Finite Group Databasebeta

← Group #72253714

Character table — Group #72253714

Order 4608.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size13339999183232327272727272727272969696128133399991832323272727272727272729696961281333999918323232727272727272727296969612813339999183232327272727272727272969696128
order12222222233324444444666344444444412121244444444121212122222222226662444444466664444444441212124444444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ32222222222-1-1000000002-1-1-12222222222-1-1000000002-1-1-12222222222-1-1000000002-1-1-12222222222-1-1000000002-1-1-1
χ4222222222-12-100000000-12-1-1222222222-12-100000000-12-1-1222222222-12-100000000-12-1-1222222222-12-100000000-12-1-1
χ5222222222-1-1200000000-1-12-1222222222-1-1200000000-1-12-1222222222-1-1200000000-1-12-1222222222-1-1200000000-1-12-1
χ6222222222-1-1-100000000-1-1-12222222222-1-1-100000000-1-1-12222222222-1-1-100000000-1-1-12222222222-1-1-100000000-1-1-12
χ7333-13-1-1-1-1003111-11-1-1-100-10333-13-1-1-1-1003111-11-1-1-100-10333-13-1-1-1-1003111-11-1-1-100-10333-13-1-1-1-1003111-11-1-1-100-10
χ8333-13-1-1-1-1003-1-1-11-111100-10333-13-1-1-1-1003-1-1-11-111100-10333-13-1-1-1-1003-1-1-11-111100-10333-13-1-1-1-1003-1-1-11-111100-10
χ933-13-13-1-1-103011-11-11-1-10-10033-13-13-1-1-103011-11-11-1-10-10033-13-13-1-1-103011-11-11-1-10-10033-13-13-1-1-103011-11-11-1-10-100
χ1033-13-13-1-1-1030-1-11-11-1110-10033-13-13-1-1-1030-1-11-11-1110-10033-13-13-1-1-1030-1-11-11-1110-10033-13-13-1-1-1030-1-11-11-1110-100
χ113-133-1-13-1-13001-111-1-11-1-10003-133-1-13-1-13001-111-1-11-1-10003-133-1-13-1-13001-111-1-11-1-10003-133-1-13-1-13001-111-1-11-1-1000
χ123-133-1-13-1-1300-11-1-111-11-10003-133-1-13-1-1300-11-1-111-11-10003-133-1-13-1-1300-11-1-111-11-10003-133-1-13-1-1300-11-1-111-11-1000
χ13666-26-2-2-2-200-3000000000010666-26-2-2-2-200-3000000000010666-26-2-2-2-200-3000000000010666-26-2-2-2-200-3000000000010
χ1466-26-26-2-2-20-3000000000010066-26-26-2-2-20-3000000000010066-26-26-2-2-20-3000000000010066-26-26-2-2-20-30000000000100
χ156-266-2-26-2-2-3000000000010006-266-2-26-2-2-3000000000010006-266-2-26-2-2-3000000000010006-266-2-26-2-2-300000000001000
χ1699-3-3-3-311100011-1-1-1-111000099-3-3-3-311100011-1-1-1-111000099-3-3-3-311100011-1-1-1-111000099-3-3-3-311100011-1-1-1-1110000
χ1799-3-3-3-3111000-1-11111-1-1000099-3-3-3-3111000-1-11111-1-1000099-3-3-3-3111000-1-11111-1-1000099-3-3-3-3111000-1-11111-1-10000
χ189-39-3-31-3110001-11-1-11-1100009-39-3-31-3110001-11-1-11-1100009-39-3-31-3110001-11-1-11-1100009-39-3-31-3110001-11-1-11-110000
