Finite Group Databasebeta

← Group #10778177

Character table — Group #10778177

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444444466668888888888888888881212121216161616161624242424242424242432324848
order12223444466622444881212121224242424444466888888812121224242424242424884424242424448888888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1111-1-11111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-111-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-111-1-11-111-1-111-1-1-111-1-11-11-1
χ611111111111111111-1-11111-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-111-1-1-11-1-11111-1-1-1-1-111-11-11
χ711111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-1111-111-1-1-1-1111-1-1111-1-11
χ811111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-1-1-1-111-11-1-111-1-111111-1-1-111-1
χ9111111111111-1-11-1-111111111111111-1-111-1-1111-1-1111-1-1-1-11111-1-11111-1-11-1-11111-1-1-1-1
χ10111111111111-1-11-1-111111111111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111
χ11111111111111-1-11-1-11111111111-1-1-1-1-1-111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-111
χ12111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-111111111-1-1
χ13111111111111-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-11-1-1111111-1-1-1111-1-1-1-1-11111-1-1-11-11
χ14111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-11-1-1111111-1-11-1-1-111-1-1-111-1-1111-11-1
χ15111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1111-1-1111-1-1-1-111-111-1
χ16111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-11111-1-1111-1-1-111111-1-111-1-11-1-11
χ17222222-2-2222222-2-2-200-222-2000022-2-2220000000-2-2-20000002-2000000002-200000000000
χ18222222-2-2222222-2-2-200-222-20000-2-222220000000-2-2-2000000-2200000000-2200000000000
χ19222222-2-22222-2-2-22200-222-2000022-2-2-2-2000000022-20000002-200000000-2200000000000
χ20222222-2-22222-2-2-22200-222-20000-2-222-2-2000000022-2000000-22000000002-200000000000
χ2122222-222-222200-200222-2-2222222222000000-20000-2-2-20000-2-22200000000-20000000000
χ2222222-222-222200-200222-2-222222-2-2-2-2000000-20000-2-2-2000022-2-20000000020000000000
χ2322222-222-222200-200-2-22-2-22-2-2-2-2222200000020000-2220000-2-2-2-20000000020000000000
χ2422222-222-222200-200-2-22-2-22-2-2-2-2-2-2-2-200000020000-2220000222200000000-20000000000
χ2522222-2-2-2-22220020000-2-2-2-2000022-2-200002i−2i000002002i2i−2i−2i-22000000000002i−2i00000000
χ2622222-2-2-2-22220020000-2-2-2-2000022-2-20000−2i2i00000200−2i−2i2i2i-2200000000000−2i2i00000000
χ2722222-2-2-2-22220020000-2-2-2-20000-2-22200002i−2i000002002i2i−2i−2i2-200000000000−2i2i00000000
χ2822222-2-2-2-22220020000-2-2-2-20000-2-2220000−2i2i00000200−2i−2i2i2i2-2000000000002i−2i00000000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-10000-1-12222222-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000-1-100
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10000-1-1-2-2222-2-2-1-1-1-1-1-1-1-1-10000-2-211110000000001100
χ312222-12222-1-1-122222-2-2-1-1-1-111110000-1-122-2-2-2-2-2-1-1-111111100002-2-1-111000000000-1100
χ322222-12222-1-1-122222-2-2-1-1-1-111110000-1-1-2-2-2-2-222-1-1-11111110000-2211-1-10000000001-100
χ332222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-100001122-2-222211-1-1-111110000-2-2-1-1-1-10000000001100
χ342222-12222-1-1-1-2-22-2-222-1-1-1-1-1-1-1-1000011-2-2-2-22-2-211-1-1-111110000221111000000000-1-100
χ352222-12222-1-1-1-2-22-2-2-2-2-1-1-1-111110000112222-2-2-211-111-1-1-1-10000-22-1-1110000000001-100
