Finite Group Databasebeta

← Group #10690280

Character table — Group #10690280

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12224444223446661212121244446612121212121244448888888812121212121212121212242424242424242444442424242424444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−iii−i−i
χ131111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111ii−i−i−i−iii1-1-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i-1111-1-1−i−iiiii−i−i
χ151111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i1-1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-1111-1-1111-1-1-1-111-1-11111-1-1-1-1-1-111−i−iiiii−i−i1-1-1-1-1-11111iiii−i−i−i−i-1-111−i−iii-1111-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-222-2-2000000000000-2-2000000000000000022220000-2-2000000000000
χ1822222222222222222222-2-2-2-222-2-222-2-2000000000000-2-20000000000000000-2-2-2-2000022000000000000
χ192222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ202222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ212222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ222222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2322222222-2-22-2-222222222-22-2-2-222-2-222000000000000-2-20000000000000000000000000000002-22-20000
χ2422222222-2-22-2-222222222-22-2-2-222-2-222000000000000-2-2000000000000000000000000000000-22-220000
χ2522222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-200002-22-2000022000000000000000000002-22-200000000000000
χ2622222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000-22-2200002200000000000000000000-22-2200000000000000
χ2722222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100002-22-20000-1-133−3−333−3−333−3−333−3−30000-11-1100000000000000
χ2822222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100002-22-20000-1-1−3−333−3−333−3−333−3−3330000-11-1100000000000000
χ2922222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111110000-22-220000-1-133−3−333−3−3−3−333−3−33300001-11-100000000000000
χ3022222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111110000-22-220000-1-1−3−333−3−33333−3−333−3−300001-11-100000000000000
χ312222-2-2-2-2222-2-2222-2-2-2-2-2-22222-2-2-2-222000000000000-22000000000000000022-2-20000-22000000000000
χ322222-2-2-2-2222-2-2222-2-2-2-2-2-22222-2-2-2-222000000000000-220000000000000000-2-22200002-2000000000000
χ332222-2-2-2-222-1-2-2-1-1-1111122-2-2-1-1-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii0000−i−iii00000000000000
χ342222-2-2-2-222-1-2-2-1-1-1111122-2-2-1-1-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000ii−i−i00000000000000
χ352222-2-2-2-222-1-2-2-1-1-1111122-2-2-1-1-1-11111-2-2222i2i−2i−2i−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i0000−i−iii00000000000000
χ362222-2-2-2-222-1-2-2-1-1-1111122-2-2-1-1-1-11111-2-222−2i−2i2i2i2i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000ii−i−i00000000000000
χ372222-2-2-2-2-2-2222222-2-2-2-22-2-22-2-22222-2-2000000000000-220000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-2222222-2-2-2-22-2-22-2-22222-2-2000000000000-22000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-2222200002i−2i−2i2i00002-2000000000000000000002i−2i−2i2i00000000000000
χ402222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-222220000−2i2i2i−2i00002-200000000000000000000−2i2i2i−2i00000000000000
χ412222-2-2-2-2-2-2-122-1-1-11111-222-21111-1-1-1-100002i−2i−2i2i0000-1133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000−iii−i00000000000000
χ422222-2-2-2-2-2-2-122-1-1-11111-222-21111-1-1-1-100002i−2i−2i2i0000-11−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000−iii−i00000000000000
χ432222-2-2-2-2-2-2-122-1-1-11111-222-21111-1-1-1-10000−2i2i2i−2i0000-1133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000i−i−ii00000000000000
χ442222-2-2-2-2-2-2-122-1-1-11111-222-21111-1-1-1-10000−2i2i2i−2i0000-11−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000i−i−ii00000000000000
χ4522-2-222-2-2-2222-22-2-2-2-2220000-22002-200000000002−22−200000000002−22−22−22−22i−2i2i−2i00000000000000−i2i2−i2i2
χ4622-2-222-2-2-2222-22-2-2-2-2220000-22002-200000000002−22−200000000002−22−22−22−2−2i2i−2i2i00000000000000i2−i2i2−i2
χ4722-2-222-2-2-2222-22-2-2-2-2220000-22002-20000000000−22−220000000000−22−22−22−222i−2i2i−2i00000000000000i2−i2i2−i2
χ4822-2-222-2-2-2222-22-2-2-2-2220000-22002-20000000000−22−220000000000−22−22−22−22−2i2i−2i2i00000000000000−i2i2−i2i2
