Finite Group Databasebeta

← Group #72278133

Character table — Group #72278133

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1234666812121224323232323232363636367272123466681212122432323232323236363636727212346668121212243232323232323636363672721234666812121224323232323232363636367272
order13222266466123336662244444124444121241212121212121212124444442622226646612666666224444412444412124121212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ3111-1111-1-111-1111-1-1-11-11-11-1111-1111-1-111-1111-1-1-11-11-11-1111-1111-1-111-1111-1-1-11-11-11-1111-1111-1-111-1111-1-1-11-11-11-1
χ4111-1111-1-111-1111-1-1-1-11-11-11111-1111-1-111-1111-1-1-1-11-11-11111-1111-1-111-1111-1-1-1-11-11-11111-1111-1-111-1111-1-1-1-11-11-11
χ5222222222222-1-1-1-1-1-1000000222222222222-1-1-1-1-1-1000000222222222222-1-1-1-1-1-1000000222222222222-1-1-1-1-1-1000000
χ6222-2222-2-222-2-1-1-1111000000222-2222-2-222-2-1-1-1111000000222-2222-2-222-2-1-1-1111000000222-2222-2-222-2-1-1-1111000000
χ72-12222-1-12-1-1-12-1-12-1-10000002-12222-1-12-1-1-12-1-12-1-10000002-12222-1-12-1-1-12-1-12-1-10000002-12222-1-12-1-1-12-1-12-1-1000000
χ82-12222-1-12-1-1-1-12-1-12-10000002-12222-1-12-1-1-1-12-1-12-10000002-12222-1-12-1-1-1-12-1-12-10000002-12222-1-12-1-1-1-12-1-12-1000000
χ92-12222-1-12-1-1-1-1-12-1-120000002-12222-1-12-1-1-1-1-12-1-120000002-12222-1-12-1-1-1-1-12-1-120000002-12222-1-12-1-1-1-1-12-1-12000000
χ102-12-222-11-2-1-112-1-1-2110000002-12-222-11-2-1-112-1-1-2110000002-12-222-11-2-1-112-1-1-2110000002-12-222-11-2-1-112-1-1-211000000
χ112-12-222-11-2-1-11-12-11-210000002-12-222-11-2-1-11-12-11-210000002-12-222-11-2-1-11-12-11-210000002-12-222-11-2-1-11-12-11-21000000
χ122-12-222-11-2-1-11-1-1211-20000002-12-222-11-2-1-11-1-1211-20000002-12-222-11-2-1-11-1-1211-20000002-12-222-11-2-1-11-1-1211-2000000
χ133333-1-133-1-1-1-10000001111-1-13333-1-133-1-1-1-10000001111-1-13333-1-133-1-1-1-10000001111-1-13333-1-133-1-1-1-10000001111-1-1
χ143333-1-133-1-1-1-1000000-1-1-1-1113333-1-133-1-1-1-1000000-1-1-1-1113333-1-133-1-1-1-1000000-1-1-1-1113333-1-133-1-1-1-1000000-1-1-1-111
χ15333-3-1-13-31-1-110000001-11-1-11333-3-1-13-31-1-110000001-11-1-11333-3-1-13-31-1-110000001-11-1-11333-3-1-13-31-1-110000001-11-1-11
χ16333-3-1-13-31-1-11000000-11-111-1333-3-1-13-31-1-11000000-11-111-1333-3-1-13-31-1-11000000-11-111-1333-3-1-13-31-1-11000000-11-111-1
χ1766-202-2-2002-20000000020-20066-202-2-2002-20000000020-20066-202-2-2002-20000000020-20066-202-2-2002-20000000020-200
χ1866-202-2-2002-200000000-2020066-202-2-2002-200000000-2020066-202-2-2002-200000000-2020066-202-2-2002-200000000-20200
