Finite Group Databasebeta

← Group #307389

Character table — Group #307389

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888224444444488888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-111-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111111-1-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1-1111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-11-1-1-11111-1-1-11
χ17222222222-222-2-22-200000000-22222-200002222-2-2-2-20000000000-2-22200-2-200000000000000000000
χ18222222222-222-2-22-200000000-22222-20000-2-2-2-222220000000000-2-2-2-2002200000000000000000000
χ19222222222-222-2-22-200000000-2-2-2-2-2-200002222-2-2-2-2000000000022-2-2002200000000000000000000
χ20222222222-222-2-22-200000000-2-2-2-2-2-20000-2-2-2-222220000000000222200-2-200000000000000000000
χ2122222222-22-2-222-2222222222-20000-2-2-2-2-20000000000000000220000220000000000-200-200000000
χ2222222222-22-2-222-2222222222-20000-2-2-2-2-20000000000000000-2-20000-2-20000000000200200000000
χ2322222222-22-2-222-22-2-2-2-2-2-2-2-2-20000-222220000000000000000220000-2-20000000000200-200000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2-20000-222220000000000000000-2-20000220000000000-200200000000
χ25222-22-2-2-20-2002-2022i2i2i2i−2i−2i−2i−2i000000000022−2−222−2−2i2i2i2i2−i2−i2−i2−i22-200002i−2i00000000000000002−2i2−i200
χ26222-22-2-2-20-2002-2022i2i2i2i−2i−2i−2i−2i000000000022−2−222−2−2i2i2i2i2−i2−i2−i2−i2-220000−2i2i0000000000000000−22−i2i200
χ27222-22-2-2-20-2002-2022i2i2i2i−2i−2i−2i−2i0000000000−2−222−2−222−i2−i2−i2−i2i2i2i2i22-200002i−2i0000000000000000−22−i2i200
χ28222-22-2-2-20-2002-2022i2i2i2i−2i−2i−2i−2i0000000000−2−222−2−222−i2−i2−i2−i2i2i2i2i2-220000−2i2i00000000000000002−2i2−i200
χ29222-22-2-2-20-2002-202−2i−2i−2i−2i2i2i2i2i000000000022−2−222−2−2−i2−i2−i2−i2i2i2i2i22-20000−2i2i00000000000000002−2−i2i200
χ30222-22-2-2-20-2002-202−2i−2i−2i−2i2i2i2i2i000000000022−2−222−2−2−i2−i2−i2−i2i2i2i2i2-2200002i−2i0000000000000000−22i2−i200
χ31222-22-2-2-20-2002-202−2i−2i−2i−2i2i2i2i2i0000000000−2−222−2−222i2i2i2i2−i2−i2−i2−i22-20000−2i2i0000000000000000−22i2−i200
χ32222-22-2-2-20-2002-202−2i−2i−2i−2i2i2i2i2i0000000000−2−222−2−222i2i2i2i2−i2−i2−i2−i2-2200002i−2i00000000000000002−2−i2i200
χ3322-22-22-2-2-202-2002022−2−222−2−202i2i−2i−2i022−2−200002-22-222−2−222−2−2000000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3422-22-22-2-2-202-2002022−2−222−2−202i2i−2i−2i022−2−20000-22-22−2−222−2−22200000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ3522-22-22-2-2-202-2002022−2−222−2−20−2i−2i2i2i022−2−200002-22-222−2−222−2−200000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3622-22-22-2-2-202-2002022−2−222−2−20−2i−2i2i2i022−2−20000-22-22−2−222−2−222000000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-22-2-2-202-20020−2−222−2−22202i2i−2i−2i0−2−22200002-22-2−2−222−2−222000000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-22-22-2-2-202-20020−2−222−2−22202i2i−2i−2i0−2−2220000-22-2222−2−222−2−200000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ3922-22-22-2-2-202-20020−2−222−2−2220−2i−2i2i2i0−2−22200002-22-2−2−222−2−22200000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ4022-22-22-2-2-202-20020−2−222−2−2220−2i−2i2i2i0−2−2220000-22-2222−2−222−2−2000000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-2-22-22202-200-202−22−22−22−202-22-202−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−2i2−i2i2−i2000000000000
χ422-22-2-22-22202-200-202−22−22−22−202-22-202−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−2−i2i2−i2i2000000000000
χ432-22-2-22-22202-200-202−22−22−22−20-22-2202−22−22i−2i2i−2i0000i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−22−i2i2−i2i2000000000000
χ442-22-2-22-22202-200-202−22−22−22−20-22-2202−22−2−2i2i−2i2i0000−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−22i2−i2i2−i2000000000000
