Finite Group Databasebeta

← Group #10772496

Character table — Group #10772496

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222222224444444444444444444444444444444444444488881212121216161616161616161616242424242424242424244848
order122222344444444666121212124466888888881212121212121212121224242424242424242424242424242424444444442466121212121212244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1
χ91111-1-111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11-11111-1-1-1-11-11-11-111-1-11-1
χ101111-1-111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-11111-1-1-1-1-11-11-11-1-111-11
χ111111-1-111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111-111-1-1111-1-1-11
χ121111-1-111-1-1-1-1111111-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-1-1-1-111111-1-111-1-1-1111-1
χ131111-1-111-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-1-111-1-1111-11-11-1-1-111-11
χ141111-1-111-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-11-1-111-1-111-11-11-1111-1-11-1
χ151111-1-111-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-111-1-111-1-1-111-1-11-1-1111-1
χ161111-1-111-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-111-1-111-1-11-1-111-111-1-1-11
χ172222222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-222-2-2-2-200000000000000000000000000000000002-200-22000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2220000000022-2-222-2-2-2-20000000000000000000000000000000000-22002-2000000
χ192222222-2-2-222-2-2-22222222-222200000000-2-2-2-2-2-2-2-22200000000000000002-22-2000000002-22-200000000000000
χ202222222-2-2-222-2-2-22222222-222200000000-2-2-2-2-2-2-2-2220000000000000000-22-2200000000-22-2200000000000000
χ212222222-2-2-2-2-222-2222-2-2-2-22-22200000000-2-222-2-222-2-20000000000000000000022-2-2000000000000-2200000000
χ222222222-2-2-2-2-222-2222-2-2-2-22-22200000000-2-222-2-222-2-200000000000000000000-2-2220000000000002-200000000
χ23222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222000022-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-211111111000000000000
χ25222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122220000-2-211-1-1-1-111000000000000
χ26222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000022-1-11111-1-1000000000000
χ27222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-2000000−i3i3-11-11−i3i3000000000000
χ28222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22-1-10000000011111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-22000000i3−i31-11-1i3−i3000000000000
χ29222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-2000000i3−i3-11-11i3−i3000000000000
χ30222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22-1-10000000011111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-22000000−i3i31-11-1−i3i3000000000000
χ312222-2-222-2-222-2-2222222222-2-2-20000000022-2-2-2-222-2-200000000000000000000000000000000002200-2-2000000
χ322222-2-222-2-222-2-2222222222-2-2-20000000022-2-2-2-222-2-20000000000000000000000000000000000-2-20022000000
χ332222-2-22-2222222-22222222-2-2-2-200000000-2-22222-2-2-2-2000000000000000000002222000000000000-2-200000000
χ342222-2-22-2222222-22222222-2-2-2-200000000-2-22222-2-2-2-200000000000000000000-2-2-2-20000000000002200000000
χ352222-2-22-222-2-2-2-2-2222-2-2-2-222-2-200000000-2-2-2-222222200000000000000002-2-22000000002-2-2200000000000000
χ362222-2-22-222-2-2-2-2-2222-2-2-2-222-2-200000000-2-2-2-22222220000000000000000-222-200000000-222-200000000000000
χ372222-2-2-12-2-2-2-2222-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-200002-2-1-1-1-11111000000000000