χ1966-20-22-200-22000000020-200066-20-22-200-22000000020-200066-20-22-200-22000000020-200066-20-22-200-22000000020-2000
χ2066-20-22-200-220000000-20200066-20-22-200-220000000-20200066-20-22-200-220000000-20200066-20-22-200-220000000-202000
χ216-366-2-2-3-3-21110000000000006-366-2-2-3-3-21110000000000006-366-2-2-3-3-21110000000000006-366-2-2-3-3-2111000000000000
χ226-36-6-2-2-33211-10000000000006-36-6-2-2-33211-10000000000006-36-6-2-2-33211-10000000000006-36-6-2-2-33211-1000000000000
χ2312-6-404-4200-22000000000000012-6-404-4200-22000000000000012-6-404-4200-22000000000000012-6-404-4200-220000000000000
χ2412-6-40-442002-2000000000000012-6-40-442002-2000000000000012-6-40-442002-2000000000000012-6-40-442002-20000000000000
χ25111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ26111111111111111111-1-1-1-1-1-1iiiiiiiiiiiiiiiiii−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii
χ27111-1111-1-111-1111-1-1-11-11-11-1iii−iiii−i−iii−iiii−i−i−ii−ii−ii−i-1-1-11-1-1-111-1-11-1-1-1111-11-11-11−i−i−ii−i−i−iii−i−ii−i−i−iiii−ii−ii−ii
χ28111-1111-1-111-1111-1-1-1-11-11-11iii−iiii−i−iii−iiii−i−i−i−ii−ii−ii-1-1-11-1-1-111-1-11-1-1-11111-11-11-1−i−i−ii−i−i−iii−i−ii−i−i−iiiii−ii−ii−i
χ29222222222222-1-1-1-1-1-10000002i2i2i2i2i2i2i2i2i2i2i2i−i−i−i−i−i−i000000-2-2-2-2-2-2-2-2-2-2-2-2111111000000−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2i−2iiiiiii000000
χ30222-2222-2-222-2-1-1-11110000002i2i2i−2i2i2i2i−2i−2i2i2i−2i−i−i−iiii000000-2-2-22-2-2-222-2-22111-1-1-1000000−2i−2i−2i2i−2i−2i−2i2i2i−2i−2i2iiii−i−i−i000000
χ312-12222-1-12-1-1-12-1-12-1-10000002i−i2i2i2i2i−i−i2i−i−i−i2i−i−i2i−i−i000000-21-2-2-2-211-2111-211-211000000−2ii−2i−2i−2i−2iii−2iiii−2iii−2iii000000
χ322-12222-1-12-1-1-1-12-1-12-10000002i−i2i2i2i2i−i−i2i−i−i−i−i2i−i−i2i−i000000-21-2-2-2-211-21111-211-21000000−2ii−2i−2i−2i−2iii−2iiiii−2iii−2ii000000
χ332-12222-1-12-1-1-1-1-12-1-120000002i−i2i2i2i2i−i−i2i−i−i−i−i−i2i−i−i2i000000-21-2-2-2-211-211111-211-2000000−2ii−2i−2i−2i−2iii−2iiiiii−2iii−2i000000
χ342-12-222-11-2-1-112-1-1-2110000002i−i2i−2i2i2i−ii−2i−i−ii2i−i−i−2iii000000-21-22-2-21-1211-1-2112-1-1000000−2ii−2i2i−2i−2ii−i2iii−i−2iii2i−i−i000000
χ352-12-222-11-2-1-11-12-11-210000002i−i2i−2i2i2i−ii−2i−i−ii−i2i−ii−2ii000000-21-22-2-21-1211-11-21-12-1000000−2ii−2i2i−2i−2ii−i2iii−ii−2ii−i2i−i000000
χ362-12-222-11-2-1-11-1-1211-20000002i−i2i−2i2i2i−ii−2i−i−ii−i−i2iii−2i000000-21-22-2-21-1211-111-2-1-12000000−2ii−2i2i−2i−2ii−i2iii−iii−2i−i−i2i000000
χ373333-1-133-1-1-1-10000001111-1-13i3i3i3i−i−i3i3i−i−i−i−i000000iiii−i−i-3-3-3-311-3-31111000000-1-1-1-111−3i−3i−3i−3iii−3i−3iiiii000000−i−i−i−iii
