Finite Group Databasebeta

← Group #10778211

Character table — Group #10778211

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444444466668888888888888888881212121216161616161624242424242424242432324848
order122234444666444448812121212242424244444888888812121212122424242424242488242424242424888888861244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1111-1-1111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111-1-11111-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-111-1-11-111-1-111-1-1-111-1-11-11-1
χ611111111111111111-1-11111-1-1-1-11111-1-1-1-1-11111111-1-1-1-1-1-111-1-1-11-1-11111-1-1-1-1-111-11-11
χ711111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-1111-111-1-1-1-1111-1-1111-1-11
χ811111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-11-1-111-1-111111-1-1-111-1
χ9111111111111-1-11-1-111111111111111111-1-111-1-11-1-111-1-1-1-11111-1-11111-1-11-1-11111-1-1-1-1
χ10111111111111-1-11-1-111111111111111-1-11-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111
χ11111111111111-1-11-1-11111111111-1-1-1-1111-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-111
χ12111111111111-1-11-1-11111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1
χ13111111111111-1-11-1-1-1-11111-1-1-1-1111111-111-1-1-1-11-1-1-1-1111111-1-1-1111-1-1-1-1-11111-1-1-11-11
χ14111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-11111-1-11-1-1-1-1111111-1-11-1-1-111-1-1-111-1-1111-11-1
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11-1-1-1-11111-1-111-1111-1-1111-1-1-1-111-111-1
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-1111-1-1-111111-1-111-1-11-1-11
χ17222222-2-2222222-2-2-200-222-2000022-2-2000000022-2-2-20000002-2000000002-200000000000
χ18222222-2-2222222-2-2-200-222-20000-2-222000000022-2-2-2000000-2200000000-2200000000000
χ19222222-2-22222-2-2-22200-222-2000022-2-20000000-2-2-2220000002-200000000-2200000000000
χ20222222-2-22222-2-2-22200-222-20000-2-2220000000-2-2-222000000-22000000002-200000000000
χ2122222-222-222200-200222-2-222222222200-2000000-200-2-20000-2-22200000000-20000000000
χ2222222-222-222200-200222-2-222222-2-2-2-200-2000000-200-2-2000022-2-20000000020000000000
χ2322222-222-222200-200-2-22-2-22-2-2-2-22222002000000-200220000-2-2-2-20000000020000000000
χ2422222-222-222200-200-2-22-2-22-2-2-2-2-2-2-2-2002000000-200220000222200000000-20000000000
χ2522222-2-2-2-22220020000-2-2-2-2000022-2-20002i−2i0000200002i2i−2i−2i-22000000000002i−2i00000000
χ2622222-2-2-2-22220020000-2-2-2-2000022-2-2000−2i2i000020000−2i−2i2i2i-2200000000000−2i2i00000000
χ2722222-2-2-2-22220020000-2-2-2-20000-2-2220002i−2i0000200002i2i−2i−2i2-200000000000−2i2i00000000
χ2822222-2-2-2-22220020000-2-2-2-20000-2-222000−2i2i000020000−2i−2i2i2i2-2000000000002i−2i00000000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000-1-100
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10000-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-10000-2-211110000000001100
χ312222-12222-1-1-122222-2-2-1-1-1-11111000022-2-2-2-2-2-1-1-1-1-111111100002-2-1-111000000000-1100
χ322222-12222-1-1-122222-2-2-1-1-1-111110000-2-2-2-2-222-1-1-1-1-11111110000-2211-1-10000000001-100
χ332222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-10000222-2-22211-111-1-111110000-2-2-1-1-1-10000000001100
χ342222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-10000-2-22-2-2-2-211-111-1-111110000221111000000000-1-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-11111000022-222-2-211-11111-1-1-1-10000-22-1-1110000000001-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-111110000-2-2-2222211-11111-1-1-1-100002-211-1-1000000000-1100
