1-1-1-1000000000011i3−i3i3−i30000
χ1422-2-22-222-2-2002-222-2-200000000002-20000000022-2-22-222-2-2002-222-2-200000000002-200000000
χ1522-2-22-222-2-2002-2-1-1110000000000-113−3−33000022-2-22-222-2-2002-2-1-1110000000000-113−3−330000
χ1622-2-22-222-2-2002-2-1-1110000000000-11−333−3000022-2-22-222-2-2002-2-1-1110000000000-11−333−30000
χ1722-2-2-2222-2-22i−2i-22-1-111000000002i−2i1-1−i−iii000022-2-2-2222-2-22i−2i-22-1-111000000002i−2i1-1−i−iii0000
χ1822-2-2-2222-2-2−2i2i-22-1-11100000000−2i2i1-1ii−i−i000022-2-2-2222-2-2−2i2i-22-1-11100000000−2i2i1-1ii−i−i0000
χ192-22i−2i002-22i−2i00002-22i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000002-22i−2i002-22i−2i00002-22i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ202-22i−2i002-22i−2i00002-22i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000002-22i−2i002-22i−2i00002-22i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ212-2−2i2i002-2−2i2i00002-2−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000002-2−2i2i002-2−2i2i00002-2−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ222-2−2i2i002-2−2i2i00002-2−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000002-2−2i2i002-2−2i2i00002-2−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ23333333-1-1-1-133-1-100001111-1-1-1-1-1-100000011-1-1333333-1-1-1-133-1-100001111-1-1-1-1-1-100000011-1-1
χ24333333-1-1-1-133-1-10000-1-1-1-11111-1-1000000-1-111333333-1-1-1-133-1-10000-1-1-1-11111-1-1000000-1-111
χ25333333-1-1-1-1-3-3-1-100001111-1-1-1-111000000-1-111333333-1-1-1-1-3-3-1-100001111-1-1-1-111000000-1-111
χ26333333-1-1-1-1-3-3-1-10000-1-1-1-111111100000011-1-1333333-1-1-1-1-3-3-1-10000-1-1-1-111111100000011-1-1
χ2733-3-3-33-1-1113i−3i1-10000ii−i−i−i−iii−ii0000001-1-1133-3-3-33-1-1113i−3i1-10000ii−i−i−i−iii−ii0000001-1-11
χ2833-3-3-33-1-1113i−3i1-10000−i−iiiii−i−i−ii000000-111-133-3-3-33-1-1113i−3i1-10000−i−iiiii−i−i−ii000000-111-1
χ2933-3-3-33-1-111−3i3i1-10000ii−i−i−i−iiii−i000000-111-133-3-3-33-1-111−3i3i1-10000ii−i−i−i−iiii−i000000-111-1
χ3033-3-3-33-1-111−3i3i1-10000−i−iiiii−i−ii−i0000001-1-1133-3-3-33-1-111−3i3i1-10000−i−iiiii−i−ii−i0000001-1-11
χ314-44i−4i004-44i−4i0000-22−2i2i000000000000000000004-44i−4i004-44i−4i0000-22−2i2i00000000000000000000
χ324-4−4i4i004-4−4i4i0000-222i−2i000000000000000000004-4−4i4i004-4−4i4i0000-222i−2i00000000000000000000
χ336666-6-6-2-2-2-200220000000000000000000000006666-6-6-2-2-2-20022000000000000000000000000
χ3466-6-66-6-2-22200-2200000000000000000000000066-6-66-6-2-22200-22000000000000000000000000
χ356-66i−6i00-22−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000006-66i−6i00-22−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ366-66i−6i00-22−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000006-66i−6i00-22−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ376-6−6i6i00-222i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000006-6−6i6i00-222i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000
χ386-6−6i6i00-222i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000006-6−6i6i00-222i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ40111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ421111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-11111-1-1-1-1
χ4311-1-1-1111-1-1i−i-1111-1-1ii−i−iii−i−ii−i-11ii−i−i1-11-1-1-1111-1-1-111−ii1-1-1-111−i−iii−i−iii−ii1-1−i−iii-11-11
χ4411-1-1-1111-1-1i−i-1111-1-1−i−iii−i−iiii−i-11ii−i−i-11-11-1-1111-1-1-111−ii1-1-1-111ii−i−iii−i−i−ii1-1−i−iii1-11-1
χ4511-1-1-1111-1-1−ii-1111-1-1ii−i−iii−i−i−ii-11−i−iii-11-11-1-1111-1-1-111i−i1-1-1-111−i−iii−i−iiii−i1-1ii−i−i1-11-1
χ4611-1-1-1111-1-1−ii-1111-1-1−i−iii−i−iii−ii-11−i−iii1-11-1-1-1111-1-1-111i−i1-1-1-111ii−i−iii−i−ii−i1-1ii−i−i-11-11
