Finite Group Databasebeta

← Group #10825715

Character table — Group #10825715

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order124488882223444688888812122424242466612121224242424242444444488888812121212121212121212121224242424242424242424242422448888222444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111
χ51111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-11-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-111
χ71111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11-1-11-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-11111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-111
χ101111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-111111-1-1
χ111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-11-1-111-1-1
χ121111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11-111-1-111
χ131111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-11111-1-1-1-1
χ141111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-11111
χ151111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111
χ161111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1
χ1722222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-11111111100000000000000000000
χ1922222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-21111-1-1-1-111111111-1-1-1-1111100000000000000000000
χ2022222222222-1222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22211111111-1-1-1-111111111-1-1-1-100000000000000000000
χ21222222222-2-222-2-2222-2-2-2-22222222-2-22-2-222-2-2-2-200002-200002-20000000022-2-20000000022-2-200000000000000000000
χ22222222222-2-222-2-2222-2-2-2-22222222-2-22-2-222-2-2-2-20000-220000-2200000000-2-22200000000-2-22200000000000000000000
χ23222222222-2-2-12-2-2-122-2-2-2-2-1-1-1-1-1-1-111-111-1-1111100002-200002-233−3−333−3−3-1-11133−3−333−3−3-1-11100000000000000000000
χ24222222222-2-2-12-2-2-122-2-2-2-2-1-1-1-1-1-1-111-111-1-1111100002-200002-2−3−333−3−333-1-111−3−333−3−333-1-11100000000000000000000
χ25222222222-2-2-12-2-2-122-2-2-2-2-1-1-1-1-1-1-111-111-1-111110000-220000-2233−3−3−3−33311-1-133−3−3−3−33311-1-100000000000000000000
χ26222222222-2-2-12-2-2-122-2-2-2-2-1-1-1-1-1-1-111-111-1-111110000-220000-22−3−33333−3−311-1-1−3−33333−3−311-1-100000000000000000000
χ2722222222-22-22-22-22-2-222-2-2222222-22-2-22-2-2-222-2-2002-200002-20000002-22-2000000002-22-2000000000000000000000000
χ2822222222-22-22-22-22-2-222-2-2222222-22-2-22-2-2-222-2-200-220000-22000000-22-2200000000-22-22000000000000000000000000
χ2922222222-22-2-1-22-2-1-2-222-2-2-1-1-1-1-1-11-111-1111-1-111002-200002-2003−33−3-11-113−33−33−33−3-11-113−33−300000000000000000000
χ3022222222-22-2-1-22-2-1-2-222-2-2-1-1-1-1-1-11-111-1111-1-111002-200002-200−33−33-11-11−33−33−33−33-11-11−33−3300000000000000000000
χ3122222222-22-2-1-22-2-1-2-222-2-2-1-1-1-1-1-11-111-1111-1-11100-220000-22003−33−31-11-1−33−333−33−31-11-1−33−3300000000000000000000
χ3222222222-22-2-1-22-2-1-2-222-2-2-1-1-1-1-1-11-111-1111-1-11100-220000-2200−33−331-11-13−33−3−33−331-11-13−33−300000000000000000000
χ3322222222-2-222-2-222-2-2-2-222222222-2-22-2-22-2-2-2-2222-200002-200002-2-22000000002-2-220000000000000000000000000000
χ3422222222-2-222-2-222-2-2-2-222222222-2-22-2-22-2-2-2-222-220000-220000-222-200000000-222-20000000000000000000000000000
χ3522222222-2-22-1-2-22-1-2-2-2-222-1-1-1-1-1-111-111-11111-1-12-200002-20000-111-13−3−33−333−3-111-13−3−33−333−300000000000000000000
χ3622222222-2-22-1-2-22-1-2-2-2-222-1-1-1-1-1-111-111-11111-1-12-200002-20000-111-1−333−33−3−33-111-1−333−33−3−3300000000000000000000
χ3722222222-2-22-1-2-22-1-2-2-2-222-1-1-1-1-1-111-111-11111-1-1-220000-2200001-1-113−3−333−3−331-1-113−3−333−3−3300000000000000000000
χ3822222222-2-22-1-2-22-1-2-2-2-222-1-1-1-1-1-111-111-11111-1-1-220000-2200001-1-11−333−3−333−31-1-11−333−3−333−300000000000000000000
χ392222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-11111112222-2-2-2-2-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-100000000000000000000
