Finite Group Databasebeta

← Group #11771826

Character table — Group #11771826

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666666634444666666666121212124121212121212121212121212121212121212121212122244666688881212121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
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
χ51111111111111111111-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iii−i−i
χ61111111111111111111-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−iii
χ71111111111111111111-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i−i−iii
χ81111111111111111111-1-1-1-1111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1−i−iii1111−i−i−i−iiiiiii−i−i
χ9222222222222222222222-2-22222222222222-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222-2-222222222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-12-1-1-12-12-1-1-1-1222222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-1000000000000
χ122222222-12-1-1-12-12-1-1-1-1222222-1-1-1-1-1-1-122222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100001111000000000000
χ132222222-12-1-1-12-12-1-1-1-122-2-222-1-1-1-1-1-1-12222-2-1-1-2-211-2-211-1-1-1-1111111110000−i3−i3i3i30000−i3−i3i3i3000000000000
χ142222222-12-1-1-12-12-1-1-1-122-2-222-1-1-1-1-1-1-12222-2-1-1-2-211-2-211-1-1-1-1111111110000i3i3−i3−i30000i3i3−i3−i3000000000000
χ152222222-12-1-1-12-12-1-1-1-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-2-21122-1-111111111-1-1-1-10000−i3−i3i3i30000i3i3−i3−i3000000000000
χ162222222-12-1-1-12-12-1-1-1-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-2-21122-1-111111111-1-1-1-10000i3i3−i3−i30000−i3−i3i3i3000000000000
χ172222222-12-1-1-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221122-1-1-2-2111111-1-1-1-1111122-2-2-1-1-1-100001111000000000000
χ182222222-12-1-1-12-12-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-221122-1-1-2-2111111-1-1-1-11111-2-22211110000-1-1-1-1000000000000
χ19222222-12-1222-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-10000
χ20222222-12-1222-12-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000111111110000
χ21222222-12-1222-12-1222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-22211-2-211-2-2-1-1-1-1111111110000000000000000−i3−i3i3i3−i3−i3i3i30000
χ22222222-12-1222-12-1222-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-22211-2-211-2-2-1-1-1-1111111110000000000000000i3i3−i3−i3i3i3−i3−i30000
χ23222222-12-1222-12-1222-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-211-2-2-1-12211111111-1-1-1-1000000000000000033−3−3−3−3330000
χ24222222-12-1222-12-1222-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-211-2-2-1-12211111111-1-1-1-10000000000000000−3−33333−3−30000
χ25222222-12-1222-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-1-12211-2-21111-1-1-1-11111000000002i2i−2i−2i0000−i−i−i−iiiii0000
χ26222222-12-1222-12-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-2-1-12211-2-21111-1-1-1-1111100000000−2i−2i2i2i0000iiii−i−i−i−i0000
χ272-22-22-222-222-222-2-2-2-22002i−2i2-222-2-2-22-2000000000002i−2i2i−2i000000002i2i−2i−2i000000001+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ282-22-22-222-222-222-2-2-2-22002i−2i2-222-2-2-22-2000000000002i−2i2i−2i000000002i2i−2i−2i00000000−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ292-22-22-222-222-222-2-2-2-2200−2i2i2-222-2-2-22-200000000000−2i2i−2i2i00000000−2i−2i2i2i000000001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ302-22-22-222-222-222-2-2-2-2200−2i2i2-222-2-2-22-200000000000−2i2i−2i2i00000000−2i−2i2i2i00000000−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ312-22-22-2-12122-2-121-2-2-2-1002i−2i-11-1-1111-11−i3i3−i3i30003−300−ii2i−2i−i3−i3i3i333−3−3−i−iii000000001+i−1−i1−i−1+i0000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000
