Finite Group Databasebeta

← Group #275813

Character table — Group #275813

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888882244888844
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
χ5111111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ91111111111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1
χ101111111111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-11
χ111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-11
χ121111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-11-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-11
χ17222222222-2222222-2-22-2-2-2220000-2-200002222222200-200-2-2-2-200000000000000000000000000
χ18222222222-2222222-2-22-2-2-2220000-2-20000-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ19222222222-2-2-2-2-222-2-22-222-2-20000-2-200002222-2-2-2-200200-2-22200000000000000000000000000
χ20222222222-2-2-2-2-222-2-22-222-2-20000-2-20000-2-2-2-222220020022-2-200000000000000000000000000
χ2122222222-222222-2-222-2222-2-22222-2-2-2-2-2-200000000-2-2-222000000000000000000000000000000
χ2222222222-222222-2-222-2222-2-2-2-2-2-2-2-222220000000022-2-2-2000000000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-22-2-2222222-2-2-2-2-2-200000000222-2-2000000000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-22-2-222-2-2-2-2-2-2222200000000-2-2222000000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-2-2-200002200000000000000200000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-2-2-20000220000000000000020000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000000000-200000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200000000000000-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2922-22-22-2-2022i2i−2i−2i00-2-2022i−2i0022-2-200000022−2−2i2i2−i2−i20002i−2i2−2i2−i200002−22−2i2−i2i2−i200000000000000
χ3022-22-22-2-2022i2i−2i−2i00-2-2022i−2i0022-2-2000000−2−222−i2−i2i2i20002i−2i−22−i2i20000−22−22−i2i2−i2i200000000000000
χ3122-22-22-2-2022i2i−2i−2i00-2-2022i−2i00-2-22200000022−2−2i2i2−i2−i2000−2i2i2−2i2−i20000−22−22−i2i2−i2i200000000000000
χ3222-22-22-2-2022i2i−2i−2i00-2-2022i−2i00-2-222000000−2−222−i2−i2i2i2000−2i2i−22−i2i200002−22−2i2−i2i2−i200000000000000
χ3322-22-22-2-202−2i−2i2i2i00-2-202−2i2i0022-2-200000022−2−2−i2−i2i2i2000−2i2i2−2−i2i200002−22−2−i2i2−i2i200000000000000
χ3422-22-22-2-202−2i−2i2i2i00-2-202−2i2i0022-2-2000000−2−222i2i2−i2−i2000−2i2i−22i2−i20000−22−22i2−i2i2−i200000000000000
χ3522-22-22-2-202−2i−2i2i2i00-2-202−2i2i00-2-22200000022−2−2−i2−i2i2i20002i−2i2−2−i2i20000−22−22i2−i2i2−i200000000000000
χ3622-22-22-2-202−2i−2i2i2i00-2-202−2i2i00-2-222000000−2−222i2i2−i2−i20002i−2i−22i2−i200002−22−2−i2i2−i2i200000000000000
χ3722-22-22-2-20-22i2i−2i−2i00220-2−2i2i000000002i2i−2i−2i22−2−2i2i2−i2−i22-2000−22−i2i20000i2−i2−i2i2−222−200000000000000
χ3822-22-22-2-20-22i2i−2i−2i00220-2−2i2i000000002i2i−2i−2i−2−222−i2−i2i2i22-20002−2i2−i20000−i2i2i2−i22−2−2200000000000000
χ3922-22-22-2-20-22i2i−2i−2i00220-2−2i2i00000000−2i−2i2i2i22−2−2i2i2−i2−i2-22000−22−i2i20000−i2i2i2−i22−2−2200000000000000
χ4022-22-22-2-20-22i2i−2i−2i00220-2−2i2i00000000−2i−2i2i2i−2−222−i2−i2i2i2-220002−2i2−i20000i2−i2−i2i2−222−200000000000000
χ4122-22-22-2-20-2−2i−2i2i2i00220-22i−2i000000002i2i−2i−2i22−2−2−i2−i2i2i2-22000−22i2−i20000i2−i2−i2i22−2−2200000000000000
χ4222-22-22-2-20-2−2i−2i2i2i00220-22i−2i000000002i2i−2i−2i−2−222i2i2−i2−i2-220002−2−i2i20000−i2i2i2−i2−222−200000000000000
χ4322-22-22-2-20-2−2i−2i2i2i00220-22i−2i00000000−2i−2i2i2i22−2−2−i2−i2i2i22-2000−22i2−i20000−i2i2i2−i2−222−200000000000000
