Finite Group Databasebeta

← Group #10858332

Character table — Group #10858332

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order122222223444444446666666441212121212121212444444448888121212121212121212122424242424242424444444448888888812121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ4111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ9111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-111-1-11-1-1-1-11
χ10111111111-1-1-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-11111-1
χ11111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-111-11
χ12111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-11-1-11-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1111111-1-11-1-1-11-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1111-11
χ15111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-11-1-1-11
χ172222222222222-2-2-2-22222222-2-22222-2-2-2-20000000000000000-2-200000000000022220000000000000000-2-20000
χ182222222222222-2-2-2-22222222-2-22222-2-2-2-20000000000000000-2-2000000000000-2-2-2-20000000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000000000002200000000000022-2-20000000000000000-220000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000000000022000000000000-2-22200000000000000002-20000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-222-2-2-2-21111-1-11111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-12222-2-2-2-2-2-222-1-1-1-1111111-1-1-1-111110000000000000000-1-111000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-122-2-2-2-22222-2-2-1-1-1-11111111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-22222-2-222-2-2111111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-21111-1-1-1-1-2-2-2-22222-2-222111111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ29222-2-22-2-2200002-22-222-2-2-22-200000022-2-22-2000000000022-2-200000000000000000022-2-222-2-200000000000000
χ30222-2-22-2-2200002-22-222-2-2-22-200000022-2-22-2000000000022-2-2000000000000000000-2-222-2-22200000000000000
χ31222-2-22-2-2200002-22-222-2-2-22-200000022-2-2-220000000000-2-22200000000000000000022-2-2-2-22200000000000000
χ32222-2-22-2-2200002-22-222-2-2-22-200000022-2-2-220000000000-2-222000000000000000000-2-22222-2-200000000000000
χ3322-222-2-2-2222-2-200002-222-2-2-20022-2-20000000000002−22−2000000000022−2−222−2−22-22-200002−22−222−2−20000000000
χ3422-222-2-2-2222-2-200002-222-2-2-20022-2-20000000000002−22−2000000000022−2−222−2−2-22-220000−22−22−2−2220000000000
χ3522-222-2-2-2222-2-200002-222-2-2-20022-2-2000000000000−22−220000000000−2−222−2−2222-22-20000−22−22−2−2220000000000
χ3622-222-2-2-2222-2-200002-222-2-2-20022-2-2000000000000−22−220000000000−2−222−2−222-22-2200002−22−222−2−20000000000
χ3722-222-2-2-22-2-22200002-222-2-2-200-2-2220000000000002−2−220000000000−2−22222−2−22-2-220000−22−2222−2−20000000000
χ3822-222-2-2-22-2-22200002-222-2-2-200-2-2220000000000002−2−220000000000−2−22222−2−2-222-200002−22−2−2−2220000000000
χ3922-222-2-2-22-2-22200002-222-2-2-200-2-222000000000000−222−2000000000022−2−2−2−2222-2-2200002−22−2−2−2220000000000
χ4022-222-2-2-22-2-22200002-222-2-2-200-2-222000000000000−222−2000000000022−2−2−2−222-222-20000−22−2222−2−20000000000
χ412-2-22-222-222i−2i2i−2i2-2-22-2-22-222-22i−2i2i−2i2i−2i2-22-2002-2002i−2i000000002i−2i00000000000000000000000000002-22i−2i000000
χ422-2-22-222-222i−2i2i−2i2-2-22-2-22-222-22i−2i2i−2i2i−2i2-22-200-2200−2i2i000000002i−2i0000000000000000000000000000-22−2i2i000000
χ432-2-22-222-222i−2i2i−2i-222-2-2-22-222-2−2i2i2i−2i2i−2i-22-220000000000000000−2i2i00000000000000002-22-2000000000000002i−2i00
χ442-2-22-222-222i−2i2i−2i-222-2-2-22-222-2−2i2i2i−2i2i−2i-22-220000000000000000−2i2i0000000000000000-22-2200000000000000−2i2i00
χ452-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-2−2i2i−2i2i−2i2i2-22-2002-200−2i2i00000000−2i2i00000000000000000000000000002-2−2i2i000000
χ462-2-22-222-22−2i2i−2i2i2-2-22-2-22-222-2−2i2i−2i2i−2i2i2-22-200-22002i−2i00000000−2i2i0000000000000000000000000000-222i−2i000000
χ472-2-22-222-22−2i2i−2i2i-222-2-2-22-222-22i−2i−2i2i−2i2i-22-2200000000000000002i−2i00000000000000002-22-200000000000000−2i2i00
χ482-2-22-222-22−2i2i−2i2i-222-2-2-22-222-22i−2i−2i2i−2i2i-22-2200000000000000002i−2i0000000000000000-22-22000000000000002i−2i00
χ492-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-112i−2i−ii−ii-11-11002-2002i−2i0000−i3i3−i3i3−ii33−3−3−i3i3−i3i33−33−30000000000000000-11−ii000000
χ502-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-112i−2i−ii−ii-11-11002-2002i−2i0000i3−i3i3−i3−ii−3−333i3−i3i3−i3−33−330000000000000000-11−ii000000