χ362222-12222-1-1-1-2-22-2-2-2-2-1-1-1-11111000011-2-222-22211-111-1-1-1-100002-211-1-1000000000-1100
χ372-2-22202-202-2-2000002-2-200222-2-22i−2i2i−2i00−i2i2000−i2i2000000000002i−2i00−i2i2−i2i2000002−22−20000
χ382-2-22202-202-2-2000002-2-200222-2-22i−2i2i−2i00i2−i2000i2−i2000000000002i−2i00i2−i2i2−i200000−22−220000
χ392-2-22202-202-2-2000002-2-200222-2-2−2i2i−2i2i00−i2i2000−i2i200000000000−2i2i00−i2i2−i2i200000−22−220000
χ402-2-22202-202-2-2000002-2-200222-2-2−2i2i−2i2i00i2−i2000i2−i200000000000−2i2i00i2−i2i2−i2000002−22−20000
χ412-2-22202-202-2-200000-22-2002-2-2222i−2i2i−2i00−i2i2000i2−i200000000000−2i2i00−i2i2i2−i2000002−2−220000
χ422-2-22202-202-2-200000-22-2002-2-2222i−2i2i−2i00i2−i2000−i2i200000000000−2i2i00i2−i2−i2i200000−222−20000
χ432-2-22202-202-2-200000-22-2002-2-222−2i2i−2i2i00−i2i2000i2−i2000000000002i−2i00−i2i2i2−i200000−222−20000
χ442-2-22202-202-2-200000-22-2002-2-222−2i2i−2i2i00i2−i2000−i2i2000000000002i−2i00i2−i2−i2i2000002−2−220000
χ454444-24-4-44-2-2-244-4-4-4002-2-2200000000-2-2000000022200000000000000000000000000000
χ464444-24-4-44-2-2-2-4-4-444002-2-2200000000220000000-2-2200000000000000000000000000000
χ474444-2-444-4-2-2-200-40044-222-2-2-2-2-20000000000-40000222000000000000000000000000000
χ484444-2-444-4-2-2-200-400-4-4-222-222220000000000400002-2-2000000000000000000000000000
χ494444-2-4-4-4-4-2-2-2004000022220000000000004i−4i00000-200−2i−2i2i2i00000000000000000000000
χ504444-2-4-4-4-4-2-2-200400002222000000000000−4i4i00000-2002i2i−2i−2i00000000000000000000000
χ5144-4-44400-4-44-44-40000004-40000000004-4000000000000000000000000000000000000000
χ5244-4-44400-4-44-4-440000004-4000000000-44000000000000000000000000000000000000000
χ5344-4-44-4004-44-40004i−4i000-440000000000000000004i−4i000000000000000000000000000000
χ5444-4-44-4004-44-4000−4i4i000-44000000000000000000−4i4i000000000000000000000000000000
χ5544-4-4-2400-42-224-4000000-2206−66−60000-2200000000006−66−66−600000000000000000000000
χ5644-4-4-2400-42-224-4000000-220−66−660000-220000000000−66−66−6600000000000000000000000
χ5744-4-4-2400-42-22-44000000-2206−66−600002-200000000006−6−66−6600000000000000000000000
χ5844-4-4-2400-42-22-44000000-220−66−6600002-20000000000−666−66−600000000000000000000000
χ5944-4-4-2-40042-220004i−4i0002-206−66−60000000000000−2i2i0−66i6−i6−i6i600000000000000000000000
χ6044-4-4-2-40042-220004i−4i0002-20−66−660000000000000−2i2i06−6−i6i6i6−i600000000000000000000000
χ6144-4-4-2-40042-22000−4i4i0002-206−66−600000000000002i−2i0−66−i6i6i6−i600000000000000000000000
χ6244-4-4-2-40042-22000−4i4i0002-20−66−6600000000000002i−2i06−6i6−i6−i6i600000000000000000000000
χ634-4-4440-4404-4-40000000400-400004i−4i−4i4i00000000000000000000000000000000000000000
χ644-4-4440-4404-4-40000000400-40000−4i4i4i−4i00000000000000000000000000000000000000000
χ654-4-44-204-40-222000004-4200-2-2-222000000−2i22i2000−2i22i2000000000000000i2−i2i2−i20000000000000
χ664-4-44-204-40-222000004-4200-2-2-2220000002i2−2i20002i2−2i2000000000000000−i2i2−i2i20000000000000
χ674-4-44-204-40-22200000-44200-222-2-2000000−2i22i20002i2−2i2000000000000000i2−i2−i2i20000000000000
χ684-4-44-204-40-22200000-44200-222-2-20000002i2−2i2000−2i22i2000000000000000−i2i2i2−i20000000000000
χ698-88-880000-8-88000000000000000000000000000000000000000000000000000000000000
χ708-88-8-4000044-40000000000026−26−2626000000000000000000000000000000000000000000000
χ718-88-8-4000044-400000000000−262626−26000000000000000000000000000000000000000000000
χ728-8-88-40-880-4440000000-40040000000000000000000000000000000000000000000000000

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