Finite Group Databasebeta

← Group #10900931

Character table — Group #10900931

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444446666888888888888888888881212121212121616161616161616161624242424242424244848
order1222222234444666666644441212121222224444888812121212242424242424242444444424661212121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ911111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-111-1-111-1-111-1-111-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-11111-1-111-1-1-1-1111-1
χ1111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-111-1-111-1-11111-1-11-1
χ1211111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-111-1-111-1-111-11
χ1311111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-111-1-1-1-111-1-1111-1
χ1411111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-11-1-11111-1-1-1-11111-1-1-11
χ1511111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-11111-1-1-1-111-11
χ1611111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-11111-1-111-1-11-1
χ17222222222-2-2-2-2222222222-2-2-2-2-2-222220000000022-2-200000000-2-222-2-200000000000000000000
χ18222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-20000000022-2-20000000022-2-22200000000000000000000
χ19222222222-2-2-2-22222222-2-222-2-2-2-2222200000000-2-22200000000-2-2-2-22200000000000000000000
χ20222222222-2-2-2-22222222-2-222-2-2-2-2-2-2-2-200000000-2-222000000002222-2-200000000000000000000
χ2122222222-12222-1-1-1-1-1-1-12222-1-1-1-1000022222222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-12222-1-1-1-100002222-2-2-2-2-1-1-1-111111111000000-2-21111-1-1-1-10000000000
χ2322222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2111111110000000000
χ2422222222-12222-1-1-1-1-1-1-12222-1-1-1-10000-2-2-2-2-2-2-2-2-1-1-1-11111111100000022-1-1-1-111110000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-222-2-21111-1-1-1-111110000002-2-1-111-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-2-22211111111-1-1-1-1000000-2211-1-1-1-1110000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22222-2-21111-1-1-1-11111000000-2211-1-111-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-222-2-22211111111-1-1-1-10000002-2-1-11111-1-10000000000
χ29222-2-2-2-222000022-2-2-22-22i−2i00000022-2-20000−i2i22−22i−2i00−i2−i2i2i222−2−2002i−2i0000000000000000−i2i22−200
χ30222-2-2-2-222000022-2-2-22-22i−2i00000022-2-20000i2−i2−222i−2i00i2i2−i2−i2−2−222002i−2i0000000000000000i2−i2−2200
χ31222-2-2-2-222000022-2-2-22-22i−2i000000-2-2220000−i2i22−22i−2i00−i2−i2i2i222−2−200−2i2i0000000000000000i2−i2−2200
χ32222-2-2-2-222000022-2-2-22-22i−2i000000-2-2220000i2−i2−222i−2i00i2i2−i2−i2−2−22200−2i2i0000000000000000−i2i22−200
χ33222-2-2-2-222000022-2-2-22-2−2i2i00000022-2-20000−i2i2−22−2i2i00−i2−i2i2i2−2−22200−2i2i0000000000000000−i2i2−2200
χ34222-2-2-2-222000022-2-2-22-2−2i2i00000022-2-20000i2−i22−2−2i2i00i2i2−i2−i222−2−200−2i2i0000000000000000i2−i22−200
χ35222-2-2-2-222000022-2-2-22-2−2i2i000000-2-2220000−i2i2−22−2i2i00−i2−i2i2i2−2−222002i−2i0000000000000000i2−i22−200
χ36222-2-2-2-222000022-2-2-22-2−2i2i000000-2-2220000i2−i22−2−2i2i00i2i2−i2−i222−2−2002i−2i0000000000000000−i2i2−2200
χ372-2-2-22-22222-22-2-2-2-22-22200002-22-22-22-2002-200000000000000002-20000000000002-2002-2000000
χ382-2-2-22-22222-22-2-2-2-22-22200002-22-22-22-200-2200000000000000002-2000000000000-2200-22000000
χ392-2-2-22-22222-22-2-2-2-22-22200002-22-2-22-22002-20000000000000000-220000000000002-200-22000000
χ402-2-2-22-22222-22-2-2-2-22-22200002-22-2-22-2200-220000000000000000-22000000000000-22002-2000000
χ412-2-2-22-2222-22-22-2-2-22-2220000-22-222-22-22-2000000000000000000-2200000000002-2002-200000000
