Finite Group Databasebeta

← Group #11787642

Character table — Group #11787642

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222222222444444444444444444888888888888888888888812121212121212121212121212121212121212122424242424242424242424242424363636367272
order1244222334446666121212121212366666666121212121212121212246666666666121212121212121212122244888888882424242424242424668812122424242424242424888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111111111-1-1
χ911-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-111-11111-1-11111-1-1-1-111-1-1-1-11-11-1ii−i−iii−i−iiiii−i−i−i−i1-11-11-1ii−i−i11-1-1ii−i−ii−i
χ1011-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-111-11111-1-11111-1-1-1-111-1-1-1-11-11-1−i−iii−i−iii−i−i−i−iiiii1-11-11-1−i−iii11-1-1−i−iii−ii
χ1111-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-111-11111-1-11111-1-1-1-111-1-1-1-1-11-11ii−i−iii−i−iiiii−i−i−i−i-11-11-11ii−i−i-1-111−i−iii−ii
χ1211-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-111-11111-1-11111-1-1-1-111-1-1-1-1-11-11−i−iii−i−iii−i−i−i−iiiii-11-11-11−i−iii-1-111ii−i−ii−i
χ1311-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111111111111-11-1ii−i−i−i−iii−i−i−i−iiiii1-1-111-1ii−i−i-1-111ii−i−i−ii
χ1411-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-111111111111-11-1−i−iiiii−i−iiiii−i−i−i−i1-1-111-1−i−iii-1-111−i−iiii−i
χ1511-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111111111-11-11ii−i−i−i−iii−i−i−i−iiiii-111-1-11ii−i−i11-1-1−i−iiii−i
χ1611-1-11-1-11111-11111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111111111-11-11−i−iiiii−i−iiiii−i−i−i−i-111-1-11−i−iii11-1-1ii−i−i−ii
χ1722222222-1222222-1-1-12222-122-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000000000000000-1-122-1-10000-1-1-1-1000000
χ1822222222-1222222-1-1-12222-122-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2000000000000000011-2-21100001111000000
χ1922222222-1222222-1-1-12222-122-1-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-211-1-11111-2-211-1-1111122220000000000000000-1-1-2-2-1-100001111000000
χ2022222222-1222222-1-1-12222-122-1-1-1-1-1-122-1-1-1-1-1-1-1-2-2-2-211-1-11111-2-211-1-11111-2-2-2-200000000000000001122110000-1-1-1-1000000
χ212222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000022222222-1-1-1-1-1-1-1-1000000-1-1-1-10000000000
χ222222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-2-2-2-2-21111111100000011110000000000
χ232222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-12-2-211-2-2-1-1111111-2-2-1-1111100002222-2-2-2-211111111000000-1-1-1-10000000000
χ242222222-12222-1-1-1222-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-12-2-211-2-2-1-1111111-2-2-1-111110000-2-2-2-22222-1-1-1-1-1-1-1-100000011110000000000
χ2522222-2-222-2-2222222222222-2-22-2-2222-2-2-222222-2000000-2-200000000-2-2000000002-22-20000000000000000002-22-20000000000
χ2622222-2-222-2-2222222222222-2-22-2-2222-2-2-222222-2000000-2-200000000-2-200000000-22-22000000000000000000-22-220000000000
χ2722222-2-2-12-2-22-1-1-1222-1-1-1-1-1112-2-2-1-1-111-22-1-1-1-1-200−i3i30011−i3−i3i3i3−i3i30011−i3−i3i3i300002-22-20000−i3−i3i3i3−i3−i3i3i3000000-11-110000000000
χ2822222-2-2-12-2-22-1-1-1222-1-1-1-1-1112-2-2-1-1-111-22-1-1-1-1-200−i3i30011−i3−i3i3i3−i3i30011−i3−i3i3i30000-22-220000i3i3−i3−i3i3i3−i3−i30000001-11-10000000000
χ2922222-2-2-12-2-22-1-1-1222-1-1-1-1-1112-2-2-1-1-111-22-1-1-1-1-200i3−i30011i3i3−i3−i3i3−i30011i3i3−i3−i300002-22-20000i3i3−i3−i3i3i3−i3−i3000000-11-110000000000