χ199-39-3-31-311000-11-111-11-100009-39-3-31-311000-11-111-11-100009-39-3-31-311000-11-111-11-100009-39-3-31-311000-11-111-11-10000
χ209-3-391-3-3110001-1-111-1-1100009-3-391-3-3110001-1-111-1-1100009-3-391-3-3110001-1-111-1-1100009-3-391-3-3110001-1-111-1-110000
χ219-3-391-3-311000-111-1-111-100009-3-391-3-311000-111-1-111-100009-3-391-3-311000-111-1-111-100009-3-391-3-311000-111-1-111-10000
χ229-3-3-31115-30001-1-1-1111-100009-3-3-31115-30001-1-1-1111-100009-3-3-31115-30001-1-1-1111-100009-3-3-31115-30001-1-1-1111-10000
χ239-3-3-31115-3000-1111-1-1-1100009-3-3-31115-3000-1111-1-1-1100009-3-3-31115-3000-1111-1-1-1100009-3-3-31115-3000-1111-1-1-110000
χ2418-6-6-6222-6200000000000000018-6-6-6222-6200000000000000018-6-6-6222-6200000000000000018-6-6-6222-62000000000000000
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
χ26111111111111-1-1-1-1-1-1-1-11111iiiiiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ272222222222-1-1000000002-1-1-12i2i2i2i2i2i2i2i2i2i−i−i000000002i−i−i−i-2-2-2-2-2-2-2-2-2-21100000000-2111−2i−2i−2i−2i−2i−2i−2i−2i−2i−2iii00000000−2iiii
χ28222222222-12-100000000-12-1-12i2i2i2i2i2i2i2i2i−i2i−i00000000−i2i−i−i-2-2-2-2-2-2-2-2-21-21000000001-211−2i−2i−2i−2i−2i−2i−2i−2i−2ii−2ii00000000i−2iii
χ29222222222-1-1200000000-1-12-12i2i2i2i2i2i2i2i2i−i−i2i00000000−i−i2i−i-2-2-2-2-2-2-2-2-211-20000000011-21−2i−2i−2i−2i−2i−2i−2i−2i−2iii−2i00000000ii−2ii
χ30222222222-1-1-100000000-1-1-122i2i2i2i2i2i2i2i2i−i−i−i00000000−i−i−i2i-2-2-2-2-2-2-2-2-211100000000111-2−2i−2i−2i−2i−2i−2i−2i−2i−2iiii00000000iii−2i
χ31333-13-1-1-1-1003111-11-1-1-100-103i3i3i−i3i−i−i−i−i003iiii−ii−i−i−i00−i0-3-3-31-3111100-3-1-1-11-11110010−3i−3i−3ii−3iiiii00−3i−i−i−ii−iiii00i0
χ32333-13-1-1-1-1003-1-1-11-111100-103i3i3i−i3i−i−i−i−i003i−i−i−ii−iiii00−i0-3-3-31-3111100-3111-11-1-1-10010−3i−3i−3ii−3iiiii00−3iiii−ii−i−i−i00i0
χ3333-13-13-1-1-103011-11-11-1-10-1003i3i−i3i−i3i−i−i−i03i0ii−ii−ii−i−i0−i00-3-31-31-31110-30-1-11-11-1110100−3i−3ii−3ii−3iiii0−3i0−i−ii−ii−iii0i00
χ3433-13-13-1-1-1030-1-11-11-1110-1003i3i−i3i−i3i−i−i−i03i0−i−ii−ii−iii0−i00-3-31-31-31110-3011-11-11-1-10100−3i−3ii−3ii−3iiii0−3i0ii−ii−ii−i−i0i00
χ353-133-1-13-1-13001-111-1-11-1-10003i−i3i3i−i−i3i−i−i3i00i−iii−i−ii−i−i000-31-3-311-311-300-11-1-111-111000−3ii−3i−3iii−3iii−3i00−ii−i−iii−iii000
χ363-133-1-13-1-1300-11-1-111-11-10003i−i3i3i−i−i3i−i−i3i00−ii−i−iii−ii−i000-31-3-311-311-3001-111-1-11-11000−3ii−3i−3iii−3iii−3i00i−iii−i−ii−ii000
χ37666-26-2-2-2-200-30000000000106i6i6i−2i6i−2i−2i−2i−2i00−3i0000000000i0-6-6-62-622220030000000000-10−6i−6i−6i2i−6i2i2i2i2i003i0000000000−i0
χ3866-26-26-2-2-20-300000000001006i6i−2i6i−2i6i−2i−2i−2i0−3i0000000000i00-6-62-62-6222030000000000-100−6i−6i2i−6i2i−6i2i2i2i03i0000000000−i00