χ4722222222222222-1-1-1-10000000022-1-1-1-1-1-10000-2-2-2-2-2-2-2-2-2-2-2-2-2-2111100000000-2-21111110000
χ482222222222-2-222-1-1-1-100000000-2-2-1-111110000-2-2-2-2-2-2-2-2-2-222-2-21111000000002211-1-1-1-10000
χ492222-2-2222200-2-222220000000000-2-200000000-2-2-2-222-2-2-2-20022-2-2-2-200000000002200000000
χ502222-2-2222200-2-2-1-1-1-1000000000011−i3i3−i3i30000-2-2-2-222-2-2-2-2002211110000000000-1-1i3−i3i3−i30000
χ512222-2-2222200-2-2-1-1-1-1000000000011i3−i3i3−i30000-2-2-2-222-2-2-2-2002211110000000000-1-1−i3i3−i3i30000
χ5222-2-22-222-2-2002-222-2-200000000002-200000000-2-222-22-2-22200-22-2-2220000000000-2200000000
χ5322-2-22-222-2-2002-2-1-1110000000000-113−3−330000-2-222-22-2-22200-2211-1-100000000001-1−333−30000
χ5422-2-22-222-2-2002-2-1-1110000000000-11−333−30000-2-222-22-2-22200-2211-1-100000000001-13−3−330000
χ5522-2-2-2222-2-22i−2i-22-1-111000000002i−2i1-1−i−iii0000-2-2222-2-2-222−2i2i2-211-1-100000000−2i2i-11ii−i−i0000
χ5622-2-2-2222-2-2−2i2i-22-1-11100000000−2i2i1-1ii−i−i0000-2-2222-2-2-2222i−2i2-211-1-1000000002i−2i-11−i−iii0000
χ572-22i−2i002-22i−2i00002-22i−2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000-22−2i2i00-22−2i2i0000-22−2i2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000
χ582-22i−2i002-22i−2i00002-22i−2i−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000-22−2i2i00-22−2i2i0000-22−2i2i1+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000
χ592-2−2i2i002-2−2i2i00002-2−2i2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000-222i−2i00-222i−2i0000-222i−2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000
χ602-2−2i2i002-2−2i2i00002-2−2i2i−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000-222i−2i00-222i−2i0000-222i−2i1−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000
χ61333333-1-1-1-133-1-100001111-1-1-1-1-1-100000011-1-1-3-3-3-3-3-31111-3-3110000-1-1-1-1111111000000-1-111
χ62333333-1-1-1-133-1-10000-1-1-1-11111-1-1000000-1-111-3-3-3-3-3-31111-3-31100001111-1-1-1-11100000011-1-1
χ63333333-1-1-1-1-3-3-1-100001111-1-1-1-111000000-1-111-3-3-3-3-3-3111133110000-1-1-1-11111-1-100000011-1-1
χ64333333-1-1-1-1-3-3-1-10000-1-1-1-111111100000011-1-1-3-3-3-3-3-31111331100001111-1-1-1-1-1-1000000-1-111
χ6533-3-3-33-1-1113i−3i1-10000ii−i−i−i−iii−ii0000001-1-11-3-3333-311-1-1−3i3i-110000−i−iiiii−i−ii−i000000-111-1
χ6633-3-3-33-1-1113i−3i1-10000−i−iiiii−i−i−ii000000-111-1-3-3333-311-1-1−3i3i-110000ii−i−i−i−iiii−i0000001-1-11
χ6733-3-3-33-1-111−3i3i1-10000ii−i−i−i−iiii−i000000-111-1-3-3333-311-1-13i−3i-110000−i−iiiii−i−i−ii0000001-1-11
χ6833-3-3-33-1-111−3i3i1-10000−i−iiiii−i−ii−i0000001-1-11-3-3333-311-1-13i−3i-110000ii−i−i−i−iii−ii000000-111-1
χ694-44i−4i004-44i−4i0000-22−2i2i00000000000000000000-44−4i4i00-44−4i4i00002-22i−2i00000000000000000000
χ704-4−4i4i004-4−4i4i0000-222i−2i00000000000000000000-444i−4i00-444i−4i00002-2−2i2i00000000000000000000
χ716666-6-6-2-2-2-20022000000000000000000000000-6-6-6-666222200-2-2000000000000000000000000
χ7266-6-66-6-2-22200-22000000000000000000000000-6-666-6622-2-2002-2000000000000000000000000
χ736-66i−6i00-22−2i2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000-66−6i6i002-22i−2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000
χ746-66i−6i00-22−2i2i00000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000-66−6i6i002-22i−2i000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000
χ756-6−6i6i00-222i−2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000-666i−6i002-2−2i2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000
χ766-6−6i6i00-222i−2i00000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000-666i−6i002-2−2i2i000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000

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