Finite Group Databasebeta

← Group #307379

Character table — Group #307379

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888244444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-1-1-1-11-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-111111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-111-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-111-1-11-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-11-1-111-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-111-1-1111-1-1-11
χ17222222222-2-222-2-2222222222-20000-2-2-2-2-20000000000000000222200000000000000-20000-2000000
χ18222222222-2-222-2-2222222222-20000-2-2-2-2-20000000000000000-2-2-2-200000000000000200002000000
χ19222222222-2-222-2-22-2-2-2-2-2-2-2-2-20000-22222000000000000000022-2-200000000000000-200002000000
χ20222222222-2-222-2-22-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-2220000000000000020000-2000000
χ2122222222-222-2-222-200000000-22222-200002222-2-2-2-2000000000000-2-222-2-200000000000000000000
χ2222222222-222-2-222-200000000-22222-20000-2-2-2-22222000000000000-2-2-2-22200000000000000000000
χ2322222222-222-2-222-200000000-2-2-2-2-2-200002222-2-2-2-200000000000022-2-22200000000000000000000
χ2422222222-222-2-222-200000000-2-2-2-2-2-20000-2-2-2-222220000000000002222-2-200000000000000000000
χ25222-2-2-2-22222-2-2-2-220000000022i2i−2i−2i-20000000000002i2i2i2i−2i−2i−2i−2i00002i−2i0000000022-2-2000000000000
χ26222-2-2-2-22222-2-2-2-220000000022i2i−2i−2i-2000000000000−2i−2i−2i−2i2i2i2i2i00002i−2i00000000-2-222000000000000
χ27222-2-2-2-22222-2-2-2-22000000002−2i−2i2i2i-20000000000002i2i2i2i−2i−2i−2i−2i0000−2i2i00000000-2-222000000000000
χ28222-2-2-2-22222-2-2-2-22000000002−2i−2i2i2i-2000000000000−2i−2i−2i−2i2i2i2i2i0000−2i2i0000000022-2-2000000000000
χ29222-2-2-2-22-22222-2-2-22222-2-2-2-2-22i2i−2i−2i222-2-200000000000000000000−2i2i00002i2i−2i−2i0000000000000000
χ30222-2-2-2-22-22222-2-2-22222-2-2-2-2-2−2i−2i2i2i222-2-2000000000000000000002i−2i0000−2i−2i2i2i0000000000000000
χ31222-2-2-2-22-22222-2-2-2-2-2-2-22222-22i2i−2i−2i2-2-22200000000000000000000−2i2i0000−2i−2i2i2i0000000000000000
χ32222-2-2-2-22-22222-2-2-2-2-2-2-22222-2−2i−2i2i2i2-2-222000000000000000000002i−2i00002i2i−2i−2i0000000000000000
χ33222-2-2-2-22-2-2-22222-22222-2-2-2-220000-2-2-222000000000000000000000000000000000002i−2i2i−2i0000000
χ34222-2-2-2-22-2-2-22222-22222-2-2-2-220000-2-2-22200000000000000000000000000000000000−2i2i−2i2i0000000
χ35222-2-2-2-22-2-2-22222-2-2-2-2-2222220000-222-2-2000000000000000000000000000000000002i−2i−2i2i0000000
χ36222-2-2-2-22-2-2-22222-2-2-2-2-2222220000-222-2-200000000000000000000000000000000000−2i2i2i−2i0000000
χ3722-222-2-2-202-2002-20i2i2−i2−i2i2i2−i2−i202-22-20i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2000000002-2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-222-2-2-202-2002-20i2i2−i2−i2i2i2−i2−i202-22-20i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i200000000-22i2−i2i2−i2−i2i2−i2i2000000000000
χ3922-222-2-2-202-2002-20i2i2−i2−i2i2i2−i2−i20-22-220i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i200000000-22−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-222-2-2-202-2002-20i2i2−i2−i2i2i2−i2−i20-22-220i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i2000000002-2−i2i2−i2i2i2−i2i2−i2000000000000
χ4122-222-2-2-202-2002-20−i2−i2i2i2−i2−i2i2i202-22-20−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i2000000002-2−i2i2−i2i2−i2i2−i2i2000000000000
χ4222-222-2-2-202-2002-20−i2−i2i2i2−i2−i2i2i202-22-20−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i200000000-22−i2i2−i2i2i2−i2i2−i2000000000000
χ4322-222-2-2-202-2002-20−i2−i2i2i2−i2−i2i2i20-22-220−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i200000000-22i2−i2i2−i2i2−i2i2−i2000000000000
χ4422-222-2-2-202-2002-20−i2−i2i2i2−i2−i2i2i20-22-220−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i2000000002-2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-2-2-222-202-200-220i2i2−i2−i2−i2−i2i2i202i−2i−2i2i0i2−i2−i2i22i2i−2i−2i000022−2−2−2−2220000002-200−222−2−i2i2i2−i2000000000000
