Finite Group Databasebeta

← Group #276408

Character table — Group #276408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ101111111111-1-1-1-1111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ17222222222-2222222-2-22-2-2-22222-2-2-2-2-2-2220000000022-2-2-2000000000000000000000000000000
χ18222222222-2222222-2-22-2-2-2-2-2-2-22222-2-22200000000-2-222-2000000000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-2222222-2-2-2-2-2-2-2-200000000-2-2222000000000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-222-2-2-2-22222-2-2-2-20000000022-2-22000000000000000000000000000000
χ2122222222-222222-2-222-222200000000-2-2-2-2222222220000-2-2-2-2-200000000000000000000000000
χ2222222222-222222-2-222-222200000000-2-2-2-2-2-2-2-2-2-2-2-20000-2222200000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-22-2-200000000-2-2222222-2-2-2-200002-2-22200000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-22-2-200000000-2-222-2-2-2-222220000222-2-200000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-20000000022-2-20000000000002000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-20000000022-2-2000000000000200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000000002222000000000000-2000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000000002222000000000000-200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-22-2-2-2200002-2-2-222002i2i−2i−2i2i2i−2i−2i2-200000000000000000002i2i−2i−2i0000000000002-200000000
χ30222-2-22-2-2-2200002-2-2-222002i2i−2i−2i2i2i−2i−2i2-20000000000000000000−2i−2i2i2i000000000000-2200000000
χ31222-2-22-2-2-2200002-2-2-22200−2i−2i2i2i−2i−2i2i2i2-200000000000000000002i2i−2i−2i000000000000-2200000000
χ32222-2-22-2-2-2200002-2-2-22200−2i−2i2i2i−2i−2i2i2i2-20000000000000000000−2i−2i2i2i0000000000002-200000000
χ33222-2-22-2-2-2-200002-2222-2002i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000022-2-2002i−2i000000
χ34222-2-22-2-2-2-200002-2222-2002i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000-2-22200−2i2i000000
χ35222-2-22-2-2-2-200002-2222-200−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000022-2-200−2i2i000000
χ36222-2-22-2-2-2-200002-2222-200−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000-2-222002i−2i000000
χ3722-22-2-2-22202i2i−2i−2i-2-200200000002-22-2002i−2i22−2−2i2i2−i2−i2002i−2i02−2i2−i200002−22−2i2−i2i2−i200000000000000
χ3822-22-2-2-22202i2i−2i−2i-2-200200000002-22-2002i−2i−2−222−i2−i2i2i2002i−2i0−22−i2i20000−22−22−i2i2−i2i200000000000000
χ3922-22-2-2-22202i2i−2i−2i-2-20020000000-22-22002i−2i22−2−2i2i2−i2−i200−2i2i02−2i2−i20000−22−22−i2i2−i2i200000000000000
χ4022-22-2-2-22202i2i−2i−2i-2-20020000000-22-22002i−2i−2−222−i2−i2i2i200−2i2i0−22−i2i200002−22−2i2−i2i2−i200000000000000
χ4122-22-2-2-2220−2i−2i2i2i-2-200200000002-22-200−2i2i22−2−2−i2−i2i2i200−2i2i02−2−i2i200002−22−2−i2i2−i2i200000000000000
χ4222-22-2-2-2220−2i−2i2i2i-2-200200000002-22-200−2i2i−2−222i2i2−i2−i200−2i2i0−22i2−i20000−22−22i2−i2i2−i200000000000000
χ4322-22-2-2-2220−2i−2i2i2i-2-20020000000-22-2200−2i2i22−2−2−i2−i2i2i2002i−2i02−2−i2i20000−22−22i2−i2i2−i200000000000000
χ4422-22-2-2-2220−2i−2i2i2i-2-20020000000-22-2200−2i2i−2−222i2i2−i2−i2002i−2i0−22i2−i200002−22−2−i2i2−i2i200000000000000
χ4522-22-2-2-22-202i2i−2i−2i2200-20002i−2i2i−2i000000−2i2i22−2−2i2i2−i2−i22-2000−22−i2i20000i2−i2−i2i2−222−200000000000000