χ383333-1-133-1-1-1-1000000-1-1-1-1113i3i3i3i−i−i3i3i−i−i−i−i000000−i−i−i−iii-3-3-3-311-3-311110000001111-1-1−3i−3i−3i−3iii−3i−3iiiii000000iiii−i−i
χ39333-3-1-13-31-1-110000001-11-1-113i3i3i−3i−i−i3i−3ii−i−ii000000i−ii−i−ii-3-3-3311-33-111-1000000-11-111-1−3i−3i−3i3iii−3i3i−iii−i000000−ii−iii−i
χ40333-3-1-13-31-1-11000000-11-111-13i3i3i−3i−i−i3i−3ii−i−ii000000−ii−iii−i-3-3-3311-33-111-10000001-11-1-11−3i−3i−3i3iii−3i3i−iii−i000000i−ii−i−ii
χ4166-202-2-2002-20000000020-2006i6i−2i02i−2i−2i002i−2i000000002i0−2i00-6-620-22200-2200000000-20200−6i−6i2i0−2i2i2i00−2i2i00000000−2i02i00
χ4266-202-2-2002-200000000-202006i6i−2i02i−2i−2i002i−2i00000000−2i02i00-6-620-22200-220000000020-200−6i−6i2i0−2i2i2i00−2i2i000000002i0−2i00
χ4366-20-22-200-22000000020-20006i6i−2i0−2i2i−2i00−2i2i00000002i0−2i000-6-6202-22002-20000000-202000−6i−6i2i02i−2i2i002i−2i0000000−2i02i000
χ4466-20-22-200-220000000-2020006i6i−2i0−2i2i−2i00−2i2i0000000−2i02i000-6-6202-22002-2000000020-2000−6i−6i2i02i−2i2i002i−2i00000002i0−2i000
χ456-366-2-2-3-3-21110000000000006i−3i6i6i−2i−2i−3i−3i−2iiii000000000000-63-6-622332-1-1-1000000000000−6i3i−6i−6i2i2i3i3i2i−i−i−i000000000000
χ466-36-6-2-2-33211-10000000000006i−3i6i−6i−2i−2i−3i3i2iii−i000000000000-63-66223-3-2-1-11000000000000−6i3i−6i6i2i2i3i−3i−2i−i−ii000000000000
χ4712-6-404-4200-22000000000000012i−6i−4i04i−4i2i00−2i2i0000000000000-12640-44-2002-20000000000000−12i6i4i0−4i4i−2i002i−2i0000000000000
χ4812-6-40-442002-2000000000000012i−6i−4i0−4i4i2i002i−2i0000000000000-126404-4-200-220000000000000−12i6i4i04i−4i−2i00−2i2i0000000000000
χ49111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ50111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111-1111-1-111-1111-1-1-11-11-11-1-1-1-11-1-1-111-1-11-1-1-1111-11-11-11111-1111-1-111-1111-1-1-11-11-11-1-1-1-11-1-1-111-1-11-1-1-1111-11-11-11
χ52111-1111-1-111-1111-1-1-1-11-11-11-1-1-11-1-1-111-1-11-1-1-11111-11-11-1111-1111-1-111-1111-1-1-1-11-11-11-1-1-11-1-1-111-1-11-1-1-11111-11-11-1
χ53222222222222-1-1-1-1-1-1000000-2-2-2-2-2-2-2-2-2-2-2-2111111000000222222222222-1-1-1-1-1-1000000-2-2-2-2-2-2-2-2-2-2-2-2111111000000
χ54222-2222-2-222-2-1-1-1111000000-2-2-22-2-2-222-2-22111-1-1-1000000222-2222-2-222-2-1-1-1111000000-2-2-22-2-2-222-2-22111-1-1-1000000
χ552-12222-1-12-1-1-12-1-12-1-1000000-21-2-2-2-211-2111-211-2110000002-12222-1-12-1-1-12-1-12-1-1000000-21-2-2-2-211-2111-211-211000000
χ562-12222-1-12-1-1-1-12-1-12-1000000-21-2-2-2-211-21111-211-210000002-12222-1-12-1-1-1-12-1-12-1000000-21-2-2-2-211-21111-211-21000000
χ572-12222-1-12-1-1-1-1-12-1-12000000-21-2-2-2-211-211111-211-20000002-12222-1-12-1-1-1-1-12-1-12000000-21-2-2-2-211-211111-211-2000000