χ4622-2-2-222-202-200-220i2i2−i2−i2−i2−i2i2i202i−2i−2i2i0i2−i2−i2i2−2i−2i2i2i0000−2−22222−2−2000000-2200−222−2i2−i2−i2i2000000000000
χ4722-2-2-222-202-200-220i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i0i2−i2−i2i22i2i−2i−2i000022−2−2−2−222000000-22002−2−22i2−i2−i2i2000000000000
χ4822-2-2-222-202-200-220i2i2−i2−i2−i2−i2i2i20−2i2i2i−2i0i2−i2−i2i2−2i−2i2i2i0000−2−22222−2−20000002-2002−2−22−i2i2i2−i2000000000000
χ4922-2-2-222-202-200-220−i2−i2i2i2i2i2−i2−i202i−2i−2i2i0−i2i2i2−i22i2i−2i−2i0000−2−22222−2−20000002-2002−2−22i2−i2−i2i2000000000000
χ5022-2-2-222-202-200-220−i2−i2i2i2i2i2−i2−i202i−2i−2i2i0−i2i2i2−i2−2i−2i2i2i000022−2−2−2−222000000-22002−2−22−i2i2i2−i2000000000000
χ5122-2-2-222-202-200-220−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i0−i2i2i2−i22i2i−2i−2i0000−2−22222−2−2000000-2200−222−2−i2i2i2−i2000000000000
χ5222-2-2-222-202-200-220−i2−i2i2i2i2i2−i2−i20−2i2i2i−2i0−i2i2i2−i2−2i−2i2i2i000022−2−2−2−2220000002-200−222−2i2−i2−i2i2000000000000
χ532-2-22-22-222002-200-22-22-22-22-200000000002−22−22−22−22−22−22−22−22i−2i2i−2i00000000000000000000i2−i2i2−i200
χ542-2-22-22-222002-200-22-22-22-22-200000000002−22−22−22−22−22−22−22−2−2i2i−2i2i00000000000000000000−i2i2−i2i200
χ552-2-22-22-222002-200-22-22-22-22-20000000000−22−22−22−22−22−22−22−222i−2i2i−2i00000000000000000000−i2i2−i2i200
χ562-2-22-22-222002-200-22-22-22-22-20000000000−22−22−22−22−22−22−22−22−2i2i−2i2i00000000000000000000i2−i2i2−i200
χ572-2-22-22-222002-200-2-22-22-22-2200000000002−22−22−22−2−22−22−22−222i−2i−2i2i00000000000000000000i2−i2−i2i200
χ582-2-22-22-222002-200-2-22-22-22-2200000000002−22−22−22−2−22−22−22−22−2i2i2i−2i00000000000000000000−i2i2i2−i200
χ592-2-22-22-222002-200-2-22-22-22-220000000000−22−22−22−222−22−22−22−22i−2i−2i2i00000000000000000000−i2i2i2−i200
χ602-2-22-22-222002-200-2-22-22-22-220000000000−22−22−22−222−22−22−22−2−2i2i2i−2i00000000000000000000i2−i2−i2i200
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-4-444-4-4-4-444400000000-40000400000000000000000000000000000000000000000000000000
χ6344-444-4-4-40-4400-4402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ6444-444-4-4-40-4400-440−2i2−2i22i22i2−2i2−2i22i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ6544-4-4-444-40-44004-402i22i2−2i2−2i2−2i2−2i22i22i2000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ6644-4-4-444-40-44004-40−2i2−2i22i22i22i22i2−2i2−2i20000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ674-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−22222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ684-444-4-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ694-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−2222−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ704-444-4-44-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ714-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000002i2−2i2−2i22i200002-2-22-222-2000000000000000000000000000000
χ724-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000−2i22i22i2−2i20000-222-22-2-22000000000000000000000000000000
χ734-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000002i2−2i2−2i22i20000-222-22-2-22000000000000000000000000000000
χ744-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000−2i22i22i2−2i200002-2-22-222-2000000000000000000000000000000
χ754-4-44-44-44-400-4400400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ764-4-44-44-44-400-44004000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ774-4-4-44-444400-4400-4000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ784-4-4-44-444400-4400-400000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ794-4-4-44-444-4004-40044-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-44-444-4004-4004-44-444-44-400000000000000000000000000000000000000000000000000000000

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