Finite Group Databasebeta

← Group #72226016

Character table — Group #72226016

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111166668888888812121212121212121818363636363636363648484848484848484848484864646464727272727272727296969696
order1244224433661212121244448888244444888866121212121212121212123612122444888824242424
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-111-1-11111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111-1-111-1-11111-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ41111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ511-1-1-1-1111111-1-1-1-1i−ii−ii−ii−i1-1i−ii−ii−ii−i-1-111ii−i−iii−i−i11-1-11-11-111-1-1i−ii−i
χ611-1-1-1-1111111-1-1-1-1i−i−iii−i−ii1-1i−i−iii−i−ii-1-111ii−i−i−i−iii11-1-1-11-11-1-111i−i−ii
χ711-1-1-1-1111111-1-1-1-1−iii−i−iii−i1-1−iii−i−iii−i-1-111−i−iiiii−i−i11-1-1-11-11-1-111−iii−i
χ811-1-1-1-1111111-1-1-1-1−ii−ii−ii−ii1-1−ii−ii−ii−ii-1-111−i−iii−i−iii11-1-11-11-111-1-1−ii−ii
χ9222222222-12-122-1-10022002222002200222-12-10000-1-1-1-1-1-1-1-10000000000-1-1
χ10222222222-12-122-1-100-2-200-2-22200-2-200-2-22-12-100001111-1-1-1-1000000000011
χ1122222222-12-12-1-122220022002222002200-12-12-1-1-1-10000-1-1-1-100000000-1-100
χ1222222222-12-12-1-122-2-200-2-20022-2-200-2-200-12-1211110000-1-1-1-1000000001100
χ1322-2-2-2-2222-12-1-2-211002i−2i002i−2i2-2002i−2i002i−2i-212-10000−i−iii-1-1110000000000−ii
χ1422-2-2-2-2222-12-1-2-21100−2i2i00−2i2i2-200−2i2i00−2i2i-212-10000ii−i−i-1-1110000000000i−i
χ1522-2-2-2-222-12-1211-2-22i−2i002i−2i002-22i−2i002i−2i001-2-12−i−iii0000-1-11100000000−ii00
χ1622-2-2-2-222-12-1211-2-2−2i2i00−2i2i002-2−2i2i00−2i2i001-2-12ii−i−i0000-1-11100000000i−i00
χ1733333-13-103030033331133-1-1-1-1-1-111-1-1-1-10-10-1000011110000-1-1111-11-100-1-1
χ1833333-13-10303003333-1-13311-1-1-1-1-1-1-1-1110-10-10000-1-1-1-1000011-1-1-11-110011
χ1933333-13-103030033-3-311-3-3-1-1-1-1111111-1-10-10-100001111000011-1-1-11-1100-1-1
χ2033333-13-103030033-3-3-1-1-3-311-1-111-1-111110-10-10000-1-1-1-10000-1-1111-11-10011
χ213333-13-13303033001133-1-133-1-111-1-1-1-1-1-1-10-10111100000000-1-111-11-11-1-100
χ223333-13-133030330011-3-3-1-1-3-3-1-11111-1-111-10-1011110000000011-1-11-11-1-1-100
χ233333-13-1330303300-1-1331133-1-1-1-1-1-111-1-1-10-10-1-1-1-10000000011-1-11-11-11100
χ243333-13-1330303300-1-1-3-311-3-3-1-1-1-1111111-10-10-1-1-1-100000000-1-111-11-111100
χ2533-3-31-3-133030-3-300i−i3i−3i−ii3i−3i-11i−i−ii−ii−ii10-10ii−i−i00000000-111-1-111-1−ii00
χ2633-3-31-3-133030-3-300i−i−3i3i−ii−3i3i-11i−ii−i−iii−i10-10ii−i−i000000001-1-111-1-11−ii00
χ2733-3-31-3-133030-3-300−ii3i−3ii−i3i−3i-11−ii−iii−i−ii10-10−i−iii000000001-1-111-1-11i−i00
χ2833-3-31-3-133030-3-300−ii−3i3ii−i−3i3i-11−iii−ii−ii−i10-10−i−iii00000000-111-1-111-1i−i00
χ2933-3-3-313-1030300-3-33i−3ii−i3i−3i−ii-11−iii−i−ii−ii010-10000ii−i−i0000-111-11-1-1100−ii
χ3033-3-3-313-1030300-3-33i−3i−ii3i−3ii−i-11−ii−ii−iii−i010-10000−i−iii00001-1-11-111-100i−i