χ422-2-2-22-2222-22-22-2-2-22-2220000-22-222-22-2-22000000000000000000-220000000000-2200-2200000000
χ432-2-2-22-2222-22-22-2-2-22-2220000-22-22-22-222-20000000000000000002-200000000002-200-2200000000
χ442-2-2-22-2222-22-22-2-2-22-2220000-22-22-22-22-220000000000000000002-20000000000-22002-200000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-244-4-42222000000000000-2-2220000000000000000000000000000000000
χ4644444444-2-4-4-4-4-2-2-2-2-2-2-2-4-444222200000000000022-2-20000000000000000000000000000000000
χ47444-4-4-4-44-20000-2-2222-224i−4i00000000000000−2i22i222−22−2i2i00i2i2−i2−i2−2−22200000000000000000000000000
χ48444-4-4-4-44-20000-2-2222-224i−4i000000000000002i2−2i2−2222−2i2i00−i2−i2i2i222−2−200000000000000000000000000
χ49444-4-4-4-44-20000-2-2222-22−4i4i00000000000000−2i22i2−22222i−2i00i2i2−i2−i222−2−200000000000000000000000000
χ50444-4-4-4-44-20000-2-2222-22−4i4i000000000000002i2−2i222−222i−2i00−i2−i2i2i2−2−22200000000000000000000000000
χ5144-444-4-4-444-4-444-4-444-4-40000-444-400000000000000000000000000000000000000000000000000
χ5244-444-4-4-44-444-44-4-444-4-400004-4-4400000000000000000000000000000000000000000000000000
χ5344-444-4-4-4-24-4-44-222-2-22200002-2-22000000000000000023−2323−23000000000000000000000000000000
χ5444-444-4-4-4-24-4-44-222-2-22200002-2-220000000000000000−2323−2323000000000000000000000000000000
χ5544-444-4-4-4-2-444-4-222-2-2220000-222-20000000000000000000023−2323−2300000000000000000000000000
χ5644-444-4-4-4-2-444-4-222-2-2220000-222-200000000000000000000−2323−232300000000000000000000000000
χ5744-4-4-444-4400004-44-4-4-44004i−4i0000000000000000004i−4i0000000000000000000000000000000000
χ5844-4-4-444-4400004-44-4-4-4400−4i4i000000000000000000−4i4i0000000000000000000000000000000000
χ5944-4-4-444-4-20000-22-2222-2004i−4i000000000000000000−2i2ii6−i6−i6i66−6−6600000000000000000000000000
χ6044-4-4-444-4-20000-22-2222-2004i−4i000000000000000000−2i2i−i6i6i6−i6−666−600000000000000000000000000
χ6144-4-4-444-4-20000-22-2222-200−4i4i0000000000000000002i−2ii6−i6−i6i6−666−600000000000000000000000000
χ6244-4-4-444-4-20000-22-2222-200−4i4i0000000000000000002i−2i−i6i6i6−i66−6−6600000000000000000000000000
χ634-444-4-44-440000-44-4-44-440000000000000000000000000000000000004i−4i00000000000000000000
χ644-444-4-44-440000-44-4-44-44000000000000000000000000000000000000−4i4i00000000000000000000
χ654-44-444-4-4444-4-4-4444-4-4-40000-4-44400000000000000000000000000000000000000000000000000
χ664-44-444-4-44-4-444-4444-4-4-4000044-4-400000000000000000000000000000000000000000000000000
χ674-44-444-4-4-244-4-42-2-2-2222000022-2-2000000000000000000000000000000000023−2300000000000000
χ684-44-444-4-4-244-4-42-2-2-2222000022-2-20000000000000000000000000000000000−232300000000000000
χ694-44-444-4-4-2-4-4442-2-2-22220000-2-22200000000000000000000000000000000−2i32i30000000000000000
χ704-44-444-4-4-2-4-4442-2-2-22220000-2-222000000000000000000000000000000002i3−2i30000000000000000
χ714-4-44-44-4440000-4-44-444-4000000004-4-440000000000000000000000000000000000000000000000
χ724-4-44-44-4440000-4-44-444-400000000-444-40000000000000000000000000000000000000000000000
χ734-4-4-44-444-24-44-4222-22-2-20000-22-220000004-4000000000000000000000000000000-220000000000
χ744-4-4-44-444-24-44-4222-22-2-20000-22-22000000-440000000000000000000000000000002-20000000000
χ754-4-4-44-444-2-44-44222-22-2-200002-22-200004-4000000000000000000000000000000-22000000000000
χ764-4-4-44-444-2-44-44222-22-2-200002-22-20000-440000000000000000000000000000002-2000000000000
χ778-888-8-88-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000
χ788-8-88-88-88-4000044-44-4-440000000000000000000000000000000000000000000000000000000000

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