χ512-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-112i−2i−ii−ii-11-1100-2200−2i2i0000−i3i3−i3i3−ii33−3−3i3−i3i3−i3−33−3300000000000000001-1i−i000000
χ522-2-22-222-2-12i−2i2i−2i2-2-2211-11-1-112i−2i−ii−ii-11-1100-2200−2i2i0000i3−i3i3−i3−ii−3−333−i3i3−i3i33−33−300000000000000001-1i−i000000
χ532-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-11−2i2ii−ii−i-11-11002-200−2i2i0000−i3i3−i3i3i−i−3−333−i3i3−i3i3−33−330000000000000000-11i−i000000
χ542-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-11−2i2ii−ii−i-11-11002-200−2i2i0000i3−i3i3−i3i−i33−3−3i3−i3i3−i33−33−30000000000000000-11i−i000000
χ552-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-11−2i2ii−ii−i-11-1100-22002i−2i0000−i3i3−i3i3i−i−3−333i3−i3i3−i33−33−300000000000000001-1−ii000000
χ562-2-22-222-2-1−2i2i−2i2i2-2-2211-11-1-11−2i2ii−ii−i-11-1100-22002i−2i0000i3−i3i3−i3i−i33−3−3−i3i3−i3i3−33−3300000000000000001-1−ii000000
χ572-2-2-222-2220000-2-222-2-2-22-222000000-222-200002-20000000000002-22-20000000000002-2-2200002-22-20000000000
χ582-2-2-222-2220000-2-222-2-2-22-222000000-222-200002-20000000000002-22-2000000000000-222-20000-22-220000000000
χ592-2-2-222-2220000-2-222-2-2-22-222000000-222-20000-22000000000000-22-220000000000002-2-220000-22-220000000000
χ602-2-2-222-2220000-2-222-2-2-22-222000000-222-20000-22000000000000-22-22000000000000-222-200002-22-20000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000000000002200000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000000000-2-200000000000000000000000000000000000000
χ63444-4-44-4-440000-44-4444-4-4-44-4000000-4-44400000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-200004-44-4-2-2222-22000000-2-2224-40000000000-2-2220000000000000000000000000000000000000000
χ65444-4-44-4-4-200004-44-4-2-2222-22000000-2-222-44000000000022-2-20000000000000000000000000000000000000000
χ66444-4-44-4-4-20000-44-44-2-2222-2200000022-2-200000000000000000023−23−23230000000000000000000000000000000000
χ67444-4-44-4-4-20000-44-44-2-2222-2200000022-2-2000000000000000000−232323−230000000000000000000000000000000000
χ6844-444-4-4-4-244-4-40000-22-2-222200-2-22200000000000022−2222−220000000000−2−222−2−22200000000000000000000000000
χ6944-444-4-4-4-244-4-40000-22-2-222200-2-222000000000000−2222−2222000000000022−2−222−2−200000000000000000000000000
χ7044-444-4-4-4-2-4-4440000-22-2-22220022-2-200000000000022−22−2222000000000022−2−2−2−22200000000000000000000000000
χ7144-444-4-4-4-2-4-4440000-22-2-22220022-2-2000000000000−222222−220000000000−2−22222−2−200000000000000000000000000
χ7244-4-4-4-4444000000004-4-4-44-4400000000000000000000000000000000000000000000000022−22−222200000000000000
χ7344-4-4-4-4444000000004-4-4-44-44000000000000000000000000000000000000000000000000−222222−2200000000000000
χ744-444-4-4-4444i−4i−4i4i0000-444-4-4-44004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ754-444-4-4-444−4i4i4i−4i0000-444-4-4-4400−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ764-444-4-4-44-24i−4i−4i4i00002-2-2222-200−2i2i2i−2i00000000000000000000000000i6−i6−i6i6−666−600000000000000000000000000
χ774-444-4-4-44-24i−4i−4i4i00002-2-2222-200−2i2i2i−2i00000000000000000000000000−i6i6i6−i66−6−6600000000000000000000000000
χ784-444-4-4-44-2−4i4i4i−4i00002-2-2222-2002i−2i−2i2i00000000000000000000000000i6−i6−i6i66−6−6600000000000000000000000000
χ794-444-4-4-44-2−4i4i4i−4i00002-2-2222-2002i−2i−2i2i00000000000000000000000000−i6i6i6−i6−666−600000000000000000000000000
χ804-44-44-44-4400000000-44-444-4-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ814-44-44-44-4400000000-44-444-4-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ824-4-44-444-4-24i−4i4i−4i-444-422-22-2-22−4i4i−2i2i−2i2i2-22-200000000000000002i−2i00000000000000000000000000000000000000
χ834-4-44-444-4-2−4i4i−4i4i-444-422-22-2-224i−4i2i−2i2i−2i2-22-20000000000000000−2i2i00000000000000000000000000000000000000
χ844-4-4-444-444000044-4-4-4-4-44-4440000004-4-4400000000000000000000000000000000000000000000000000000000
χ854-4-4-444-44-2000044-4-4222-22-2-2000000-222-2000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ864-4-4-444-44-2000044-4-4222-22-2-2000000-222-20000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ874-4-4-444-44-20000-4-444222-22-2-20000002-2-2200004-4000000000000-22-220000000000000000000000000000000000
χ884-4-4-444-44-20000-4-444222-22-2-20000002-2-220000-440000000000002-22-20000000000000000000000000000000000
χ8988-8-8-8-888-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000
χ908-88-88-88-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000

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