Finite Group Databasebeta

← Group #312666

Character table — Group #312666

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11-1-11-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-111-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111111-1-1-111-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1111-1-11-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-111-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-11111-1-1-1-111-1-1-11-1-111-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1-1111-111-1-11-1
χ17222222222-22-22-22-200000000-22222-200002222-2-2-2-20000000022-2-2-2-2000000000000000000000000
χ18222222222-22-22-22-200000000-22222-20000-2-2-2-2222200000000-2-2-2-222000000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-22222000000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-22222000000002222-2-2000000000000000000000000
χ2122222222-22-22-22-2222222222-20000-2-2-2-2-2000000000000000000000022220000000000-200-2000000
χ2222222222-22-22-22-2222222222-20000-2-2-2-2-20000000000000000000000-2-2-2-200000000002002000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-22222000000000000000000000022-2-20000000000200-2000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-222220000000000000000000000-2-2220000000000-2002000000
χ25222-22-2-2-2-20-2020202222−2−2−2−202i2i−2i−2i022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22-200000000i2i2−i2−i222−2−2000000000000
χ26222-22-2-2-2-20-2020202222−2−2−2−202i2i−2i−2i022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2-2200000000i2i2−i2−i2−2−222000000000000
χ27222-22-2-2-2-20-2020202222−2−2−2−20−2i−2i2i2i022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2-2200000000−i2−i2i2i2−2−222000000000000
χ28222-22-2-2-2-20-2020202222−2−2−2−20−2i−2i2i2i022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22-200000000−i2−i2i2i222−2−2000000000000
χ29222-22-2-2-2-20-202020−2−2−2−2222202i2i−2i−2i0−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i22-200000000−i2−i2i2i2−2−222000000000000
χ30222-22-2-2-2-20-202020−2−2−2−2222202i2i−2i−2i0−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2-2200000000−i2−i2i2i222−2−2000000000000
χ31222-22-2-2-2-20-202020−2−2−2−222220−2i−2i2i2i0−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2-2200000000i2i2−i2−i222−2−2000000000000
χ32222-22-2-2-2-20-202020−2−2−2−222220−2i−2i2i2i0−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i22-200000000i2i2−i2−i2−2−222000000000000
χ3322-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i202-22-20i2−i2i2−i200002i2i−2i−2i22−2−222−2−200002i−2i0000i2−i2i2−i22−22−2000000000000
χ3422-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i202-22-20i2−i2i2−i20000−2i−2i2i2i−2−222−2−2220000−2i2i0000i2−i2i2−i2−22−22000000000000
χ3522-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i20-22-220i2−i2i2−i200002i2i−2i−2i22−2−222−2−20000−2i2i0000−i2i2−i2i2−22−22000000000000
χ3622-22-2-2-22-202020-20i2i2−i2−i2i2i2−i2−i20-22-220i2−i2i2−i20000−2i−2i2i2i−2−222−2−22200002i−2i0000−i2i2−i2i22−22−2000000000000
χ3722-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i202-22-20−i2i2−i2i200002i2i−2i−2i−2−222−2−22200002i−2i0000−i2i2−i2i2−22−22000000000000
χ3822-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i202-22-20−i2i2−i2i20000−2i−2i2i2i22−2−222−2−20000−2i2i0000−i2i2−i2i22−22−2000000000000
χ3922-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i20-22-220−i2i2−i2i200002i2i−2i−2i−2−222−2−2220000−2i2i0000i2−i2i2−i22−22−2000000000000
χ4022-22-2-2-22-202020-20−i2−i2i2i2−i2−i2i2i20-22-220−i2i2−i2i20000−2i−2i2i2i22−2−222−2−200002i−2i0000i2−i2i2−i2−22−22000000000000
χ4122-2-2-222-222-2-222-2-22i2i−2i−2i−2i−2i2i2i-22i−2i−2i2i22i−2i−2i2i0000000000000000002i−2i000000-222-20000000000000000
χ4222-2-2-222-222-2-222-2-22i2i−2i−2i−2i−2i2i2i-2−2i2i2i−2i22i−2i−2i2i000000000000000000−2i2i0000002-2-220000000000000000