χ322-22-22-2-12122-2-121-2-2-2-1002i−2i-11-1-1111-11−i3i3−i3i30003−300−ii2i−2i−i3−i3i3i333−3−3−i−iii00000000−1−i1+i−1+i1−i0000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000
χ332-22-22-2-12122-2-121-2-2-2-1002i−2i-11-1-1111-11i3−i3i3−i3000−3300−ii2i−2ii3i3−i3−i3−3−333−i−iii000000001+i−1−i1−i−1+i0000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000
χ342-22-22-2-12122-2-121-2-2-2-1002i−2i-11-1-1111-11i3−i3i3−i3000−3300−ii2i−2ii3i3−i3−i3−3−333−i−iii00000000−1−i1+i−1+i1−i0000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000
χ352-22-22-2-12122-2-121-2-2-2-100−2i2i-11-1-1111-11−i3i3−i3i3000−3300i−i−2i2i−i3−i3i3i3−3−333ii−i−i000000001−i−1+i1+i−1−i0000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000
χ362-22-22-2-12122-2-121-2-2-2-100−2i2i-11-1-1111-11−i3i3−i3i3000−3300i−i−2i2i−i3−i3i3i3−3−333ii−i−i00000000−1+i1−i−1−i1+i0000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000
χ372-22-22-2-12122-2-121-2-2-2-100−2i2i-11-1-1111-11i3−i3i3−i30003−300i−i−2i2ii3i3−i3−i333−3−3ii−i−i000000001−i−1+i1+i−1−i0000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ140000
χ382-22-22-2-12122-2-121-2-2-2-100−2i2i-11-1-1111-11i3−i3i3−i30003−300i−i−2i2ii3i3−i3−i333−3−3ii−i−i00000000−1+i1−i−1−i1+i0000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000
χ392-22-2-2222-2-2-2-222-2-22222-200-22-2-222-22-222-2-202-2000000002-22-200000000000000000000000000000000−i2i2−i2i2
χ402-22-2-2222-2-2-2-222-2-22222-200-22-2-222-22-222-2-202-2000000002-22-200000000000000000000000000000000i2−i2i2−i2
χ412-22-2-2222-2-2-2-222-2-2222-2200-22-2-222-22-2-2-2220-2200000000-22-22000000000000000000000000000000002−2−22
χ422-22-2-2222-2-2-2-222-2-2222-2200-22-2-222-22-2-2-2220-2200000000-22-2200000000000000000000000000000000−222−2
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
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-4222222-2-2-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-211111112222422-2-2-2-22222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ474444-4-4444-4-444444-4-440000-4-4-4-4-4-44440000000000000000000000000000000000000000000000000000000
χ484444-4-44-2422-24-24-222-20000-4-42222-2-2-2000000000−2i32i300000000−2i32i3−2i32i300000000000000000000000000000000
χ494444-4-44-2422-24-24-222-20000-4-42222-2-2-20000000002i3−2i3000000002i3−2i32i3−2i300000000000000000000000000000000
χ504444-4-4-24-2-4-44-24-24-4-4-20000222222-2-2-2−2i32i32i3−2i300000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ514444-4-4-24-2-4-44-24-24-4-4-20000222222-2-2-22i3−2i3−2i32i3000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ524444-4-4-2-2-222-2-2-2-2-2221000022-1-1-1-1111−2i32i32i3−2i300000−2i32i30000i3−i3−i3i3i3−i3i3−i33-33-30000000000000000000000000000
χ534444-4-4-2-2-222-2-2-2-2-2221000022-1-1-1-1111−2i32i32i3−2i3000002i3−2i30000i3−i3−i3i3−i3i3−i3i3-33-330000000000000000000000000000
χ544444-4-4-2-2-222-2-2-2-2-2221000022-1-1-1-11112i3−2i3−2i32i300000−2i32i30000−i3i3i3−i3i3−i3i3−i3-33-330000000000000000000000000000
χ554444-4-4-2-2-222-2-2-2-2-2221000022-1-1-1-11112i3−2i3−2i32i3000002i3−2i30000−i3i3i3−i3−i3i3−i3i33-33-30000000000000000000000000000
χ5644-4-400444004-4-4-4-400400000000004-4-4000000000000000000000000000002i−2i000000002i−2i2i−2i000000000000
χ5744-4-400444004-4-4-4-400400000000004-4-400000000000000000000000000000−2i2i00000000−2i2i−2i2i000000000000