χ396-266-2-26-2-2-3000000000010006i−2i6i6i−2i−2i6i−2i−2i−3i0000000000i000-62-6-622-62230000000000-1000−6i2i−6i−6i2i2i−6i2i2i3i0000000000−i000
χ4099-3-3-3-311100011-1-1-1-11100009i9i−3i−3i−3i−3iiii000ii−i−i−i−iii0000-9-93333-1-1-1000-1-11111-1-10000−9i−9i3i3i3i3i−i−i−i000−i−iiiii−i−i0000
χ4199-3-3-3-3111000-1-11111-1-100009i9i−3i−3i−3i−3iiii000−i−iiiii−i−i0000-9-93333-1-1-100011-1-1-1-1110000−9i−9i3i3i3i3i−i−i−i000ii−i−i−i−iii0000
χ429-39-3-31-3110001-11-1-11-1100009i−3i9i−3i−3ii−3iii000i−ii−i−ii−ii0000-93-933-13-1-1000-11-111-11-10000−9i3i−9i3i3i−i3i−i−i000−ii−iii−ii−i0000
χ439-39-3-31-311000-11-111-11-100009i−3i9i−3i−3ii−3iii000−ii−iii−ii−i0000-93-933-13-1-10001-11-1-11-110000−9i3i−9i3i3i−i3i−i−i000i−ii−i−ii−ii0000
χ449-3-391-3-3110001-1-111-1-1100009i−3i−3i9ii−3i−3iii000i−i−iii−i−ii0000-933-9-133-1-1000-111-1-111-10000−9i3i3i−9i−i3i3i−i−i000−iii−i−iii−i0000
χ459-3-391-3-311000-111-1-111-100009i−3i−3i9ii−3i−3iii000−iii−i−iii−i0000-933-9-133-1-10001-1-111-1-110000−9i3i3i−9i−i3i3i−i−i000i−i−iii−i−ii0000
χ469-3-3-31115-30001-1-1-1111-100009i−3i−3i−3iiii5i−3i000i−i−i−iiii−i0000-9333-1-1-1-53000-1111-1-1-110000−9i3i3i3i−i−i−i−5i3i000−iiii−i−i−ii0000
χ479-3-3-31115-3000-1111-1-1-1100009i−3i−3i−3iiii5i−3i000−iiii−i−i−ii0000-9333-1-1-1-530001-1-1-1111-10000−9i3i3i3i−i−i−i−5i3i000i−i−i−iiii−i0000
χ4818-6-6-6222-6200000000000000018i−6i−6i−6i2i2i2i−6i2i000000000000000-18666-2-2-26-2000000000000000−18i6i6i6i−2i−2i−2i6i−2i000000000000000
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
χ50111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ512222222222-1-1000000002-1-1-1-2-2-2-2-2-2-2-2-2-21100000000-21112222222222-1-1000000002-1-1-1-2-2-2-2-2-2-2-2-2-21100000000-2111
χ52222222222-12-100000000-12-1-1-2-2-2-2-2-2-2-2-21-21000000001-211222222222-12-100000000-12-1-1-2-2-2-2-2-2-2-2-21-21000000001-211
χ53222222222-1-1200000000-1-12-1-2-2-2-2-2-2-2-2-211-20000000011-21222222222-1-1200000000-1-12-1-2-2-2-2-2-2-2-2-211-20000000011-21
χ54222222222-1-1-100000000-1-1-12-2-2-2-2-2-2-2-2-211100000000111-2222222222-1-1-100000000-1-1-12-2-2-2-2-2-2-2-2-211100000000111-2
χ55333-13-1-1-1-1003111-11-1-1-100-10-3-3-31-3111100-3-1-1-11-11110010333-13-1-1-1-1003111-11-1-1-100-10-3-3-31-3111100-3-1-1-11-11110010
χ56333-13-1-1-1-1003-1-1-11-111100-10-3-3-31-3111100-3111-11-1-1-10010333-13-1-1-1-1003-1-1-11-111100-10-3-3-31-3111100-3111-11-1-1-10010
χ5733-13-13-1-1-103011-11-11-1-10-100-3-31-31-31110-30-1-11-11-111010033-13-13-1-1-103011-11-11-1-10-100-3-31-31-31110-30-1-11-11-1110100
χ5833-13-13-1-1-1030-1-11-11-1110-100-3-31-31-31110-3011-11-11-1-1010033-13-13-1-1-1030-1-11-11-1110-100-3-31-31-31110-3011-11-11-1-10100