χ4622-22-2-2-22-202i2i−2i−2i2200-20002i−2i2i−2i000000−2i2i−2−222−i2−i2i2i22-20002−2i2−i20000−i2i2i2−i22−2−2200000000000000
χ4722-22-2-2-22-202i2i−2i−2i2200-2000−2i2i−2i2i000000−2i2i22−2−2i2i2−i2−i2-22000−22−i2i20000−i2i2i2−i22−2−2200000000000000
χ4822-22-2-2-22-202i2i−2i−2i2200-2000−2i2i−2i2i000000−2i2i−2−222−i2−i2i2i2-220002−2i2−i20000i2−i2−i2i2−222−200000000000000
χ4922-22-2-2-22-20−2i−2i2i2i2200-20002i−2i2i−2i0000002i−2i22−2−2−i2−i2i2i2-22000−22i2−i20000i2−i2−i2i22−2−2200000000000000
χ5022-22-2-2-22-20−2i−2i2i2i2200-20002i−2i2i−2i0000002i−2i−2−222i2i2−i2−i2-220002−2−i2i20000−i2i2i2−i2−222−200000000000000
χ5122-22-2-2-22-20−2i−2i2i2i2200-2000−2i2i−2i2i0000002i−2i22−2−2−i2−i2i2i22-2000−22i2−i20000−i2i2i2−i2−222−200000000000000
χ5222-22-2-2-22-20−2i−2i2i2i2200-2000−2i2i−2i2i0000002i−2i−2−222i2i2−i2−i22-20002−2−i2i20000i2−i2−i2i22−2−2200000000000000
χ532-2222-2-2-20-22-22-2002-2022-20000000000002-22-22-22-2000000000i2−i2i2−i200000000i2−i2i2−i20000i2−i2i2−i200
χ542-2222-2-2-20-22-22-2002-2022-20000000000002-22-22-22-2000000000−i2i2−i2i200000000−i2i2−i2i20000−i2i2−i2i200
χ552-2222-2-2-20-22-22-2002-2022-2000000000000-22-22-22-22000000000i2−i2i2−i200000000i2−i2i2−i20000−i2i2−i2i200
χ562-2222-2-2-20-22-22-2002-2022-2000000000000-22-22-22-22000000000−i2i2−i2i200000000−i2i2−i2i20000i2−i2i2−i200
χ572-2222-2-2-20-2-22-22002-202-220000000000002-22-2-22-22000000000i2−i2i2−i200000000−i2i2−i2i20000i2−i2−i2i200
χ582-2222-2-2-20-2-22-22002-202-220000000000002-22-2-22-22000000000−i2i2−i2i200000000i2−i2i2−i20000−i2i2i2−i200
χ592-2222-2-2-20-2-22-22002-202-22000000000000-22-222-22-2000000000i2−i2i2−i200000000−i2i2−i2i20000−i2i2i2−i200
χ602-2222-2-2-20-2-22-22002-202-22000000000000-22-222-22-2000000000−i2i2−i2i200000000i2−i2i2−i20000i2−i2−i2i200
χ61444-4-44-4-4440000-44-4-4-440000000000-44000000000000000000000000000000000000000000000
χ62444-4-44-4-44-40000-4444-4-400000000004-4000000000000000000000000000000000000000000000
χ6344-4-44-44-44000004-400-40004-4-44000000000000000000000000000000000000000000000000000
χ6444-4-44-44-44000004-400-4000-444-4000000000000000000000000000000000000000000000000000
χ6544-4-44-44-4-400000-4400400000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6644-4-44-44-4-400000-440040000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ674-4444-4-4-4044-44-400-440-4-440000000000000000000000000000000000000000000000000000000
χ684-4444-4-4-404-44-4400-440-44-40000000000000000000000000000000000000000000000000000000
χ694-44-4-4-444040000004-40-400000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-44-4-4-444040000004-40-40000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-44-4-4-4440-4000000-4404000000000000000000000000000000022−22−22220000000000000000000000
χ724-44-4-4-4440-4000000-44040000000000000000000000000000000−222222−220000000000000000000000
χ734-4-44-444-4004i−4i−4i4i0000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-44-444-4004i−4i−4i4i00000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-44-444-400−4i4i4i−4i0000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000000000
χ764-4-44-444-400−4i4i4i−4i00000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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