χ382222-2-2-12-2-2-2-2222-1-1-11111-22112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-2220000-221111-1-1-1-1000000000000
χ392222-2-2-12-2-2-2-2222-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-20000-2211-1-111-1-1000000000000
χ402222-2-2-12-2-2-2-2222-1-1-11111-2211-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22200002-2-1-111-1-111000000000000
χ412222-2-2-1-222-2-2-2-2-2-1-1-111112211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-22000000−i3i3-111-1i3−i3000000000000
χ422222-2-2-1-222-2-2-2-2-2-1-1-111112211000000001111-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-2000000i3−i31-1-11−i3i3000000000000
χ432222-2-2-1-222-2-2-2-2-2-1-1-111112211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-22000000i3−i3-111-1−i3i3000000000000
χ442222-2-2-1-222-2-2-2-2-2-1-1-111112211000000001111-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-2000000−i3i31-1-11i3−i3000000000000
χ452-22-200202i−2i2i−2i2-202-2-22i2i−2i−2i0000−i2−i2i2i222−2−2002-22i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−200002i−2i2-200000000000000002−2−i2i200
χ462-22-200202i−2i2i−2i2-202-2-22i2i−2i−2i0000−i2−i2i2i222−2−2002-22i−2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−20000−2i2i-220000000000000000−22i2−i200
χ472-22-200202i−2i2i−2i2-202-2-22i2i−2i−2i0000i2i2−i2−i2−2−222002-22i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−22200002i−2i2-20000000000000000−22i2−i200
χ482-22-200202i−2i2i−2i2-202-2-22i2i−2i−2i0000i2i2−i2−i2−2−222002-22i−2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−2220000−2i2i-2200000000000000002−2−i2i200
χ492-22-20020−2i2i−2i2i2-202-2-2−2i−2i2i2i0000−i2−i2i2i2−2−222002-2−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−22200002i−2i-2200000000000000002−2i2−i200
χ502-22-20020−2i2i−2i2i2-202-2-2−2i−2i2i2i0000−i2−i2i2i2−2−222002-2−2i2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000−2i2i2-20000000000000000−22−i2i200
χ512-22-20020−2i2i−2i2i2-202-2-2−2i−2i2i2i0000i2i2−i2−i222−2−2002-2−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−200002i−2i-220000000000000000−22−i2i200
χ522-22-20020−2i2i−2i2i2-202-2-2−2i−2i2i2i0000i2i2−i2−i222−2−2002-2−2i2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−20000−2i2i2-200000000000000002−2i2−i200
χ53444444-2444-4-4-4-44-2-2-22222-4-4-2-200000000-2-222-2-222220000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-444-4-2-2-222224-4-2-20000000022-2-222-2-2220000000000000000000000000000000000000000000000
χ554444-4-4-24-4-444-4-44-2-2-2-2-2-2-24-42200000000-2-22222-2-2220000000000000000000000000000000000000000000000
χ564444-4-4-2-4444444-4-2-2-2-2-2-2-2-4-4220000000022-2-2-2-222220000000000000000000000000000000000000000000000
χ5744-4-40044000000-4-44-40000000022−2222−2200004-40000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ5844-4-40044000000-4-44-400000000−2222−222200004-400000000−2222−2222−2222−222200000000000000000000000000000000000000
χ5944-4-4004-40000004-44-4000000000000−2i22i2−2i22i2-440000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ6044-4-4004-40000004-44-40000000000002i2−2i22i2−2i2-4400000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ6144-4-400-24000000-42-2223−2323−23000022−2222−220000-22000023−2300−22−22−22−226−66−6−66−66000000000000000000000000000000
χ6244-4-400-24000000-42-2223−2323−230000−2222−22220000-22000023−23002−22−22−22−2−66−666−66−6000000000000000000000000000000
χ6344-4-400-24000000-42-22−2323−2323000022−2222−220000-220000−232300−22−22−22−22−66−666−66−6000000000000000000000000000000
χ6444-4-400-24000000-42-22−2323−23230000−2222−22220000-220000−2323002−22−22−22−26−66−6−66−66000000000000000000000000000000