χ582-12-222-11-2-1-112-1-1-211000000-21-22-2-21-1211-1-2112-1-10000002-12-222-11-2-1-112-1-1-211000000-21-22-2-21-1211-1-2112-1-1000000
χ592-12-222-11-2-1-11-12-11-21000000-21-22-2-21-1211-11-21-12-10000002-12-222-11-2-1-11-12-11-21000000-21-22-2-21-1211-11-21-12-1000000
χ602-12-222-11-2-1-11-1-1211-2000000-21-22-2-21-1211-111-2-1-120000002-12-222-11-2-1-11-1-1211-2000000-21-22-2-21-1211-111-2-1-12000000
χ613333-1-133-1-1-1-10000001111-1-1-3-3-3-311-3-31111000000-1-1-1-1113333-1-133-1-1-1-10000001111-1-1-3-3-3-311-3-31111000000-1-1-1-111
χ623333-1-133-1-1-1-1000000-1-1-1-111-3-3-3-311-3-311110000001111-1-13333-1-133-1-1-1-1000000-1-1-1-111-3-3-3-311-3-311110000001111-1-1
χ63333-3-1-13-31-1-110000001-11-1-11-3-3-3311-33-111-1000000-11-111-1333-3-1-13-31-1-110000001-11-1-11-3-3-3311-33-111-1000000-11-111-1
χ64333-3-1-13-31-1-11000000-11-111-1-3-3-3311-33-111-10000001-11-1-11333-3-1-13-31-1-11000000-11-111-1-3-3-3311-33-111-10000001-11-1-11
χ6566-202-2-2002-20000000020-200-6-620-22200-2200000000-2020066-202-2-2002-20000000020-200-6-620-22200-2200000000-20200
χ6666-202-2-2002-200000000-20200-6-620-22200-220000000020-20066-202-2-2002-200000000-20200-6-620-22200-220000000020-200
χ6766-20-22-200-22000000020-2000-6-6202-22002-20000000-20200066-20-22-200-22000000020-2000-6-6202-22002-20000000-202000
χ6866-20-22-200-220000000-202000-6-6202-22002-2000000020-200066-20-22-200-220000000-202000-6-6202-22002-2000000020-2000
χ696-366-2-2-3-3-2111000000000000-63-6-622332-1-1-10000000000006-366-2-2-3-3-2111000000000000-63-6-622332-1-1-1000000000000
χ706-36-6-2-2-33211-1000000000000-63-66223-3-2-1-110000000000006-36-6-2-2-33211-1000000000000-63-66223-3-2-1-11000000000000
χ7112-6-404-4200-220000000000000-12640-44-2002-2000000000000012-6-404-4200-220000000000000-12640-44-2002-20000000000000
χ7212-6-40-442002-20000000000000-126404-4-200-22000000000000012-6-40-442002-20000000000000-126404-4-200-220000000000000
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χ74111111111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiiiiiiiiiiiiiiiii−i−i−i−i−i−i
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χ76111-1111-1-111-1111-1-1-1-11-11-11−i−i−ii−i−i−iii−i−ii−i−i−iiiii−ii−ii−i-1-1-11-1-1-111-1-11-1-1-11111-11-11-1iii−iiii−i−iii−iiii−i−i−i−ii−ii−ii
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χ78222-2222-2-222-2-1-1-1111000000−2i−2i−2i2i−2i−2i−2i2i2i−2i−2i2iiii−i−i−i000000-2-2-22-2-2-222-2-22111-1-1-10000002i2i2i−2i2i2i2i−2i−2i2i2i−2i−i−i−iiii000000