χ402222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-111111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ412222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2222222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ422222-2-2-2-2222-1222-1-2-2-2-2-2-2-1-11111-1-1-1-1-1-1111111-2-2-2-2-2-2222222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ432222-2-2-2-22-2-222-2-22-2-2222222-2-2-2-22-2-22-2-2-2-2222200002-20000-220000000022-2-200000000-2-22200000000000000000000
χ442222-2-2-2-22-2-222-2-22-2-2222222-2-2-2-22-2-22-2-2-2-222220000-2200002-200000000-2-2220000000022-2-200000000000000000000
χ452222-2-2-2-22-2-2-12-2-2-1-2-22222-1-11111-111-11111-1-1-1-100002-20000-2233−3−3−3−333-1-111−3−33333−3−311-1-100000000000000000000
χ462222-2-2-2-22-2-2-12-2-2-1-2-22222-1-11111-111-11111-1-1-1-100002-20000-22−3−33333−3−3-1-11133−3−3−3−33311-1-100000000000000000000
χ472222-2-2-2-22-2-2-12-2-2-1-2-22222-1-11111-111-11111-1-1-1-10000-2200002-233−3−333−3−311-1-1−3−333−3−333-1-11100000000000000000000
χ482222-2-2-2-22-2-2-12-2-2-1-2-22222-1-11111-111-11111-1-1-1-10000-2200002-2−3−333−3−33311-1-133−3−333−3−3-1-11100000000000000000000
χ492222-2-2-2-2-22-22-22-2222-2-22222-2-2-2-2-22-2-22-222-2-222002-20000-220000002-22-200000000-22-22000000000000000000000000
χ502222-2-2-2-2-22-22-22-2222-2-22222-2-2-2-2-22-2-22-222-2-22200-2200002-2000000-22-22000000002-22-2000000000000000000000000
χ512222-2-2-2-2-22-2-1-22-2-122-2-222-1-111111-111-11-1-111-1-1002-20000-22003−33−3-11-11−33−33−33−331-11-13−33−300000000000000000000
χ522222-2-2-2-2-22-2-1-22-2-122-2-222-1-111111-111-11-1-111-1-1002-20000-2200−33−33-11-113−33−33−33−31-11-1−33−3300000000000000000000
χ532222-2-2-2-2-22-2-1-22-2-122-2-222-1-111111-111-11-1-111-1-100-2200002-2003−33−31-11-13−33−3−33−33-11-11−33−3300000000000000000000
χ542222-2-2-2-2-22-2-1-22-2-122-2-222-1-111111-111-11-1-111-1-100-2200002-200−33−331-11-1−33−333−33−3-11-113−33−300000000000000000000
χ552222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-2-22-2-222222-2-22-20000-2200002-2-2200000000-222-20000000000000000000000000000
χ562222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-2-22-2-222222-2-2-2200002-20000-222-2000000002-2-220000000000000000000000000000
χ572222-2-2-2-2-2-22-1-2-22-12222-2-2-1-1111111-111-1-1-1-1-1112-20000-220000-111-13−3−333−3−331-1-11−333−3−333−300000000000000000000
χ582222-2-2-2-2-2-22-1-2-22-12222-2-2-1-1111111-111-1-1-1-1-1112-20000-220000-111-1−333−3−333−31-1-113−3−333−3−3300000000000000000000
χ592222-2-2-2-2-2-22-1-2-22-12222-2-2-1-1111111-111-1-1-1-1-111-2200002-200001-1-113−3−33−333−3-111-1−333−33−3−3300000000000000000000
χ602222-2-2-2-2-2-22-1-2-22-12222-2-2-1-1111111-111-1-1-1-1-111-2200002-200001-1-11−333−33−3−33-111-13−3−33−333−300000000000000000000
χ6122-2-22i2i−2i−2i2222-2-2-222i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i00000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ6222-2-22i2i−2i−2i2222-2-2-222i−2i2i−2i2i−2i-2-22i2i−2i−2i222-2-2-22i−2i2i−2i2i−2i000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ6322-2-22i2i−2i−2i2-2-22-22222i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000200-200002i−2i
χ6422-2-22i2i−2i−2i2-2-22-22222i−2i−2i2i−2i2i-2-22i2i−2i−2i2-2-2-2222i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000-20020000−2i2i
χ6522-2-22i2i−2i−2i-22-222-222−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000200-20002i−2i00
χ6622-2-22i2i−2i−2i-22-222-222−2i2i2i−2i−2i2i-2-22i2i−2i−2i-22-22-22−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000-2002000−2i2i00
χ6722-2-22i2i−2i−2i-2-22222-22−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000200-2002i−2i0000
χ6822-2-22i2i−2i−2i-2-22222-22−2i2i−2i2i2i−2i-2-22i2i−2i−2i-2-2222-2−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000-200200−2i2i0000
χ6922-2-2−2i−2i2i2i2222-2-2-22−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i00000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ7022-2-2−2i−2i2i2i2222-2-2-22−2i2i−2i2i−2i2i-2-2−2i−2i2i2i222-2-2-2−2i2i−2i2i−2i2i000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ7122-2-2−2i−2i2i2i2-2-22-2222−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000200-20000−2i2i
χ7222-2-2−2i−2i2i2i2-2-22-2222−2i2i2i−2i2i−2i-2-2−2i−2i2i2i2-2-2-222−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000-200200002i−2i