χ3022222-2-2-12-2-22-1-1-1222-1-1-1-1-1112-2-2-1-1-111-22-1-1-1-1-200i3−i30011i3i3−i3−i3i3−i30011i3i3−i3−i30000-22-220000−i3−i3i3i3−i3−i3i3i30000001-11-10000000000
χ312222-22-222-22-2-2-2222222-2-222-2-22-2-2-222-2-2-222-2-220000002-2000000002-200002-2-2200000000000000002-200-2200000000000000
χ322222-22-222-22-2-2-2222222-2-222-2-22-2-2-222-2-2-222-2-220000002-2000000002-20000-222-20000000000000000-22002-200000000000000
χ332222-22-22-1-22-2-2-22-1-1-122-2-2-12-21-1111-12-211-1-111-10000−i3i3-11−i3i3−i3i300−i3i3-11−i3i3−i3i32-2-220000000000000000-11001-10000−i3i3−i3i3000000
χ342222-22-22-1-22-2-2-22-1-1-122-2-2-12-21-1111-12-211-1-111-10000−i3i3-11−i3i3−i3i300−i3i3-11−i3i3−i3i3-222-200000000000000001-100-110000i3−i3i3−i3000000
χ352222-22-22-1-22-2-2-22-1-1-122-2-2-12-21-1111-12-211-1-111-10000i3−i3-11i3−i3i3−i300i3−i3-11i3−i3i3−i32-2-220000000000000000-11001-10000i3−i3i3−i3000000
χ362222-22-22-1-22-2-2-22-1-1-122-2-2-12-21-1111-12-211-1-111-10000i3−i3-11i3−i3i3−i300i3−i3-11i3−i3i3−i3-222-200000000000000001-100-110000−i3i3−i3i3000000
χ372222-2-22222-2-2-2-2222222-2-22-22-2-22-2-22-222-222-2-2-2000000-2200000000-22000000000000000000000000000000000000002-22-200
χ382222-2-22222-2-2-2-2222222-2-22-22-2-22-2-22-222-222-2-2-2000000-2200000000-2200000000000000000000000000000000000000-22-2200
χ3922-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000002200000000-2-2000000002i−2i−2i2i0000000000000000002i−2i−2i2i0000000000
χ4022-2-222222-2-2-22222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000002200000000-2-200000000−2i2i2i−2i000000000000000000−2i2i2i−2i0000000000
χ4122-2-2222-12-2-2-2-1-1-12-2-21111-1-1-1222-1-1-111-2-21111-200−i3i300-1-1−i3−i3i3i3i3−i30011i3i3−i3−i300002i−2i−2i2i000033−3−3−3−333000000−iii−i0000000000
χ4222-2-2222-12-2-2-2-1-1-12-2-21111-1-1-1222-1-1-111-2-21111-200−i3i300-1-1−i3−i3i3i3i3−i30011i3i3−i3−i30000−2i2i2i−2i0000−3−33333−3−3000000i−i−ii0000000000
χ4322-2-2222-12-2-2-2-1-1-12-2-21111-1-1-1222-1-1-111-2-21111-200i3−i300-1-1i3i3−i3−i3−i3i30011−i3−i3i3i300002i−2i−2i2i0000−3−33333−3−3000000−iii−i0000000000
χ4422-2-2222-12-2-2-2-1-1-12-2-21111-1-1-1222-1-1-111-2-21111-200i3−i300-1-1i3i3−i3−i3−i3i30011−i3−i3i3i30000−2i2i2i−2i000033−3−3−3−333000000i−i−ii0000000000
χ4522-2-22-2-22-122-2222-111-2-2-2-2-1-2-2-111-1-1-122-111111-12-222-1-111-1-1-1-1-2-211-1-111112-22-20000000000000000-112-2-110000-1-111000000
χ4622-2-22-2-22-122-2222-111-2-2-2-2-1-2-2-111-1-1-122-111111-12-222-1-111-1-1-1-1-2-211-1-11111-22-2200000000000000001-1-221-1000011-1-1000000
χ4722-2-22-2-22-122-2222-111-2-2-2-2-1-2-2-111-1-1-122-111111-1-22-2-21111111122-1-1-1-1-1-1-1-12-22-20000000000000000-11-22-11000011-1-1000000
χ4822-2-22-2-22-122-2222-111-2-2-2-2-1-2-2-111-1-1-122-111111-1-22-2-21111111122-1-1-1-1-1-1-1-1-22-2200000000000000001-12-21-10000-1-111000000
χ4922-2-22-2-2-1222-2-1-1-12-2-21111-1112-2-2-1-1-1-1-12-2111122-2-1-12211-1-1-1-111-2-2-1-1111100002i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000−i−iii0000000000
χ5022-2-22-2-2-1222-2-1-1-12-2-21111-1112-2-2-1-1-1-1-12-2111122-2-1-12211-1-1-1-111-2-2-1-111110000−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000ii−i−i0000000000
χ5122-2-22-2-2-1222-2-1-1-12-2-21111-1112-2-2-1-1-1-1-12-211112-2211-2-2111111-1-122-1-1-1-1-1-100002i2i−2i−2i−2i−2i2i2iiiii−i−i−i−i000000−i−iii0000000000
χ5222-2-22-2-2-1222-2-1-1-12-2-21111-1112-2-2-1-1-1-1-12-211112-2211-2-2111111-1-122-1-1-1-1-1-10000−2i−2i2i2i2i2i−2i−2i−i−i−i−iiiii000000ii−i−i0000000000