χ4422-22-22-2-20-2−2i−2i2i2i00220-22i−2i00000000−2i−2i2i2i−2−222i2i2−i2−i22-20002−2−i2i20000i2−i2−i2i22−2−2200000000000000
χ452-2-222-2-22202-22-22-200-20002-200000000002i−2i2i−2i2i−2i2i−2i00000000022−2−20000000022−2−20000i2−i2i2−i200
χ462-2-222-2-22202-22-22-200-20002-200000000002i−2i2i−2i2i−2i2i−2i000000000−2−22200000000−2−2220000−i2i2−i2i200
χ472-2-222-2-22202-22-22-200-20002-20000000000−2i2i−2i2i−2i2i−2i2i00000000022−2−20000000022−2−20000−i2i2−i2i200
χ482-2-222-2-22202-22-22-200-20002-20000000000−2i2i−2i2i−2i2i−2i2i000000000−2−22200000000−2−2220000i2−i2i2−i200
χ492-2-222-2-2220-22-222-200-2000-2200000000002i−2i2i−2i−2i2i−2i2i00000000022−2−200000000−2−2220000i2−i2−i2i200
χ502-2-222-2-2220-22-222-200-2000-2200000000002i−2i2i−2i−2i2i−2i2i000000000−2−2220000000022−2−20000−i2i2i2−i200
χ512-2-222-2-2220-22-222-200-2000-220000000000−2i2i−2i2i2i−2i2i−2i00000000022−2−200000000−2−2220000−i2i2i2−i200
χ522-2-222-2-2220-22-222-200-2000-220000000000−2i2i−2i2i2i−2i2i−2i000000000−2−2220000000022−2−20000i2−i2−i2i200
χ532-2-2-2222-2220000-2-22-22-200002i−2i2i−2i2-22i−2i2i−2i000000000000000002-22-2000000000000002i−2i000000
χ542-2-2-2222-2220000-2-22-22-200002i−2i2i−2i2-22i−2i2i−2i00000000000000000-22-2200000000000000−2i2i000000
χ552-2-2-2222-2220000-2-22-22-20000−2i2i−2i2i2-2−2i2i−2i2i000000000000000002-22-200000000000000−2i2i000000
χ562-2-2-2222-2220000-2-22-22-20000−2i2i−2i2i2-2−2i2i−2i2i00000000000000000-22-22000000000000002i−2i000000
χ572-2-2-2222-2-220000222-2-2-200002i−2i2i−2i-22−2i2i−2i2i000000000000000000000000000002i−2i2i−2i2-200000000
χ582-2-2-2222-2-220000222-2-2-200002i−2i2i−2i-22−2i2i−2i2i00000000000000000000000000000−2i2i−2i2i-2200000000
χ592-2-2-2222-2-220000222-2-2-20000−2i2i−2i2i-222i−2i2i−2i000000000000000000000000000002i−2i2i−2i-2200000000
χ602-2-2-2222-2-220000222-2-2-20000−2i2i−2i2i-222i−2i2i−2i00000000000000000000000000000−2i2i−2i2i2-200000000
χ61444-44-4-4-4400000-4400-40000000000000000000000000000000022−22−22220000000000000000000000
χ62444-44-4-4-4400000-4400-400000000000000000000000000000000−222222−220000000000000000000000
χ63444-44-4-4-4-4000004-4004000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ64444-44-4-4-4-4000004-400400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ654-444-4-44-4004i−4i−4i4i000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000000
χ664-444-4-44-4004i−4i−4i4i00000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000000
χ674-444-4-44-400−4i4i4i−4i000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000000
χ684-444-4-44-400−4i4i4i−4i00000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000000
χ694-44-4-44-4404000000-440-400004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ704-44-4-44-4404000000-440-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ714-44-4-44-440-40000004-40400000000004-4-440000000000000000000000000000000000000000000
χ724-44-4-44-440-40000004-4040000000000-444-40000000000000000000000000000000000000000000
χ734-4-444-4-44-404-44-4-44004000-4400000000000000000000000000000000000000000000000000000
χ744-4-444-4-44-40-44-44-440040004-400000000000000000000000000000000000000000000000000000
χ754-4-4-4444-44-40000-4-4-444400000000-4400000000000000000000000000000000000000000000000
χ764-4-4-4444-4-4-4000044-44-44000000004-400000000000000000000000000000000000000000000000
χ7788-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000

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