χ593-133-1-13-1-13001-111-1-11-1-1000-31-3-311-311-300-11-1-111-1110003-133-1-13-1-13001-111-1-11-1-1000-31-3-311-311-300-11-1-111-111000
χ603-133-1-13-1-1300-11-1-111-11-1000-31-3-311-311-3001-111-1-11-110003-133-1-13-1-1300-11-1-111-11-1000-31-3-311-311-3001-111-1-11-11000
χ61666-26-2-2-2-200-3000000000010-6-6-62-622220030000000000-10666-26-2-2-2-200-3000000000010-6-6-62-622220030000000000-10
χ6266-26-26-2-2-20-30000000000100-6-62-62-6222030000000000-10066-26-26-2-2-20-30000000000100-6-62-62-6222030000000000-100
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χ6499-3-3-3-311100011-1-1-1-1110000-9-93333-1-1-1000-1-11111-1-1000099-3-3-3-311100011-1-1-1-1110000-9-93333-1-1-1000-1-11111-1-10000
χ6599-3-3-3-3111000-1-11111-1-10000-9-93333-1-1-100011-1-1-1-111000099-3-3-3-3111000-1-11111-1-10000-9-93333-1-1-100011-1-1-1-1110000
χ669-39-3-31-3110001-11-1-11-110000-93-933-13-1-1000-11-111-11-100009-39-3-31-3110001-11-1-11-110000-93-933-13-1-1000-11-111-11-10000
χ679-39-3-31-311000-11-111-11-10000-93-933-13-1-10001-11-1-11-1100009-39-3-31-311000-11-111-11-10000-93-933-13-1-10001-11-1-11-110000
χ689-3-391-3-3110001-1-111-1-110000-933-9-133-1-1000-111-1-111-100009-3-391-3-3110001-1-111-1-110000-933-9-133-1-1000-111-1-111-10000
χ699-3-391-3-311000-111-1-111-10000-933-9-133-1-10001-1-111-1-1100009-3-391-3-311000-111-1-111-10000-933-9-133-1-10001-1-111-1-110000
χ709-3-3-31115-30001-1-1-1111-10000-9333-1-1-1-53000-1111-1-1-1100009-3-3-31115-30001-1-1-1111-10000-9333-1-1-1-53000-1111-1-1-110000
χ719-3-3-31115-3000-1111-1-1-110000-9333-1-1-1-530001-1-1-1111-100009-3-3-31115-3000-1111-1-1-110000-9333-1-1-1-530001-1-1-1111-10000
χ7218-6-6-6222-62000000000000000-18666-2-2-26-200000000000000018-6-6-6222-62000000000000000-18666-2-2-26-2000000000000000
χ73111111111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiii
χ74111111111111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−iiiii
χ752222222222-1-1000000002-1-1-1−2i−2i−2i−2i−2i−2i−2i−2i−2i−2iii00000000−2iiii-2-2-2-2-2-2-2-2-2-21100000000-21112i2i2i2i2i2i2i2i2i2i−i−i000000002i−i−i−i
χ76222222222-12-100000000-12-1-1−2i−2i−2i−2i−2i−2i−2i−2i−2ii−2ii00000000i−2iii-2-2-2-2-2-2-2-2-21-21000000001-2112i2i2i2i2i2i2i2i2i−i2i−i00000000−i2i−i−i
χ77222222222-1-1200000000-1-12-1−2i−2i−2i−2i−2i−2i−2i−2i−2iii−2i00000000ii−2ii-2-2-2-2-2-2-2-2-211-20000000011-212i2i2i2i2i2i2i2i2i−i−i2i00000000−i−i2i−i
χ78222222222-1-1-100000000-1-1-12−2i−2i−2i−2i−2i−2i−2i−2i−2iiii00000000iii−2i-2-2-2-2-2-2-2-2-211100000000111-22i2i2i2i2i2i2i2i2i−i−i−i00000000−i−i−i2i
