Finite Group Databasebeta

← Group #10696041

Character table — Group #10696041

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order12224444223446661212121244446612121212121244448888121212121212121212122424242424242424882424242444444444888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ922222222222222222222-2-2-2-22222-2-2-2-200000000-2-20000000000000000000000000022-2-2000000
χ1022222222222222222222-2-2-2-22222-2-2-2-200000000-2-200000000000000000000000000-2-222000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2111100000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-2111100000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-100000000000000
χ1522222222-2-22-2-222222222-22-2-2-2-2-22222000022-2-2-2-2000000002222-2-2-2-200000000000000000000
χ1622222222-2-22-2-222222222-22-2-2-2-2-222220000-2-222-2-200000000-2-2-2-2222200000000000000000000
χ1722222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2000000002200000000000000000000000000000022-2-200
χ1822222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000000022000000000000000000000000000000-2-22200
χ1922222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-211−i3−i3−i3−i3i3i3i3i3-1-1-1-1111100−i3−i3i3i300000000000000
χ2022222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-211i3i3i3i3−i3−i3−i3−i3-1-1-1-1111100i3i3−i3−i300000000000000
χ2122222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-22211−i3−i3−i3−i3i3i3i3i31111-1-1-1-100i3i3−i3−i300000000000000
χ2222222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-22211i3i3i3i3−i3−i3−i3−i31111-1-1-1-100−i3−i3i3i300000000000000
χ232222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-222-2-200002-222-2-222-2-20000000000000000000000000000
χ242222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-2-2-22200002-2-2-222-2-2220000000000000000000000000000
χ252222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22200000000-22000000000000000000000022-2-20000000000
χ262222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22200000000-220000000000000000000000-2-2220000000000
χ272222-2-2-2-222-1-2-2-1-1-111112-2-22-1-111-1-11122-2-20000-11-1-111-1-11133−3−333−3−3003−33−300000000000000
χ282222-2-2-2-222-1-2-2-1-1-111112-2-22-1-111-1-11122-2-20000-11-1-111-1-111−3−333−3−33300−33−3300000000000000
χ292222-2-2-2-222-1-2-2-1-1-111112-2-22-1-111-1-111-2-2220000-1111-1-111-1-133−3−333−3−300−33−3300000000000000
χ302222-2-2-2-222-1-2-2-1-1-111112-2-22-1-111-1-111-2-2220000-1111-1-111-1-1−3−333−3−333003−33−300000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-2200000000000000002i−2i2i−2i−2i2i00000000000000
χ322222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-200000000-220000000000000000−2i2i−2i2i2i−2i00000000000000
χ332222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-222000000002-200000000000000000000000000000000002-2
χ342222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-222000000002-20000000000000000000000000000000000-22
χ352222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1−i3−i3i3i3i3i3−i3−i333−3−3−3−3332i−2i−iii−i00000000000000
χ362222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1−i3−i3i3i3i3i3−i3−i3−3−33333−3−3−2i2ii−i−ii00000000000000
χ372222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1i3i3−i3−i3−i3−i3i3i333−3−3−3−333−2i2ii−i−ii00000000000000
χ382222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-1-1-111000000001-1i3i3−i3−i3−i3−i3i3i3−3−33333−3−32i−2i−iii−i00000000000000
χ3922-2-2-2-2222-222-22-2-2-2-22200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000000000002-2−i2i2−i2i200
χ4022-2-2-2-2222-222-22-2-2-2-22200002-22-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000-22i2−i2i2−i200
χ4122-2-2-2-2222-222-22-2-2-2-22200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000000000002-2i2−i2i2−i200
χ4222-2-2-2-2222-222-22-2-2-2-22200002-22-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000000000-22−i2i2−i2i200
χ4322-2-2-2-222-222-222-2-2-2-2220000-22-2200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200000000002-200−i2i2i2−i200
