Finite Group Databasebeta

← Group #11778143

Character table — Group #11778143

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666634444666666666121212124121212121212121212121212121212121212121212122244444466661212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111-11-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-11-11-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-1-1-1-1111111-1-111-1-1-1-111
χ81111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1111-1-1-1-11111-1-111-1-11111-1-1
χ9222222222222222222222-2-22222222222222-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-22-2-2-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-1-1-1-12-1-1-1-122-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000022-1-1-1-1-1-1-1-1000000000000
χ122222222-1-1-1-12-1-1-1-122-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-211111111000000000000
χ132222222-1-1-1-12-1-1-1-122-122-2-222-1-1-1-1-1-1-12222-2-1-11111-2-2-2-2-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ142222222-1-1-1-12-1-1-1-122-122-2-222-1-1-1-1-1-1-12222-2-1-11111-2-2-2-2-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ152222222-1-1-1-12-1-1-1-122-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-11122-2-21111-1-1-1-11111220000-2-2-1-1-1-11111000000000000
χ162222222-1-1-1-12-1-1-1-122-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-11122-2-21111-1-1-1-11111-2-20000221111-1-1-1-1000000000000
χ172222222-1-1-1-12-1-1-1-122-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221111-1-1-2-22211111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ182222222-1-1-1-12-1-1-1-122-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221111-1-1-2-22211111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ19222222-12222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000000000-1-1-1-1-1-1-1-10000
χ20222222-12222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000111111110000
χ21222222-12222-12222-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-2-2-21111-1-1-1-1111111110000000000000000−i3i3−i3i3−i3i3−i3i30000
χ22222222-12222-12222-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-222-2-2-2-21111-1-1-1-1111111110000000000000000i3−i3i3−i3i3−i3i3−i30000
χ23222222-12222-12222-1-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-2-2-1-1111111-1-1-1-11111002-22-20000000000-1-111-1-1110000
χ24222222-12222-12222-1-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-2-2-1-1111111-1-1-1-1111100-22-22000000000011-1-111-1-10000
χ25222222-12222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-2-22211-1-111111111-1-1-1-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ26222222-12222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-2-22211-1-111111111-1-1-1-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ272222-2-2222-2-2222-2-2222002-2-2-22-2-2-2-22200000002-2002-200000022-2-2000000020-20000000000002200-2-20000
χ282222-2-2222-2-2222-2-2222002-2-2-22-2-2-2-22200000002-2002-200000022-2-20000000-202000000000000-2-200220000
χ292222-2-2222-2-2222-2-222200-22-2-22-2-2-2-2220000000-2200-22000000-2-22200000020-2000000000002200-2-2000000
χ302222-2-2222-2-2222-2-222200-22-2-22-2-2-2-2220000000-2200-22000000-2-222000000-20200000000000-2-20022000000
χ312222-2-2-122-2-2-122-2-2-1-1-1002-211-11111-1-1−i3−i3i3i30002-200-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i300020-20000000000−i3i3-1-1i3−i3110000
χ322222-2-2-122-2-2-122-2-2-1-1-1002-211-11111-1-1−i3−i3i3i30002-200-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i3000-2020000000000i3−i311−i3i3-1-10000
χ332222-2-2-122-2-2-122-2-2-1-1-1002-211-11111-1-1i3i3−i3−i30002-200-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i300020-20000000000i3−i3-1-1−i3i3110000
χ342222-2-2-122-2-2-122-2-2-1-1-1002-211-11111-1-1i3i3−i3−i30002-200-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i3000-2020000000000−i3i311i3−i3-1-10000
χ352222-2-2-122-2-2-122-2-2-1-1-100-2211-11111-1-1−i3−i3i3i3000-22001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i30020-200000000000-1-1−i3i311i3−i30000
χ362222-2-2-122-2-2-122-2-2-1-1-100-2211-11111-1-1−i3−i3i3i3000-22001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i300-2020000000000011i3−i3-1-1−i3i30000
χ372222-2-2-122-2-2-122-2-2-1-1-100-2211-11111-1-1i3i3−i3−i3000-22001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i30020-200000000000-1-1i3−i311−i3i30000
χ382222-2-2-122-2-2-122-2-2-1-1-100-2211-11111-1-1i3i3−i3−i3000-22001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i300-2020000000000011−i3i3-1-1i3−i30000
χ3922-2-2-2222-2-2-222-222-2-222-2002-2-222-2-22-22-22-202-2000000002-22-200000000000000000000000000000000−i2i2−i2i2
χ4022-2-2-2222-2-2-222-222-2-222-2002-2-222-2-22-22-22-202-2000000002-22-200000000000000000000000000000000i2−i2i2−i2
χ4122-2-2-2222-2-2-222-222-2-22-22002-2-222-2-22-2-22-220-2200000000-22-2200000000000000000000000000000000−i2i2i2−i2
χ4222-2-2-2222-2-2-222-222-2-22-22002-2-222-2-22-2-22-220-2200000000-22-2200000000000000000000000000000000i2−i2−i2i2