χ5844-4-4004-24−2i32i3-2-42-42−2i32i3-2000000−2i32i3−2i32i3-222000000000000000000000000000002i−2i000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ5944-4-4004-24−2i32i3-2-42-42−2i32i3-2000000−2i32i3−2i32i3-22200000000000000000000000000000−2i2i00000000−2ζ142ζ14−2ζ222ζ22000000000000
χ6044-4-4004-242i3−2i3-2-42-422i3−2i3-20000002i3−2i32i3−2i3-222000000000000000000000000000002i−2i000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ6144-4-4004-242i3−2i3-2-42-422i3−2i3-20000002i3−2i32i3−2i3-22200000000000000000000000000000−2i2i00000000−2ζ222ζ22−2ζ142ζ14000000000000
χ624-44-44-44-2-4-2-224-2-4222-2004i−4i4-4-2-2222-22000000000004i−4i−2i2i00000000−2i−2i2i2i0000000000000000000000000000
χ634-44-44-44-2-4-2-224-2-4222-200−4i4i4-4-2-2222-2200000000000−4i4i2i−2i000000002i2i−2i−2i0000000000000000000000000000
χ644-44-44-4-2-22-2-22-2-222221004i−4i-2211-1-1-11-1−2i32i3−2i32i300023−2300−2i2i−2i2ii3i3−i3−i3−3−333ii−i−i0000000000000000000000000000
χ654-44-44-4-2-22-2-22-2-222221004i−4i-2211-1-1-11-12i3−2i32i3−2i3000−232300−2i2i−2i2i−i3−i3i3i333−3−3ii−i−i0000000000000000000000000000
χ664-44-44-4-2-22-2-22-2-22222100−4i4i-2211-1-1-11-1−2i32i3−2i32i3000−2323002i−2i2i−2ii3i3−i3−i333−3−3−i−iii0000000000000000000000000000
χ674-44-44-4-2-22-2-22-2-22222100−4i4i-2211-1-1-11-12i3−2i32i3−2i300023−23002i−2i2i−2i−i3−i3i3i3−3−333−i−iii0000000000000000000000000000
χ684-44-4-444-2-42224-2-42-2-2-24-400-4422-2-22-2244-4-40-2200000000-22-22000000000000000000000000000000000000
χ694-44-4-444-2-42224-2-42-2-2-2-4400-4422-2-22-22-4-44402-2000000002-22-2000000000000000000000000000000000000
χ704-44-4-44-242-4-4-4-242-444-24-4002-222-2-22-22-2-22204-400000000-22-22000000000000000000000000000000000000
χ714-44-4-44-242-4-4-4-242-444-2-44002-222-2-22-2222-2-20-44000000002-22-2000000000000000000000000000000000000
χ724-44-4-44-2-22222-2-222-2-214-4002-2-1-111-11-1-2-2220-22000000001-11-13i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ734-44-4-44-2-22222-2-222-2-214-4002-2-1-111-11-1-2-2220-22000000001-11-1−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ744-44-4-44-2-22222-2-222-2-21-44002-2-1-111-11-122-2-202-200000000-11-113i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ754-44-4-44-2-22222-2-222-2-21-44002-2-1-111-11-122-2-202-200000000-11-11−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ764-4-440044-400-4-4-4440040000000000-4-440000000000000000000000000002-2002-22-200000000000000000000
χ774-4-440044-400-4-4-4440040000000000-4-44000000000000000000000000000-2200-22-2200000000000000000000
χ784-4-44004-2-4−2i32i32-424-22i3−2i3-2000000−2i32i32i3−2i322-20000000000000000000000000002-200−1−i31+i3−1+i31−i300000000000000000000
χ794-4-44004-2-4−2i32i32-424-22i3−2i3-2000000−2i32i32i3−2i322-2000000000000000000000000000-22001+i3−1−i31−i3−1+i300000000000000000000
χ804-4-44004-2-42i3−2i32-424-2−2i32i3-20000002i3−2i3−2i32i322-20000000000000000000000000002-200−1+i31−i3−1−i31+i300000000000000000000
χ814-4-44004-2-42i3−2i32-424-2−2i32i3-20000002i3−2i3−2i32i322-2000000000000000000000000000-22001−i3−1+i31+i3−1−i300000000000000000000
χ8288-8-800-48-40084-84-800-40000000000-4440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4−4i34i3-44444−4i34i320000002i3−2i32i3−2i32-2-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-4-44i3−4i3-444444i3−4i32000000−2i32i3−2i32i32-2-20000000000000000000000000000000000000000000000000000000
χ858-8-8800-48400-84-8-4800-4000000000044-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i3444-4-44i3−4i320000002i3−2i3−2i32i3-2-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i3444-4-4−4i34i32000000−2i32i32i3−2i3-2-220000000000000000000000000000000000000000000000000000000

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