χ4922-2-2-2-222-222-222-2-222-2-20000-2200-220000000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i22i−2i−2i2i00000000000000−222−2
χ5022-2-2-2-222-222-222-2-222-2-20000-2200-220000000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2−2i2i2i−2i000000000000002−2−22
χ5122-2-2-2-222-222-222-2-222-2-20000-2200-220000000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i22i−2i−2i2i000000000000002−2−22
χ5222-2-2-2-222-222-222-2-222-2-20000-2200-220000000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2−2i2i2i−2i00000000000000−222−2
χ534444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-222-2-2220000000000002200000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-2-2-2-2-2-2-24-44-422-2-222-2-20000000000002200000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-2-2-22222-4-444-2-22222-2-20000000000002-200000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-244-2-2-222224-4-4422-2-2-2-2220000000000002-200000000000000000000000000000000000000
χ5744-4-444-4-44-44-444-4-4-4-44400004-400-44000000000000000000000000000000000000000000000000000000
χ5844-4-444-4-44-4-2-44-22222-2-20000-22002-20000000000000000000000006−6−666−6−660000000000000000000000
χ5944-4-444-4-44-4-2-44-22222-2-20000-22002-2000000000000000000000000−666−6−666−60000000000000000000000
χ6044-4-444-4-4-44-24-4-22222-2-200002-200-22000000000022−2222−220000000000−22−22−22−220000000000000000000000
χ6144-4-444-4-4-44-24-4-22222-2-200002-200-220000000000−2222−222200000000002−22−22−22−20000000000000000000000
χ6244-4-4-4-4444-444-44-4-444-4-400004-4004-4000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-24-4-222-2-2220000-2200-22000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ6444-4-4-4-4444-4-24-4-222-2-2220000-2200-22000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ6544-4-4-4-444-44-2-44-222-2-22200002-2002-20000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ6644-4-4-4-444-44-2-44-222-2-22200002-2002-200000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ674-44-44i−4i4i−4i00400-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000002-22i−2i00000000
χ684-44-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000-22−2i2i00000000
χ694-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000002-2−2i2i00000000
χ704-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000-222i−2i00000000
χ714-4-444i−4i−4i4i00400-4-44−4i4i4i−4i0000000000002i−2i2-200000000002i−2i2i−2i2-22-2000000000000000000000000000000
χ724-4-444i−4i−4i4i00400-4-44−4i4i4i−4i000000000000−2i2i-220000000000−2i2i−2i2i-22-22000000000000000000000000000000
χ734-4-444i−4i−4i4i00-20022-22i−2i−2i2i00000023−2300−2i32i32i−2i2-20000000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−1−31+3−1+31−3000000000000000000000000000000
χ744-4-444i−4i−4i4i00-20022-22i−2i−2i2i00000023−2300−2i32i3−2i2i-220000000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ221+3−1−31−3−1+3000000000000000000000000000000
χ754-4-444i−4i−4i4i00-20022-22i−2i−2i2i000000−2323002i3−2i32i−2i2-20000000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−1+31−3−1−31+3000000000000000000000000000000
χ764-4-444i−4i−4i4i00-20022-22i−2i−2i2i000000−2323002i3−2i3−2i2i-220000000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ221−3−1+31+3−1−3000000000000000000000000000000
χ774-4-44−4i4i4i−4i00400-4-444i−4i−4i4i0000000000002i−2i-2200000000002i−2i2i−2i-22-22000000000000000000000000000000
χ784-4-44−4i4i4i−4i00400-4-444i−4i−4i4i000000000000−2i2i2-20000000000−2i2i−2i2i2-22-2000000000000000000000000000000
χ794-4-44−4i4i4i−4i00-20022-2−2i2i2i−2i00000023−23002i3−2i32i−2i-220000000000−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ221+3−1−31−3−1+3000000000000000000000000000000
χ804-4-44−4i4i4i−4i00-20022-2−2i2i2i−2i00000023−23002i3−2i3−2i2i2-20000000000ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−1−31+3−1+31−3000000000000000000000000000000
χ814-4-44−4i4i4i−4i00-20022-2−2i2i2i−2i000000−232300−2i32i32i−2i-220000000000ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ221−3−1+31+3−1−3000000000000000000000000000000
χ824-4-44−4i4i4i−4i00-20022-2−2i2i2i−2i000000−232300−2i32i3−2i2i2-20000000000−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−1+31−3−1−31+3000000000000000000000000000000
χ838-88-88i−8i8i−8i00-4004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i−8i8i00-4004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000

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