χ7322-2-2−2i−2i2i2i-22-222-2222i−2i−2i2i2i−2i-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i000000000000000000000000000000000000000000000200-2000−2i2i00
χ7422-2-2−2i−2i2i2i-22-222-2222i−2i−2i2i2i−2i-2-2−2i−2i2i2i-22-22-222i−2i−2i2i2i−2i000000000000000000000000000000000000000000000-20020002i−2i00
χ7522-2-2−2i−2i2i2i-2-22222-222i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i00000000000000000000000000000000000000000000200-200−2i2i0000
χ7622-2-2−2i−2i2i2i-2-22222-222i−2i2i−2i−2i2i-2-2−2i−2i2i2i-2-2222-22i−2i2i−2i−2i2i00000000000000000000000000000000000000000000-2002002i−2i0000
χ7744-4-44i4i−4i−4i444-2-4-4-4-24i−4i4i−4i4i−4i22−2i−2i2i2i-2-2-2222−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ7844-4-44i4i−4i−4i4-4-4-2-444-24i−4i−4i4i−4i4i22−2i−2i2i2i-2222-2-2−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ7944-4-44i4i−4i−4i-44-4-24-44-2−4i4i4i−4i−4i4i22−2i−2i2i2i2-22-22-22i−2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8044-4-44i4i−4i−4i-4-44-244-4-2−4i4i−4i4i4i−4i22−2i−2i2i2i22-2-2-222i−2i2i−2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8144-4-4−4i−4i4i4i444-2-4-4-4-2−4i4i−4i4i−4i4i222i2i−2i−2i-2-2-22222i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8244-4-4−4i−4i4i4i4-4-4-2-444-2−4i4i4i−4i4i−4i222i2i−2i−2i-2222-2-22i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8344-4-4−4i−4i4i4i-44-4-24-44-24i−4i−4i4i4i−4i222i2i−2i−2i2-22-22-2−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8444-4-4−4i−4i4i4i-4-44-244-4-24i−4i4i−4i−4i4i222i2i−2i−2i22-2-2-22−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000
χ854-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130004000-40000004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130000000000000000000000000000000000000000000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ864-44i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ130004000-40000004i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000000000000000000000000000000000000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ874-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130004000-40000004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000000000000000000000000000000000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ884-44i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130004000-40000004i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13000000000000000000000000000000000000000000000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ894-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230004000-4000000−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000000000000000000000000000000000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ904-4−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230004000-4000000−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23000000000000000000000000000000000000000000000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ914-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230004000-4000000−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000000000000000000000000000000000000000000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ924-4−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230004000-4000000−4i4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000000000000000000000000000000000000000000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ938-88i−8i8ζ7+8ζ23−8ζ7−8ζ23−8ζ5−8ζ138ζ5+8ζ13000-40004000000−4i4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300000000000000000000000000000000000000000000000000000000000000000000
χ948-88i−8i−8ζ7−8ζ238ζ7+8ζ238ζ5+8ζ13−8ζ5−8ζ13000-40004000000−4i4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300000000000000000000000000000000000000000000000000000000000000000000
χ958-8−8i8i−8ζ5−8ζ138ζ5+8ζ138ζ7+8ζ23−8ζ7−8ζ23000-400040000004i−4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ2300000000000000000000000000000000000000000000000000000000000000000000
χ968-8−8i8i8ζ5+8ζ13−8ζ5−8ζ13−8ζ7−8ζ238ζ7+8ζ23000-400040000004i−4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ2300000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.