Finite Group Databasebeta

← Group #11779877

Character table — Group #11779877

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222244444444444444444888888888888888888888888121224242424242424242424242424363636363636484848484872
order122233444466666634666121212121212121212121212881212121212122424242424242424242424242424242444222668812122424242444888846612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ5111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-1-1-1-111-1-11
χ6111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111111-1-11111-1-1-1-1-1-1
χ7111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ8111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-1111
χ92222222-22-22222222-22222-2-2-22222222-200-2-2-2-2-2-2000000000000000022-200-2-200220000000000000000
χ102222222-22-22222222-22222-2-2-22222222-200-2-2-2-2-2-20000000000000000-2-22002200-2-20000000000000000
χ11222222-22-222222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-2000000000000000000000000000000022000000000-2
χ12222222-22-222222222-2222-2222-2-2-2-2-2-2-2200-2-222-2-20000000000000000000000000000000-2-20000000002
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-22200000000000000000002-2000000000000000002-2000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-20022-2-2220000000000000000000-2200000000000000000-22000
χ1522222-122222-1-1-122-12-1-1-1-1-1222-1-1-12-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100022002200-1-1-1-10000000-1-1000
χ1622222-122222-1-1-122-12-1-1-1-1-1222-1-1-12-1-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000-2-200-2-2001111000000011000
χ1722222-122222-1-1-122-12-1-1-1-1-1222-1-1-12-1-1-1-2-22-1-1-1-1-1-2-2-2-21111111111110002200-2-20011110000000-1-1000
χ1822222-122222-1-1-122-12-1-1-1-1-1222-1-1-12-1-1-1-2-22-1-1-1-1-1-2-2-2-2111111111111000-2-2002200-1-1-1-1000000011000
χ1922222-1-2-2-2-22-1-1-122-12-1-1-111-2-2-2111-2111002-111-1-10000333333−3−3−3−3−3−30002-200000033−3−30000000-11000
χ2022222-1-2-2-2-22-1-1-122-12-1-1-111-2-2-2111-2111002-111-1-10000333333−3−3−3−3−3−3000-22000000−3−33300000001-1000
χ2122222-1-2-2-2-22-1-1-122-12-1-1-111-2-2-2111-2111002-111-1-10000−3−3−3−3−3−33333330002-2000000−3−3330000000-11000
χ2222222-1-2-2-2-22-1-1-122-12-1-1-111-2-2-2111-2111002-111-1-10000−3−3−3−3−3−3333333000-2200000033−3−300000001-1000
χ232222-122222-1222-1-1-12-1-1-122-1-1-1-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122200-1-100-1-10000000000200-1-10
χ242222-122222-1222-1-1-12-1-1-122-1-1-1-1-12-1-1-1222-12-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2001100110000000000-200110
χ252222-122222-1222-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-2-12-1-1-1-11111-2-21111-2-2111122200-1-100-1-10000000000-200110
χ262222-122222-1222-1-1-12-1-1-122-1-1-1-1-12-1-1-12-2-2-12-1-1-1-11111-2-21111-2-21111-2-2-2001100110000000000200-1-10
χ272222-122-22-2-1222-1-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i322-2001100-1-10000000000000−i3i30
χ282222-122-22-2-1222-1-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-21111−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2200-1-100110000000000000i3−i30
χ292222-122-22-2-1222-1-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i322-2001100-1-10000000000000i3−i30
χ302222-122-22-2-1222-1-1-1-2-1-1-12-211-1-1-12-1-1-1-2001-21111i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2200-1-100110000000000000−i3i30
χ3122-2-22220-20-22-2-2-22202-2-22000222-2-2-2-200000000000000000000000002i−2i00000−i2i22i−2i−i2i2−i2i20022−2−2000000
χ3222-2-22220-20-22-2-2-22202-2-22000222-2-2-2-200000000000000000000000002i−2i00000i2−i22i−2ii2−i2i2−i200−2−222000000
χ3322-2-22220-20-22-2-2-22202-2-22000222-2-2-2-20000000000000000000000000−2i2i00000−i2i2−2i2i−i2i2−i2i200−2−222000000
χ3422-2-22220-20-22-2-2-22202-2-22000222-2-2-2-20000000000000000000000000−2i2i00000i2−i2−2i2ii2−i2i2−i20022−2−2000000
χ352-2-2222020-2-2-22-22-220-22-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000002-2−i2i2−i2i2000000
χ362-2-2222020-2-2-22-22-220-22-2022-20000000-2−i2i2002-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000-22i2−i2i2−i2000000
χ372-2-2222020-2-2-22-22-220-22-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000002-2i2−i2i2−i2000000
χ382-2-2222020-2-2-22-22-220-22-2022-20000000-2i2−i2002-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000-22−i2i2−i2i2000000
χ3944444-24-44-44-2-2-244-2-4-2-2-2-22-4-44-2-2-24-2-2200-4222220000000000000000000000000000000000000000000
χ4044444-2-44-444-2-2-244-2-4-2-2-22-244-4222-422-200-42-2-2220000000000000000000000000000000000000000000
χ414444-24-44-44-2444-2-2-2-4-2-2-2-44-2-2222-42224002-4-2-2220000000000000000000000000000000000000000000
χ424444-24-4-4-4-4-2444-2-2-24-2-2-2-4-422222-4222-400-2422-2-20000000000000000000000000000000000000000000
χ434444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-244-2-21111-2-2-2-2-2-21111-2-21111000000000000000000000000000