χ4422-2-2-2-222-222-222-2-2-2-2220000-22-2200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000-2200i2−i2−i2i200
χ4522-2-2-2-222-222-222-2-2-2-2220000-22-2200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200000000002-200i2−i2−i2i200
χ4622-2-2-2-222-222-222-2-2-2-2220000-22-2200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000-2200−i2i2i2−i200
χ474444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000022000000000000000000000000000000000000
χ4844444444-4-4-2-4-4-2-2-2-2-2-2-2-44-442222222200000000-2-2000000000000000000000000000000000000
χ494444-4-4-4-444-2-4-4-2-2-22222-444-4-2-22222-2-2000000002-2000000000000000000000000000000000000
χ504444-4-4-4-4-4-4-244-2-2-22222-4-44422-2-222-2-200000000-22000000000000000000000000000000000000
χ5144-4-444-4-44-44-444-4-444-4-400004-4-4400000000000000000000000000000000000000000000000000
χ5244-4-444-4-44-4-2-44-222-2-2220000-222-20000000000000000000000i6−i6−i6i6i6−i6−i6i600000000000000000000
χ5344-4-444-4-44-4-2-44-222-2-2220000-222-20000000000000000000000−i6i6i6−i6−i6i6i6−i600000000000000000000
χ5444-4-444-4-4-4444-44-4-444-4-40000-444-400000000000000000000000000000000000000000000000000
χ5544-4-444-4-4-44-24-4-222-2-22200002-2-220000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000
χ5644-4-444-4-4-44-24-4-222-2-22200002-2-220000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000
χ5744-4-4-4-4444-4-24-4-22222-2-20000-22-2200000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i200000000000000000000
χ5844-4-4-4-4444-4-24-4-22222-2-20000-22-22000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i200000000000000000000
χ5944-4-4-4-444-44-2-44-22222-2-200002-22-200000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i200000000000000000000
χ6044-4-4-4-444-44-2-44-22222-2-200002-22-2000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i200000000000000000000
χ614-44-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000002-22i−2i0000002-22i−2i2-22i−2i0000000000000000000000000000
χ624-44-44i−4i4i−4i00400-44-44i−4i4i−4i000000000000-22−2i2i000000-22−2i2i-22−2i2i0000000000000000000000000000
χ634-44-44i−4i4i−4i00-2002-22−2i2i−2i2i00000000−2i32i323−232-22i−2i000000−1−i31+i32ζ22−2ζ22−1+i31−i32ζ14−2ζ140000000000000000000000000000
χ644-44-44i−4i4i−4i00-2002-22−2i2i−2i2i00000000−2i32i323−23-22−2i2i0000001+i3−1−i3−2ζ222ζ221−i3−1+i3−2ζ142ζ140000000000000000000000000000
χ654-44-44i−4i4i−4i00-2002-22−2i2i−2i2i000000002i3−2i3−23232-22i−2i000000−1+i31−i32ζ14−2ζ14−1−i31+i32ζ22−2ζ220000000000000000000000000000
χ664-44-44i−4i4i−4i00-2002-22−2i2i−2i2i000000002i3−2i3−2323-22−2i2i0000001−i3−1+i3−2ζ142ζ141+i3−1−i3−2ζ222ζ220000000000000000000000000000
χ674-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000002-2−2i2i0000002-2−2i2i2-2−2i2i0000000000000000000000000000
χ684-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i000000000000-222i−2i000000-222i−2i-222i−2i0000000000000000000000000000
χ694-44-4−4i4i−4i4i00-2002-222i−2i2i−2i00000000−2i32i3−23232-2−2i2i000000−1−i31+i3−2ζ222ζ22−1+i31−i3−2ζ142ζ140000000000000000000000000000
χ704-44-4−4i4i−4i4i00-2002-222i−2i2i−2i00000000−2i32i3−2323-222i−2i0000001+i3−1−i32ζ22−2ζ221−i3−1+i32ζ14−2ζ140000000000000000000000000000
χ714-44-4−4i4i−4i4i00-2002-222i−2i2i−2i000000002i3−2i323−232-2−2i2i000000−1+i31−i3−2ζ142ζ14−1−i31+i3−2ζ222ζ220000000000000000000000000000
χ724-44-4−4i4i−4i4i00-2002-222i−2i2i−2i000000002i3−2i323−23-222i−2i0000001−i3−1+i32ζ14−2ζ141+i3−1−i32ζ22−2ζ220000000000000000000000000000
χ734-4-444i−4i−4i4i00400-4-444i−4i−4i4i000000000000000000000000000000000000000000002i−2i2-20000000000
χ744-4-444i−4i−4i4i00400-4-444i−4i−4i4i00000000000000000000000000000000000000000000−2i2i-220000000000
χ754-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i000000000000000000000000000000000000000000002i−2i-220000000000
χ764-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i00000000000000000000000000000000000000000000−2i2i2-20000000000
χ778-8-888i−8i−8i8i00-40044-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i8i−8i00-40044-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000

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