χ6544-4-400-2-400000042-2223−2323−2300000000−2i22i2−2i22i22-20000−232300i6−i6i6−i6−i6i6−i6i6i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ6644-4-400-2-400000042-2223−2323−23000000002i2−2i22i2−2i22-20000−232300−i6i6−i6i6i6−i6i6−i6−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ6744-4-400-2-400000042-22−2323−232300000000−2i22i2−2i22i22-2000023−2300−i6i6−i6i6i6−i6i6−i6i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000
χ6844-4-400-2-400000042-22−2323−2323000000002i2−2i22i2−2i22-2000023−2300i6−i6i6−i6−i6i6−i6i6−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000
χ694-44-400404i−4i−4i4i-4404-4-4−4i−4i4i4i00000000000000-444i−4i00000000000000000000000000000000000000000000000000
χ704-44-40040−4i4i4i−4i-4404-4-44i4i−4i−4i00000000000000-44−4i4i00000000000000000000000000000000000000000000000000
χ714-44-400-204i−4i4i−4i4-40-222−2i−2i2i2i0000−2i2−2i22i22i22222−22−2200-22−2i2i0000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000000000000000
χ724-44-400-204i−4i4i−4i4-40-222−2i−2i2i2i00002i22i2−2i2−2i2−22−22222200-22−2i2i0000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000000000000000
χ734-44-400-204i−4i−4i4i-440-2222i2i−2i−2i000000000000002-2−2i2i000066−6−6−6−666−i6−i6i6i6i6i6−i6−i6000000000000000000000000000000
χ744-44-400-204i−4i−4i4i-440-2222i2i−2i−2i000000000000002-2−2i2i0000−6−66666−6−6i6i6−i6−i6−i6−i6i6i6000000000000000000000000000000
χ754-44-400-20−4i4i4i−4i-440-222−2i−2i2i2i000000000000002-22i−2i000066−6−6−6−666i6i6−i6−i6−i6−i6i6i6000000000000000000000000000000
χ764-44-400-20−4i4i4i−4i-440-222−2i−2i2i2i000000000000002-22i−2i0000−6−66666−6−6−i6−i6i6i6i6i6−i6−i6000000000000000000000000000000
χ774-44-400-20−4i4i−4i4i4-40-2222i2i−2i−2i0000−2i2−2i22i22i2−22−22222200-222i−2i0000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000000000000000
χ784-44-400-20−4i4i−4i4i4-40-2222i2i−2i−2i00002i22i2−2i2−2i22222−22−2200-222i−2i0000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000000000000000
χ794-4-444-4400000000-4-440000004-42i−2i−2i2i2i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ804-4-444-4400000000-4-440000004-4−2i2i2i−2i−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ814-4-444-4-20000000022-2−2i32i32i3−2i300-222i−2i−2i2i2i−2i−2i2i00000000−2i32i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000000000
χ824-4-444-4-20000000022-2−2i32i32i3−2i300-22−2i2i2i−2i−2i2i2i−2i00000000−2i32i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000000000
χ834-4-444-4-20000000022-22i3−2i3−2i32i300-222i−2i−2i2i2i−2i−2i2i000000002i3−2i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000000000
χ844-4-444-4-20000000022-22i3−2i3−2i32i300-22−2i2i2i−2i−2i2i2i−2i000000002i3−2i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000000000
χ854-4-44-44400000000-4-44000000-442i−2i−2i2i−2i2i2i−2i00000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ864-4-44-44400000000-4-44000000-44−2i2i2i−2i2i−2i−2i2i0000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ874-4-44-44-20000000022-2−2i32i32i3−2i3002-22i−2i−2i2i−2i2i2i−2i000000002i3−2i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22000000000000000000000000000000
χ884-4-44-44-20000000022-2−2i32i32i3−2i3002-2−2i2i2i−2i2i−2i−2i2i000000002i3−2i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22000000000000000000000000000000
χ894-4-44-44-20000000022-22i3−2i3−2i32i3002-22i−2i−2i2i−2i2i2i−2i00000000−2i32i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14000000000000000000000000000000
χ904-4-44-44-20000000022-22i3−2i3−2i32i3002-2−2i2i2i−2i2i−2i−2i2i00000000−2i32i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14000000000000000000000000000000

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