χ444444-2-24444-2-2-2-2-2-214111-2-2-2-2-211-2-211-2-4-4-2-21111222222-1-1-1-122-1-1-1-1000000000000000000000000000
χ454444-2-24-44-4-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-1−2i3−2i32i32i300i3i3−i3−i300i3i3−i3−i3000000000000000000000000000
χ464444-2-24-44-4-2-2-2-2-2-21-4111-2222-211-2-21120022-1-1-1-12i32i3−2i3−2i300−i3−i3i3i300−i3−i3i3i3000000000000000000000000000
χ474444-2-2-44-44-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-10000003i3i−3i−3i00−3i−3i3i3i000000000000000000000000000
χ484444-2-2-44-44-2-2-2-2-2-21-41112-2-2-22-1-122-1-1-2002211-1-1000000−3i−3i3i3i003i3i−3i−3i000000000000000000000000000
χ494444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-11100002323−3−3−3−3−23−233333000000000000000000000000000
χ504444-2-2-4-4-4-4-2-2-2-2-2-21411122222-1-122-1-1200-2-2-1-1110000−23−2333332323−3−3−3−3000000000000000000000000000
χ5144-4-444-4040-44-4-4-44404-4-4-4000-4-4-444440000000000000000000000000000000000000000000000000000
χ5244-4-44-240-40-4-222-44-20-222-20004-2-22-42200000000000000000000000000000000−2i22i200i2−i2i2−i2000000000000
χ5344-4-44-240-40-4-222-44-20-222-20004-2-22-422000000000000000000000000000000002i2−2i200−i2i2−i2i2000000000000
χ5444-4-44-2-4040-4-222-44-20-2222000-422-24-2-2000000000000000000000000000000000000i6−i6−i6i6000000000000
χ5544-4-44-2-4040-4-222-44-20-2222000-422-24-2-2000000000000000000000000000000000000−i6i6i6−i6000000000000
χ5644-4-4-2440-4024-4-42-2-20-2224000-2-2-2-422200000000000000000000000004i−4i0000000−2i2i0000000000000000
χ5744-4-4-2440-4024-4-42-2-20-2224000-2-2-2-42220000000000000000000000000−4i4i00000002i−2i0000000000000000
χ5844-4-4-24-404024-4-42-2-20-222-40002224-2-2-2000000000000000000000000000000−2i32i300000000000000000000
χ5944-4-4-24-404024-4-42-2-20-222-40002224-2-2-20000000000000000000000000000002i3−2i300000000000000000000
χ604-44-44400004-4-44-4-440-4-44000000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ614-44-44400004-4-44-4-440-4-4400000000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ624-4-44440-404-4-44-44-440-44-40-4-44000000040000-44000000000000000000000000000000000000000000000
χ634-4-444-2040-4-42-224-4-202-220-24-400000002−2i22i200-2200−2i22i2−2i22i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000
χ644-4-444-2040-4-42-224-4-202-220-24-4000000022i2−2i200-22002i2−2i22i2−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000
χ654-4-444-20-404-42-224-4-202-2202-440000000-200002-2000000i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6000000000000000000000000000
χ664-4-444-20-404-42-224-4-202-2202-440000000-200002-2000000−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6000000000000000000000000000
χ674-4-44-24040-42-44-4-22-202-2204-220000000-4−2i22i200-2200i2−i2i2−i2−2i22i2i2−i2i2−i2−2i22i2i2−i2i2−i2000000000000000000000000000
χ684-4-44-24040-42-44-4-22-202-2204-220000000-42i2−2i200-2200−i2i2−i2i22i2−2i2−i2i2−i2i22i2−2i2−i2i2−i2i2000000000000000000000000000
χ694-4-44-240-4042-44-4-22-202-220-42-20000000400002-2006−6−66006−6−66006−6−66000000000000000000000000000
χ704-4-44-240-4042-44-4-22-202-220-42-20000000400002-200−666−600−666−600−666−6000000000000000000000000000
χ714-4-44-2-2040-422-22-2210-11-10-2-2203i−3i003i−3i2−2i22i2001-13i−3ii2−i2i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23000000000000000000000000000
χ724-4-44-2-2040-422-22-2210-11-10-2-2203i−3i003i−3i22i2−2i2001-13i−3i−i2i2−i2i2−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23000000000000000000000000000
χ734-4-44-2-2040-422-22-2210-11-10-2-220−3i3i00−3i3i2−2i22i2001-1−3i3ii2−i2i2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23000000000000000000000000000
χ744-4-44-2-2040-422-22-2210-11-10-2-220−3i3i00−3i3i22i2−2i2001-1−3i3i−i2i2−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−i2i22ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23000000000000000000000000000
χ754-4-44-2-20-40422-22-2210-11-1022-203i−3i003i−3i-20000-11−3i3i6−6−66−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000
χ764-4-44-2-20-40422-22-2210-11-1022-203i−3i003i−3i-20000-11−3i3i−666−6i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000
χ774-4-44-2-20-40422-22-2210-11-1022-20−3i3i00−3i3i-20000-113i−3i6−6−66i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000
χ784-4-44-2-20-40422-22-2210-11-1022-20−3i3i00−3i3i-20000-113i−3i−666−6−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000
χ7988-8-8-4-480-804-4444-4202-2-2-4000-42244-2-20000000000000000000000000000000000000000000000000000
χ8088-8-8-4-4-80804-4444-4202-2-240004-2-2-4-4220000000000000000000000000000000000000000000000000000
χ818-88-88-40000844-4-8-8-4044-4000000000000000000000000000000000000000000000000000000000000000
χ828-88-8-480000-4-8-8844-4044-4000000000000000000000000000000000000000000000000000000000000000
χ838-88-8-4-40000-444-44420-2-22000006i−6i00−6i6i0000000000000000000000000000000000000000000000000000
χ848-88-8-4-40000-444-44420-2-2200000−6i6i006i−6i0000000000000000000000000000000000000000000000000000

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