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-21111111-2-2-2-2-4-2-2222222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-422-2-222-2-222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-21111111222242222-2-222-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ474444-4-44-2-2224-2-22244-2004-4-4-4-22222-2-20000000-22004-4000000-2-22200000000000000000000000000000000
χ484444-4-44-2-2224-2-22244-200-44-4-4-22222-2-200000002-200-4400000022-2-200000000000000000000000000000000
χ494444-4-4-2-2-222-2-2-222-2-21004-4221-1-1-1-111−2i3−2i32i32i3000-2200-22−2i32i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-2-222-2-2-222-2-21004-4221-1-1-1-1112i32i3−2i3−2i3000-2200-222i3−2i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-2-222-2-2-222-2-2100-44221-1-1-1-111−2i3−2i32i32i30002-2002-22i3−2i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-222-2-2100-44221-1-1-1-1112i32i3−2i3−2i30002-2002-2−2i32i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ5344-4-44-444-44444-4-4-4-4-440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ5444-4-44-44-22-2-24-2222-4-4-20000-44222-2-2-2200000000023−2300000000000023−2323−230000000000000000000000000000
χ5544-4-44-44-22-2-24-2222-4-4-20000-44222-2-2-22000000000−2323000000000000−2323−23230000000000000000000000000000
χ5644-4-44-4-24-444-24-4-4-422-200002-2222-2-2-22−2i32i32i3−2i300000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ5744-4-44-4-24-444-24-4-4-422-200002-2222-2-2-222i3−2i3−2i32i3000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ5844-4-44-4-2-22-2-2-2-222222100002-2-1-1-1111-1−2i32i32i3−2i30000023−230000i3−i3−i3i33i−3i3i−3i−33−330000000000000000000000000000
χ5944-4-44-4-2-22-2-2-2-222222100002-2-1-1-1111-1−2i32i32i3−2i300000−23230000i3−i3−i3i3−3i3i−3i3i3−33−30000000000000000000000000000
χ6044-4-44-4-2-22-2-2-2-222222100002-2-1-1-1111-12i3−2i3−2i32i30000023−230000−i3i3i3−i3−3i3i−3i3i−33−330000000000000000000000000000
χ6144-4-44-4-2-22-2-2-2-222222100002-2-1-1-1111-12i3−2i3−2i32i300000−23230000−i3i3i3−i33i−3i3i−3i3−33−30000000000000000000000000000
χ6244-4-4-444-22224-22-2-2-4-4-24-4004-42-2-222-224-44-40-2200000000-22-22000000000000000000000000000000000000
χ6344-4-4-444-22224-22-2-2-4-4-2-44004-42-2-222-22-44-4402-2000000002-22-2000000000000000000000000000000000000
χ6444-4-4-44-24-4-4-4-24-44422-24-400-222-2-222-22-22-2204-400000000-22-22000000000000000000000000000000000000
χ6544-4-4-44-24-4-4-4-24-44422-2-4400-222-2-222-222-22-20-44000000002-22-2000000000000000000000000000000000000
χ6644-4-4-44-2-2222-2-22-2-22214-400-22-111-1-11-1-22-220-22000000001-11-13i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ6744-4-4-44-2-2222-2-22-2-22214-400-22-111-1-11-1-22-220-22000000001-11-1−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ6844-4-4-44-2-2222-2-22-2-2221-4400-22-111-1-11-12-22-202-200000000-11-113i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ6944-4-4-44-2-2222-2-22-2-2221-4400-22-111-1-11-12-22-202-200000000-11-11−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ704-44-40044400-4-4-4004-4400000040000-4-40000000000000000000000000000000002i−2i00002i−2i2i−2i000000000000
χ714-44-40044400-4-4-4004-4400000040000-4-4000000000000000000000000000000000−2i2i0000−2i2i−2i2i000000000000
χ724-44-4004-2-2−2i32i3-422−2i32i34-4-2000000-2−2i32i3−2i32i3220000000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ22000000000000
χ734-44-4004-2-2−2i32i3-422−2i32i34-4-2000000-2−2i32i3−2i32i322000000000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ22000000000000
χ744-44-4004-2-22i3−2i3-4222i3−2i34-4-2000000-22i3−2i32i3−2i3220000000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ14000000000000
χ754-44-4004-2-22i3−2i3-4222i3−2i34-4-2000000-22i3−2i32i3−2i322000000000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ14000000000000
χ764-4-440044-400-4-4400-444000000-40000-440000000000000000000000000002-20000002-22-20000000000000000
χ774-4-440044-400-4-4400-444000000-40000-44000000000000000000000000000-22000000-22-220000000000000000
χ784-4-44004-22−2i32i3-42-22i3−2i3-44-200000022i3−2i3−2i32i32-20000000000000000000000000002-2000000−1−i31+i3−1+i31−i30000000000000000
χ794-4-44004-22−2i32i3-42-22i3−2i3-44-200000022i3−2i3−2i32i32-2000000000000000000000000000-220000001+i3−1−i31−i3−1+i30000000000000000
χ804-4-44004-222i3−2i3-42-2−2i32i3-44-20000002−2i32i32i3−2i32-20000000000000000000000000002-2000000−1+i31−i3−1−i31+i30000000000000000
χ814-4-44004-222i3−2i3-42-2−2i32i3-44-20000002−2i32i32i3−2i32-2000000000000000000000000000-220000001−i3−1+i31+i3−1−i30000000000000000
χ828-88-800-488004-8-800-44-4000000-40000440000000000000000000000000000000000000000000000000000000
χ838-88-800-4-4-4−4i34i3444−4i34i3-44200000022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000
χ848-88-800-4-4-44i3−4i34444i3−4i3-4420000002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ858-8-8800-48-8004-88004-4-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i344-44i3−4i34-42000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i344-4−4i34i34-42000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000

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