Finite Group Databasebeta

← Group #10696050

Character table — Group #10696050

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222244444444888888888888888816161616161616161616161624242424242424242424242424242424
order12224444223446661212121244446612124444121212121212121212121212448812121212242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ152222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000−i3−i3i3i3−i3−i3i3i30000000000000000
χ162222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000i3i3−i3−i3i3i3−i3−i30000000000000000
χ172222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3−i3i3i3i3i3−i3−i30000000000000000
χ182222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3i3−i3−i3−i3−i3i3i30000000000000000
χ1922222222-2-22-2-222222222-22-2-2-2-2-2000022-2-20000000000000000000000000000000022-2-2
χ2022222222-2-22-2-222222222-22-2-2-2-2-2000022-2-200000000000000000000000000000000-2-222
χ2122222222-2-22-2-22222222-22-22-2-2-2-20000-2-222000000000000000000000000000022-2-20000
χ2222222222-2-22-2-22222222-22-22-2-2-2-20000-2-2220000000000000000000000000000-2-2220000
χ232222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-200002-22-20000000000000000000022-2-2000000000000
χ242222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-200002-22-200000000000000000000-2-222000000000000
χ252222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-20000-22-2200000000000000000000000022-2-200000000
χ262222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-20000-22-22000000000000000000000000-2-22200000000
χ272222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22200002-2-2200000000002i−2i00002i−2i2i−2i0000000000000000
χ282222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22200002-2-220000000000−2i2i0000−2i2i−2i2i0000000000000000
χ292222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2220000-222-2000000002-2002-22-200000000000000000000
χ302222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2220000-222-200000000-2200-22-2200000000000000000000
χ312222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-10000-111-133−3−333−3−3002i−2i−i3i3i3−i3−ii−ii0000000000000000
χ322222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-10000-111-133−3−333−3−300−2i2ii3−i3−i3i3i−ii−i0000000000000000
χ332222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-10000-111-1−3−333−3−333002i−2ii3−i3−i3i3−ii−ii0000000000000000
χ342222-2-2-2-2-2-2-122-1-1-1111122-2-211-1-10000-111-1−3−333−3−33300−2i2i−i3i3i3−i3i−ii−i0000000000000000
χ352222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-100001-1-1133−3−3−3−3332-200-11-113−3−330000000000000000
χ362222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-100001-1-1133−3−3−3−333-22001-11-1−333−30000000000000000
χ372222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-100001-1-11−3−33333−3−32-200-11-11−333−30000000000000000
χ382222-2-2-2-2-2-2-122-1-1-11111-2-22211-1-100001-1-11−3−33333−3−3-22001-11-13−3−330000000000000000
χ3922-2-2-2-2222-222-22-2-2-2-22200002-22-2002i−2i000000002i−2i2i−2i00000000000000000000−i2i2−i2i22−22−2
χ4022-2-2-2-2222-222-22-2-2-2-22200002-22-2002i−2i000000002i−2i2i−2i00000000000000000000i2−i2i2−i2−22−22
χ4122-2-2-2-2222-222-22-2-2-2-22200002-22-200−2i2i00000000−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−22
χ4222-2-2-2-2222-222-22-2-2-2-22200002-22-200−2i2i00000000−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−2
χ4322-2-2-2-222-222-222-2-2-2-2220000-22-222i−2i0000002i−2i2i−2i000000000000000000000000−i2i2i2−i22−2−22
χ4422-2-2-2-222-222-222-2-2-2-2220000-22-222i−2i0000002i−2i2i−2i000000000000000000000000i2−i2−i2i2−222−2
χ4522-2-2-2-222-222-222-2-2-2-2220000-22-22−2i2i000000−2i2i−2i2i000000000000000000000000−i2i2i2−i2−222−2
χ4622-2-2-2-222-222-222-2-2-2-2220000-22-22−2i2i000000−2i2i−2i2i000000000000000000000000i2−i2−i2i22−2−22
χ4744444444-4-4-2-4-4-2-2-2-2-2-2-24-44-422220000-2-222000000000000000000000000000000000000
χ4844444444-4-4-2-4-4-2-2-2-2-2-2-2-44-442222000022-2-2000000000000000000000000000000000000
χ494444-4-4-4-444-2-4-4-2-2-222224-4-44-2-2220000-22-22000000000000000000000000000000000000
χ504444-4-4-4-444-2-4-4-2-2-22222-444-4-2-22200002-22-2000000000000000000000000000000000000
χ5144-4-444-4-44-44-444-4-444-4-400004-4-4400000000000000000000000000000000000000000000
χ5244-4-444-4-44-4-2-44-222-2-2220000-222-200000000−2i32i32i3−2i300000000000000000000000000000000
χ5344-4-444-4-44-4-2-44-222-2-2220000-222-2000000002i3−2i3−2i32i300000000000000000000000000000000
χ5444-4-444-4-4-4444-44-4-444-4-40000-444-400000000000000000000000000000000000000000000
χ5544-4-444-4-4-44-24-4-222-2-22200002-2-22000000000000−2i32i32i3−2i30000000000000000000000000000
χ5644-4-444-4-4-44-24-4-222-2-22200002-2-220000000000002i3−2i3−2i32i30000000000000000000000000000
χ5744-4-4-4-4444-4-24-4-22222-2-20000-22-22004i−4i00000000−2i2i−2i2i0000000000000000000000000000
χ5844-4-4-4-4444-4-24-4-22222-2-20000-22-2200−4i4i000000002i−2i2i−2i0000000000000000000000000000
χ5944-4-4-4-444-44-2-44-22222-2-200002-22-24i−4i000000−2i2i−2i2i00000000000000000000000000000000
χ6044-4-4-4-444-44-2-44-22222-2-200002-22-2−4i4i0000002i−2i2i−2i00000000000000000000000000000000
χ614-44-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000000000000000000000000000002-22i−2i000000000000
χ624-44-44i−4i4i−4i00400-44-44i−4i4i−4i000000000000000000000000000000000000-22−2i2i000000000000
χ634-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000000000000000000000000000002-2−2i2i000000000000
χ644-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i000000000000000000000000000000000000-222i−2i000000000000
χ654-4-444i−4i−4i4i00400-4-444i−4i−4i4i00000000000000000000000000000000000000002i−2i2-200000000
χ664-4-444i−4i−4i4i00400-4-444i−4i−4i4i0000000000000000000000000000000000000000−2i2i-2200000000
χ674-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i00000000000000000000000000000000000000002i−2i-2200000000
χ684-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i0000000000000000000000000000000000000000−2i2i2-200000000
χ698-88-88i−8i8i−8i00-4004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ708-88-8−8i8i−8i8i00-4004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ718-8-888i−8i−8i8i00-40044-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ728-8-88−8i8i8i−8i00-40044-44i−4i−4i4i0000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).