χ4322-2-2-222-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i-22i−2i−2i2i2−2i2i2i−2i0000000000000000002i−2i0000002-2-220000000000000000
χ4422-2-2-222-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i-2−2i2i2i−2i2−2i2i2i−2i000000000000000000−2i2i000000-222-20000000000000000
χ4522-2-2-222-22-2-222-2-220000000022i−2i−2i2i-20000000000002i2i−2i−2i−2i−2i2i2i00−2i2i00000000002-2-22000000000000
χ4622-2-2-222-22-2-222-2-220000000022i−2i−2i2i-2000000000000−2i−2i2i2i2i2i−2i−2i00−2i2i0000000000-222-2000000000000
χ4722-2-2-222-22-2-222-2-22000000002−2i2i2i−2i-20000000000002i2i−2i−2i−2i−2i2i2i002i−2i0000000000-222-2000000000000
χ4822-2-2-222-22-2-222-2-22000000002−2i2i2i−2i-2000000000000−2i−2i2i2i2i2i−2i−2i002i−2i00000000002-2-22000000000000
χ4922-2-2-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i20000-2−2i2i2i−2i00000000000000000000000000000000002-202i−2i0000000
χ5022-2-2-222-2-222-2-222-22i2i−2i−2i−2i−2i2i2i20000-2−2i2i2i−2i0000000000000000000000000000000000-220−2i2i0000000
χ5122-2-2-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i20000-22i−2i−2i2i00000000000000000000000000000000002-20−2i2i0000000
χ5222-2-2-222-2-222-2-222-2−2i−2i2i2i2i2i−2i−2i20000-22i−2i−2i2i0000000000000000000000000000000000-2202i−2i0000000
χ532-2-2222-2-2020-20-2022-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000002i−2i2i−2i000000000000002−22−200
χ542-2-2222-2-2020-20-2022-22-22-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000−2i2i−2i2i00000000000000−22−2200
χ552-2-2222-2-2020-20-2022-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000002i−2i2i−2i00000000000000−22−2200
χ562-2-2222-2-2020-20-2022-22-22-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000−2i2i−2i2i000000000000002−22−200
χ572-2-2222-2-2020-20-202-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000002i−2i−2i2i000000000000002−2−2200
χ582-2-2222-2-2020-20-202-22-22-22-220000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000−2i2i2i−2i00000000000000−222−200
χ592-2-2222-2-2020-20-202-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000002i−2i−2i2i00000000000000−222−200
χ602-2-2222-2-2020-20-202-22-22-22-220000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000−2i2i2i−2i000000000000002−2−2200
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-44040-40-4022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-44-4-4-44040-40-40−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-44-4-4-4440-40-40402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ6544-44-4-4-4440-40-4040−2i2−2i22i22i2−2i2−2i22i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ6644-4-4-444-4-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ674-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−2222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ684-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ694-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−22222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ704-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-44-4-44-4404040-40-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ724-44-4-44-4404040-40-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ734-44-4-44-440-40-404040000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ744-44-4-44-440-40-4040400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ754-4-4444-4-40-404040-40000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ764-4-4444-4-40-404040-4000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ774-4-4-44-4440000000022−2222−22−2222−2222000000000022−22−222200002-22-2-22-22000000000000000000000000000000
χ784-4-4-44-4440000000022−2222−22−2222−22220000000000−222222−220000-22-222-22-2000000000000000000000000000000
χ794-4-4-44-44400000000−2222−222222−2222−22000000000022−22−22220000-22-222-22-2000000000000000000000000000000
χ804-4-4-44-44400000000−2222−222222−2222−220000000000−222222−2200002-22-2-22-22000000000000000000000000000000

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