χ372-22-2202-202-2-2000002i−2i-20022i2i−2i−2i2i−2i2i−2i−i2i20002−200000000000002-200−i2i22−2000002−2−i2i20000
χ382-22-2202-202-2-2000002i−2i-20022i2i−2i−2i2i−2i2i−2ii2−i2000−2200000000000002-200i2−i2−2200000−22i2−i20000
χ392-22-2202-202-2-2000002i−2i-20022i2i−2i−2i−2i2i−2i2i−i2i20002−20000000000000-2200−i2i22−200000−22i2−i20000
χ402-22-2202-202-2-2000002i−2i-20022i2i−2i−2i−2i2i−2i2ii2−i2000−220000000000000-2200i2−i2−22000002−2−i2i20000
χ412-22-2202-202-2-200000−2i2i-2002−2i−2i2i2i2i−2i2i−2i−i2i2000−220000000000000-2200−i2i2−22000002−2i2−i20000
χ422-22-2202-202-2-200000−2i2i-2002−2i−2i2i2i2i−2i2i−2ii2−i20002−20000000000000-2200i2−i22−200000−22−i2i20000
χ432-22-2202-202-2-200000−2i2i-2002−2i−2i2i2i−2i2i−2i2i−i2i2000−2200000000000002-200−i2i2−2200000−22−i2i20000
χ442-22-2202-202-2-200000−2i2i-2002−2i−2i2i2i−2i2i−2i2ii2−i20002−200000000000002-200i2−i22−2000002−2i2−i20000
χ454444-24-4-44-2-2-244-4-4-4002-2-22000000000000000-2-222200000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444002-2-22000000000000000222-2-200000000000000000000000000000
χ474444-2-444-4-2-2-200-40044-222-2-2-2-2-2000000-400000020022000000000000000000000000000
χ484444-2-444-4-2-2-200-400-4-4-222-222220000004000000200-2-2000000000000000000000000000
χ494444-2-4-4-4-4-2-2-200400002222000000000004i−4i0000-20000−2i−2i2i2i00000000000000000000000
χ504444-2-4-4-4-4-2-2-20040000222200000000000−4i4i0000-200002i2i−2i−2i00000000000000000000000
χ5144-4-44400-4-44-44-40000004-400000000000000004-400000000000000000000000000000000
χ5244-4-44400-4-44-4-440000004-40000000000000000-4400000000000000000000000000000000
χ5344-4-44-4004-44-40004i−4i000-4400000000000000000004i−4i00000000000000000000000000000
χ5444-4-44-4004-44-4000−4i4i000-440000000000000000000−4i4i00000000000000000000000000000
χ5544-4-4-2400-42-224-4000000-2206−66−600000000000-220006−66−66−600000000000000000000000
χ5644-4-4-2400-42-224-4000000-220−66−6600000000000-22000−66−66−6600000000000000000000000
χ5744-4-4-2400-42-22-44000000-2206−66−6000000000002-20006−6−66−6600000000000000000000000
χ5844-4-4-2400-42-22-44000000-220−66−66000000000002-2000−666−66−600000000000000000000000
χ5944-4-4-2-40042-220004i−4i0002-206−66−600000000000000−2i2i−66i6−i6−i6i600000000000000000000000
χ6044-4-4-2-40042-220004i−4i0002-20−66−6600000000000000−2i2i6−6−i6i6i6−i600000000000000000000000
χ6144-4-4-2-40042-22000−4i4i0002-206−66−6000000000000002i−2i−66−i6i6i6−i600000000000000000000000
χ6244-4-4-2-40042-22000−4i4i0002-20−66−66000000000000002i−2i6−6i6−i6−i6i600000000000000000000000
χ634-44-440-4404-4-40000000400-400004i−4i−4i4i00000000000000000000000000000000000000000
χ644-44-440-4404-4-40000000400-40000−4i4i4i−4i00000000000000000000000000000000000000000
χ654-44-4-204-40-222000004i−4i200-2−2i−2i2i2i0000−2i22i200022−2200000000000000000i2−i2−220000000000000
χ664-44-4-204-40-222000004i−4i200-2−2i−2i2i2i00002i2−2i2000−222200000000000000000−i2i22−20000000000000
χ674-44-4-204-40-22200000−4i4i200-22i2i−2i−2i0000−2i22i2000−222200000000000000000i2−i22−20000000000000
χ684-44-4-204-40-22200000−4i4i200-22i2i−2i−2i00002i2−2i200022−2200000000000000000−i2i2−220000000000000
χ698-88-8-40-880-4440000000-40040000000000000000000000000000000000000000000000000
χ708-8-8880000-8-88000000000000000000000000000000000000000000000000000000000000
χ718-8-88-4000044-4000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ728-8-88-4000044-400000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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