χ5322-2-2-22-2222-22-2-222-2-2-2-22222-2-22-2-2-22-2222-2-222-20000002-200000000-22000000000000000000000000000000000000002i−2i−2i2i00
χ5422-2-2-22-2222-22-2-222-2-2-2-22222-2-22-2-2-22-2222-2-222-20000002-200000000-2200000000000000000000000000000000000000−2i2i2i−2i00
χ5522-2-2-2-2222-222-2-222-2-2-2-2222-22-2-22-2-222-2-22-2-2222000000-22000000002-2000022-2-200000000000000002200-2-200000000000000
χ5622-2-2-2-2222-222-2-222-2-2-2-2222-22-2-22-2-222-2-22-2-2222000000-22000000002-20000-2-2220000000000000000-2-2002200000000000000
χ5722-2-2-2-222-1-222-2-22-111-2-222-1-2211-111-12-21-111-1-1-10000−i3i31-1−i3i3−i3i300i3−i3-11i3−i3i3−i322-2-20000000000000000-1-100110000−i3i3i3−i3000000
χ5822-2-2-2-222-1-222-2-22-111-2-222-1-2211-111-12-21-111-1-1-10000−i3i31-1−i3i3−i3i300i3−i3-11i3−i3i3−i3-2-22200000000000000001100-1-10000i3−i3−i3i3000000
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χ614444444-2-2444-2-2-2-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-2-21111-244-2-2-2-2111111-2-2-2-21111110000000000000000000000000000000000000000
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χ8444-4-4-4-44-2-2-44422-2-22222-2-212-222-2-1-11-222-2-1-111-200002i3−2i3-11−i3i3−i3i300−2i32i31-1i3−i3i3−i30000000000000000000000000000000000000000
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χ874-44i−4i000-24000−2i32i32-44i−4i−2i2i23−23-200000−2i32i320000−2i2i23−2300000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ500000000000000000000
χ884-44i−4i000-24000−2i32i32-44i−4i−2i2i23−23-200000−2i32i320000−2i2i23−230000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ500000000000000000000
χ894-44i−4i000-240002i3−2i32-44i−4i−2i2i−2323-2000002i3−2i320000−2i2i−232300000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ1300000000000000000000
χ904-44i−4i000-240002i3−2i32-44i−4i−2i2i−2323-2000002i3−2i320000−2i2i−23230000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ1300000000000000000000
χ914-4−4i4i0004400000-4-4−4i4i−4i4i0040000000-40000−4i4i000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ924-4−4i4i0004400000-4-4−4i4i−4i4i0040000000-40000−4i4i0000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ934-4−4i4i000-24000−2i32i32-4−4i4i2i−2i−2323-200000−2i32i3200002i−2i−23230000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ2300000000000000000000
χ944-4−4i4i000-24000−2i32i32-4−4i4i2i−2i−2323-200000−2i32i3200002i−2i−232300000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ2300000000000000000000
χ954-4−4i4i000-240002i3−2i32-4−4i4i2i−2i23−23-2000002i3−2i3200002i−2i23−230000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ700000000000000000000
χ964-4−4i4i000-240002i3−2i32-4−4i4i2i−2i23−23-2000002i3−2i3200002i−2i23−2300000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ700000000000000000000
χ978-88i−8i0008-400000-84−4i4i8i−8i00-4000000040000−4i4i00000000000000000000000000000000000000000000000000000000000000000
χ988-88i−8i000-4-4000−4i34i344−4i4i−4i4i43−432000002i3−2i3-200002i−2i−2323000000000000000000000000000000000000000000000000000000000000000
χ998-88i−8i000-4-40004i3−4i344−4i4i−4i4i−4343200000−2i32i3-200002i−2i23−23000000000000000000000000000000000000000000000000000000000000000
χ1008-8−8i8i0008-400000-844i−4i−8i8i00-40000000400004i−4i00000000000000000000000000000000000000000000000000000000000000000
χ1018-8−8i8i000-4-4000−4i34i3444i−4i4i−4i−43432000002i3−2i3-20000−2i2i23−23000000000000000000000000000000000000000000000000000000000000000
χ1028-8−8i8i000-4-40004i3−4i3444i−4i4i−4i43−43200000−2i32i3-20000−2i2i−2323000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.