χ3133-3-3-313-1030300-3-3−3i3ii−i−3i3i−ii-11i−ii−ii−i−ii010-10000ii−i−i00001-1-11-111-100−ii
χ3233-3-3-313-1030300-3-3−3i3i−ii−3i3ii−i-11i−i−iii−ii−i010-10000−i−iii0000-111-11-1-1100i−i
χ3344444444-2-2-2-2-2-2-2-2000000004400000000-2-2-2-2000000001111000000000000
χ3444-4-4-4-444-2-2-2-22222000000004-40000000022-2-20000000011-1-1000000000000
χ3566666-26-20-30-300-3-3002200-2-2-2-2002200-2-201010000-1-1-1-10000000000000011
χ3666666-26-20-30-300-3-300-2-20022-2-200-2-2002201010000111100000000000000-1-1
χ376666-26-26-30-30-3-3002200-2-200-2-22200-2-2001010-1-1-1-100000000000000001100
χ386666-26-26-30-30-3-300-2-2002200-2-2-2-2002200101011110000000000000000-1-100
χ3966-6-62-6-26-30-3033002i−2i00−2i2i00-222i−2i00−2i2i00-1010−i−iii0000000000000000i−i00
χ4066-6-62-6-26-30-303300−2i2i002i−2i00-22−2i2i002i−2i00-1010ii−i−i0000000000000000−ii00
χ4166-6-6-626-20-30-30033002i−2i00−2i2i-22002i−2i00−2i2i0-1010000−i−iii00000000000000i−i
χ4266-6-6-626-20-30-3003300−2i2i002i−2i-2200−2i2i002i−2i0-1010000ii−i−i00000000000000−ii
χ438-88i−8i00002-4-242i−2i4i−4i0000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000-11i−i000000000000
χ448-88i−8i00002-4-242i−2i4i−4i0000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000-11i−i000000000000
χ458-88i−8i0000-424-2−4i4i−2i2i00000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11-11i−i000000000000
χ468-88i−8i0000-424-2−4i4i−2i2i00000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11-11i−i000000000000
χ478-88i−8i0000-4-444−4i4i4i−4i0000000000000000000000000000002-2−2i2i000000000000
χ488-8−8i8i00002-4-24−2i2i−4i4i0000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000-11−ii000000000000
χ498-8−8i8i00002-4-24−2i2i−4i4i0000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000-11−ii000000000000
χ508-8−8i8i0000-424-24i−4i2i−2i00000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11-11−ii000000000000
χ518-8−8i8i0000-424-24i−4i2i−2i00000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11-11−ii000000000000
χ528-8−8i8i0000-4-4444i−4i−4i4i0000000000000000000000000000002-22i−2i000000000000
χ539999-3-3-3-3000000003333-3-3-3-311-1-1-1-1111100000000000000001111-1-1-1-10000
χ549999-3-3-3-30000000033-3-3-3-33311-1-11111-1-10000000000000000-1-1-1-111110000
χ559999-3-3-3-300000000-3-33333-3-31111-1-1-1-1110000000000000000-1-1-1-111110000
χ569999-3-3-3-300000000-3-3-3-33333111111-1-1-1-100000000000000001111-1-1-1-10000
χ5799-9-933-3-3000000003i−3i3i−3i−3i3i−3i3i1-1−ii−iii−ii−i00000000000000001-11-1-1-1110000
χ5899-9-933-3-3000000003i−3i−3i3i−3i3i3i−3i1-1−iii−ii−i−ii0000000000000000-11-1111-1-10000
χ5999-9-933-3-300000000−3i3i3i−3i3i−3i−3i3i1-1i−i−ii−iii−i0000000000000000-11-1111-1-10000
χ6099-9-933-3-300000000−3i3i−3i3i3i−3i3i−3i1-1i−ii−i−ii−ii00000000000000001-11-1-1-1110000
χ6116-1616i−16i000044-4-44i−4i−4i4i0000000000000000000000000000001-1−ii000000000000
χ6216-16−16i16i000044-4-4−4i4i4i−4i0000000000000000000000000000001-1i−i000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.