χ452-22-2-22-22202-200-20−22−22−22−2202-22-20−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i200002i−2i0000−22−22−i2i2−i2i2000000000000
χ462-22-2-22-22202-200-20−22−22−22−2202-22-20−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i20000−2i2i0000−22−22i2−i2i2−i2000000000000
χ472-22-2-22-22202-200-20−22−22−22−220-22-220−22−222i−2i2i−2i0000−i2i2−i2i2−i2i2−i2i20000−2i2i00002−22−2i2−i2i2−i2000000000000
χ482-22-2-22-22202-200-20−22−22−22−220-22-220−22−22−2i2i−2i2i0000i2−i2i2−i2i2−i2i2−i200002i−2i00002−22−2−i2i2−i2i2000000000000
χ492-2-2-2222-22-2-2-2222-22-2-222-2-2220000-2-222-2000000000000000000000000000000000002i−2i02i−2i000000
χ502-2-2-2222-22-2-2-2222-22-2-222-2-2220000-2-222-200000000000000000000000000000000000−2i2i0−2i2i000000
χ512-2-2-2222-22-2-2-2222-2-222-2-222-220000-22-2-22000000000000000000000000000000000002i−2i0−2i2i000000
χ522-2-2-2222-22-2-2-2222-2-222-2-222-220000-22-2-2200000000000000000000000000000000000−2i2i02i−2i000000
χ532-2-2-2222-2-2222-2-2-220000000022i−2i−2i2i-20000000000002i−2i−2i2i2i−2i−2i2i002i−2i0000000000-222-2000000000000
χ542-2-2-2222-2-2222-2-2-220000000022i−2i−2i2i-2000000000000−2i2i2i−2i−2i2i2i−2i002i−2i00000000002-2-22000000000000
χ552-2-2-2222-2-2222-2-2-22000000002−2i2i2i−2i-20000000000002i−2i−2i2i2i−2i−2i2i00−2i2i00000000002-2-22000000000000
χ562-2-2-2222-2-2222-2-2-22000000002−2i2i2i−2i-2000000000000−2i2i2i−2i−2i2i2i−2i00−2i2i0000000000-222-2000000000000
χ572-2-2-2222-2-2-22222-2-22-2-222-2-22-22i−2i−2i2i22-2-22000000000000000000−2i2i0000002i−2i−2i2i0000000000000000
χ582-2-2-2222-2-2-22222-2-22-2-222-2-22-2−2i2i2i−2i22-2-220000000000000000002i−2i000000−2i2i2i−2i0000000000000000
χ592-2-2-2222-2-2-22222-2-2-222-2-222-2-22i−2i−2i2i2-222-2000000000000000000−2i2i000000−2i2i2i−2i0000000000000000
χ602-2-2-2222-2-2-22222-2-2-222-2-222-2-2−2i2i2i−2i2-222-20000000000000000002i−2i0000002i−2i−2i2i0000000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-40400-440-40000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ63444-44-4-4-40400-440-4000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6444-44-44-4-440-4400-402222−22−222222−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6544-44-44-4-440-4400-40−22−222222−22−2222220000002222−22−220000000000000000000000000000000000000000000000
χ6644-4-4-4-444000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000022−22−22222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-4-4-444000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−222222−22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-4-4-44400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000022−22−2222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6944-4-4-4-44400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−222222−222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000002i2−2i2−2i22i20000-22-222-22-2000000000000000000000000000000
χ714-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000−2i22i22i2−2i200002-22-2-22-22000000000000000000000000000000
χ724-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000002i2−2i2−2i22i200002-22-2-22-22000000000000000000000000000000
χ734-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000−2i22i22i2−2i20000-22-222-22-2000000000000000000000000000000
χ744-44-4-44-44-40-44004022−2222−2222−2222−22000000−2222−22220000000000000000000000000000000000000000000000
χ754-44-4-44-44-40-440040−2222−2222−2222−222200000022−2222−220000000000000000000000000000000000000000000000
χ764-4-444-4-4404004-40-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ774-4-444-4-4404004-40-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ784-4-444-4-440-400-44040000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ794-4-444-4-440-400-440400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ804-4-4-4444-444-4-4-4-44400000000-40000400000000000000000000000000000000000000000000000000

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