χ79333-13-1-1-1-1003111-11-1-1-100-10−3i−3i−3ii−3iiiii00−3i−i−i−ii−iiii00i0-3-3-31-3111100-3-1-1-11-111100103i3i3i−i3i−i−i−i−i003iiii−ii−i−i−i00−i0
χ80333-13-1-1-1-1003-1-1-11-111100-10−3i−3i−3ii−3iiiii00−3iiii−ii−i−i−i00i0-3-3-31-3111100-3111-11-1-1-100103i3i3i−i3i−i−i−i−i003i−i−i−ii−iiii00−i0
χ8133-13-13-1-1-103011-11-11-1-10-100−3i−3ii−3ii−3iiii0−3i0−i−ii−ii−iii0i00-3-31-31-31110-30-1-11-11-11101003i3i−i3i−i3i−i−i−i03i0ii−ii−ii−i−i0−i00
χ8233-13-13-1-1-1030-1-11-11-1110-100−3i−3ii−3ii−3iiii0−3i0ii−ii−ii−i−i0i00-3-31-31-31110-3011-11-11-1-101003i3i−i3i−i3i−i−i−i03i0−i−ii−ii−iii0−i00
χ833-133-1-13-1-13001-111-1-11-1-1000−3ii−3i−3iii−3iii−3i00−ii−i−iii−iii000-31-3-311-311-300-11-1-111-1110003i−i3i3i−i−i3i−i−i3i00i−iii−i−ii−i−i000
χ843-133-1-13-1-1300-11-1-111-11-1000−3ii−3i−3iii−3iii−3i00i−iii−i−ii−ii000-31-3-311-311-3001-111-1-11-110003i−i3i3i−i−i3i−i−i3i00−ii−i−iii−ii−i000
χ85666-26-2-2-2-200-3000000000010−6i−6i−6i2i−6i2i2i2i2i003i0000000000−i0-6-6-62-622220030000000000-106i6i6i−2i6i−2i−2i−2i−2i00−3i0000000000i0
χ8666-26-26-2-2-20-30000000000100−6i−6i2i−6i2i−6i2i2i2i03i0000000000−i00-6-62-62-6222030000000000-1006i6i−2i6i−2i6i−2i−2i−2i0−3i0000000000i00
χ876-266-2-26-2-2-300000000001000−6i2i−6i−6i2i2i−6i2i2i3i0000000000−i000-62-6-622-62230000000000-10006i−2i6i6i−2i−2i6i−2i−2i−3i0000000000i000
χ8899-3-3-3-311100011-1-1-1-1110000−9i−9i3i3i3i3i−i−i−i000−i−iiiii−i−i0000-9-93333-1-1-1000-1-11111-1-100009i9i−3i−3i−3i−3iiii000ii−i−i−i−iii0000
χ8999-3-3-3-3111000-1-11111-1-10000−9i−9i3i3i3i3i−i−i−i000ii−i−i−i−iii0000-9-93333-1-1-100011-1-1-1-11100009i9i−3i−3i−3i−3iiii000−i−iiiii−i−i0000
χ909-39-3-31-3110001-11-1-11-110000−9i3i−9i3i3i−i3i−i−i000−ii−iii−ii−i0000-93-933-13-1-1000-11-111-11-100009i−3i9i−3i−3ii−3iii000i−ii−i−ii−ii0000
χ919-39-3-31-311000-11-111-11-10000−9i3i−9i3i3i−i3i−i−i000i−ii−i−ii−ii0000-93-933-13-1-10001-11-1-11-1100009i−3i9i−3i−3ii−3iii000−ii−iii−ii−i0000
χ929-3-391-3-3110001-1-111-1-110000−9i3i3i−9i−i3i3i−i−i000−iii−i−iii−i0000-933-9-133-1-1000-111-1-111-100009i−3i−3i9ii−3i−3iii000i−i−iii−i−ii0000
χ939-3-391-3-311000-111-1-111-10000−9i3i3i−9i−i3i3i−i−i000i−i−iii−i−ii0000-933-9-133-1-10001-1-111-1-1100009i−3i−3i9ii−3i−3iii000−iii−i−iii−i0000
χ949-3-3-31115-30001-1-1-1111-10000−9i3i3i3i−i−i−i−5i3i000−iiii−i−i−ii0000-9333-1-1-1-53000-1111-1-1-1100009i−3i−3i−3iiii5i−3i000i−i−i−iiii−i0000
χ959-3-3-31115-3000-1111-1-1-110000−9i3i3i3i−i−i−i−5i3i000i−i−i−iiii−i0000-9333-1-1-1-530001-1-1-1111-100009i−3i−3i−3iiii5i−3i000−iiii−i−i−ii0000
χ9618-6-6-6222-62000000000000000−18i6i6i6i−2i−2i−2i6i−2i000000000000000-18666-2-2-26-200000000000000018i−6i−6i−6i2i2i2i−6i2i000000000000000

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