χ792-12222-1-12-1-1-12-1-12-1-1000000−2ii−2i−2i−2i−2iii−2iiii−2iii−2iii000000-21-2-2-2-211-2111-211-2110000002i−i2i2i2i2i−i−i2i−i−i−i2i−i−i2i−i−i000000
χ802-12222-1-12-1-1-1-12-1-12-1000000−2ii−2i−2i−2i−2iii−2iiiii−2iii−2ii000000-21-2-2-2-211-21111-211-210000002i−i2i2i2i2i−i−i2i−i−i−i−i2i−i−i2i−i000000
χ812-12222-1-12-1-1-1-1-12-1-12000000−2ii−2i−2i−2i−2iii−2iiiiii−2iii−2i000000-21-2-2-2-211-211111-211-20000002i−i2i2i2i2i−i−i2i−i−i−i−i−i2i−i−i2i000000
χ822-12-222-11-2-1-112-1-1-211000000−2ii−2i2i−2i−2ii−i2iii−i−2iii2i−i−i000000-21-22-2-21-1211-1-2112-1-10000002i−i2i−2i2i2i−ii−2i−i−ii2i−i−i−2iii000000
χ832-12-222-11-2-1-11-12-11-21000000−2ii−2i2i−2i−2ii−i2iii−ii−2ii−i2i−i000000-21-22-2-21-1211-11-21-12-10000002i−i2i−2i2i2i−ii−2i−i−ii−i2i−ii−2ii000000
χ842-12-222-11-2-1-11-1-1211-2000000−2ii−2i2i−2i−2ii−i2iii−iii−2i−i−i2i000000-21-22-2-21-1211-111-2-1-120000002i−i2i−2i2i2i−ii−2i−i−ii−i−i2iii−2i000000
χ853333-1-133-1-1-1-10000001111-1-1−3i−3i−3i−3iii−3i−3iiiii000000−i−i−i−iii-3-3-3-311-3-31111000000-1-1-1-1113i3i3i3i−i−i3i3i−i−i−i−i000000iiii−i−i
χ863333-1-133-1-1-1-1000000-1-1-1-111−3i−3i−3i−3iii−3i−3iiiii000000iiii−i−i-3-3-3-311-3-311110000001111-1-13i3i3i3i−i−i3i3i−i−i−i−i000000−i−i−i−iii
χ87333-3-1-13-31-1-110000001-11-1-11−3i−3i−3i3iii−3i3i−iii−i000000−ii−iii−i-3-3-3311-33-111-1000000-11-111-13i3i3i−3i−i−i3i−3ii−i−ii000000i−ii−i−ii
χ88333-3-1-13-31-1-11000000-11-111-1−3i−3i−3i3iii−3i3i−iii−i000000i−ii−i−ii-3-3-3311-33-111-10000001-11-1-113i3i3i−3i−i−i3i−3ii−i−ii000000−ii−iii−i
χ8966-202-2-2002-20000000020-200−6i−6i2i0−2i2i2i00−2i2i00000000−2i02i00-6-620-22200-2200000000-202006i6i−2i02i−2i−2i002i−2i000000002i0−2i00
χ9066-202-2-2002-200000000-20200−6i−6i2i0−2i2i2i00−2i2i000000002i0−2i00-6-620-22200-220000000020-2006i6i−2i02i−2i−2i002i−2i00000000−2i02i00
χ9166-20-22-200-22000000020-2000−6i−6i2i02i−2i2i002i−2i0000000−2i02i000-6-6202-22002-20000000-2020006i6i−2i0−2i2i−2i00−2i2i00000002i0−2i000
χ9266-20-22-200-220000000-202000−6i−6i2i02i−2i2i002i−2i00000002i0−2i000-6-6202-22002-2000000020-20006i6i−2i0−2i2i−2i00−2i2i0000000−2i02i000
χ936-366-2-2-3-3-2111000000000000−6i3i−6i−6i2i2i3i3i2i−i−i−i000000000000-63-6-622332-1-1-10000000000006i−3i6i6i−2i−2i−3i−3i−2iiii000000000000
χ946-36-6-2-2-33211-1000000000000−6i3i−6i6i2i2i3i−3i−2i−i−ii000000000000-63-66223-3-2-1-110000000000006i−3i6i−6i−2i−2i−3i3i2iii−i000000000000
χ9512-6-404-4200-220000000000000−12i6i4i0−4i4i−2i002i−2i0000000000000-12640-44-2002-2000000000000012i−6i−4i04i−4i2i00−2i2i0000000000000
χ9612-6-40-442002-20000000000000−12i6i4i04i−4i−2i00−2i2i0000000000000-126404-4-200-22000000000000012i−6i−4i0−4i4i2i002i−2i0000000000000

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