Finite Group Databasebeta

← Group #10822196

Character table — Group #10822196

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order124422222223444444466612121212666666121212121212224444444444666612121212121212121212121212121212121212122222444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-11-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-111-1-1
χ1011-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-11-11-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111-1-111
χ1111-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-1111-1-1-1-111
χ1211-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11-1111-1-1-11111-1-1
χ1311-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-1-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-11-1-1-111-1-111
χ1411-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-1-11-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111-1111-1-111-1-1
χ1511-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-1-11-11-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-111-11-1-1-11-1-11111-1-1
χ1611-1-11-1-1-1-111111-1-1-111-1-1111-1-11-1-1-111111-1-1-1-11-11-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-11-1111-111-1-1-1-111
χ1722222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ1922222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ212222222-2-2-2-22222-2-2-2-2222222222-2-2-2-22-2-22-2-2000000002i−2i2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222-2-2-2-22222-2-2-2-2222222222-2-2-2-22-2-22-2-200000000−2i2i−2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ232222222-2-2-2-2-1222-2-2-2-2-1-1-1-1-1-1-1-1-11111-111-111000000002i−2i2i−2i−i3i3−i3i3−i3i3−i3i333−3−333−3−3−i−iii−i−iii0000000000000000
χ242222222-2-2-2-2-1222-2-2-2-2-1-1-1-1-1-1-1-1-11111-111-111000000002i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−3−333−3−333−i−iii−i−iii0000000000000000
χ252222222-2-2-2-2-1222-2-2-2-2-1-1-1-1-1-1-1-1-11111-111-11100000000−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3−3−333−3−333ii−i−iii−i−i0000000000000000
χ262222222-2-2-2-2-1222-2-2-2-2-1-1-1-1-1-1-1-1-11111-111-11100000000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i333−3−333−3−3ii−i−iii−i−i0000000000000000
χ2722222-2-222-2-22-2-22-2-222-2-22-2-2222-222-2-2-2222-2-22-2-220000000022-2-2-2-22200000000000000000000000000000000
χ2822222-2-222-2-22-2-22-2-222-2-22-2-2222-222-2-2-2222-2-2-222-200000000-2-22222-2-200000000000000000000000000000000
χ2922222-2-222-2-2-1-2-22-2-22211-111-1-1-11-1-1111-1-1-1112-2-2200000000-1-11111-1-13−33−33−33−33−33−33−33−30000000000000000
χ3022222-2-222-2-2-1-2-22-2-22211-111-1-1-11-1-1111-1-1-1112-2-2200000000-1-11111-1-1−33−33−33−33−33−33−33−330000000000000000
χ3122222-2-222-2-2-1-2-22-2-22211-111-1-1-11-1-1111-1-1-111-222-20000000011-1-1-1-1113−33−33−33−3−33−33−33−330000000000000000
χ3222222-2-222-2-2-1-2-22-2-22211-111-1-1-11-1-1111-1-1-111-222-20000000011-1-1-1-111−33−33−33−333−33−33−33−30000000000000000
χ3322222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-2-222-2-2-222200002-22-20000000000002-2-222-2-22000000000000000000000000
χ3422222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-2-222-2-2-22220000-22-22000000000000-222-2-222-2000000000000000000000000
χ3522222-2-2-2-222-1-2-2222-2-211-111-1-1-1111-1-1111-1-1-100002-22-20000−i3i3i3−i3i3−i3−i3i3-111-1-111-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ3622222-2-2-2-222-1-2-2222-2-211-111-1-1-1111-1-1111-1-1-100002-22-20000i3−i3−i3i3−i3i3i3−i3-111-1-111-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ3722222-2-2-2-222-1-2-2222-2-211-111-1-1-1111-1-1111-1-1-10000-22-220000−i3i3i3−i3i3−i3−i3i31-1-111-1-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ3822222-2-2-2-222-1-2-2222-2-211-111-1-1-1111-1-1111-1-1-10000-22-220000i3−i3−i3i3−i3i3i3−i31-1-111-1-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ392222-22-22-22-222-2-22-22-22222222-2-22-22-2-22-2-22-2000000000000000000000000000000000000002-200-2200000000
χ402222-22-22-22-222-2-22-22-22222222-2-22-22-2-22-2-22-200000000000000000000000000000000000000-22002-200000000
χ412222-22-2-22-2222-2-2-22-222222222-2-2-22-22-2-22-2-22000000000000000000000000000000000000000000002-22-20000
χ422222-22-2-22-2222-2-2-22-222222222-2-2-22-22-2-22-2-2200000000000000000000000000000000000000000000-22-220000
χ432222-2-222-2-222-22-2-222-2-2-22-2-222-222-2-2222-2-2-220000000000000000000000000000000000000000000000002-22-2
χ442222-2-222-2-222-22-2-222-2-2-22-2-222-222-2-2222-2-2-22000000000000000000000000000000000000000000000000-22-22
χ452222-2-22-222-22-22-22-2-22-2-22-2-222-22-222-22-22-22-20000000000000000000000000000000000002-2002-20000000000
χ462222-2-22-222-22-22-22-2-22-2-22-2-222-22-222-22-22-22-2000000000000000000000000000000000000-2200-220000000000
χ4722-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-200002-2-220000000000002-2-22-222-2000000000000000000000000
χ4822-2-222222222-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000-222-2000000000000-222-22-2-22000000000000000000000000
χ4922-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002-2-220000−i3i3−i3i3i3−i3i3−i3-111-11-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ5022-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111100002-2-220000i3−i3i3−i3−i3i3−i3i3-111-11-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ5122-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000-222-20000−i3i3−i3i3i3−i3i3−i31-1-11-111-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ5222-2-22222222-1-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111110000-222-20000i3−i3i3−i3−i3i3−i3i31-1-11-111-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ5322-2-2222-2-2-2-22-2-2-22222222-2-2-2-222-2-2-2-2-222-22222-2-2000000002222-2-2-2-200000000000000000000000000000000
χ5422-2-2222-2-2-2-22-2-2-22222222-2-2-2-222-2-2-2-2-222-222-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ5522-2-2222-2-2-2-2-1-2-2-22222-1-1-11111-1-111111-1-11-1-122-2-200000000-1-1-1-111113−33−3−33−333−33−3−33−330000000000000000
χ5622-2-2222-2-2-2-2-1-2-2-22222-1-1-11111-1-111111-1-11-1-122-2-200000000-1-1-1-11111−33−333−33−3−33−333−33−30000000000000000
χ5722-2-2222-2-2-2-2-1-2-2-22222-1-1-11111-1-111111-1-11-1-1-2-222000000001111-1-1-1-13−33−3−33−33−33−333−33−30000000000000000
χ5822-2-2222-2-2-2-2-1-2-2-22222-1-1-11111-1-111111-1-11-1-1-2-222000000001111-1-1-1-1−33−333−33−33−33−3−33−330000000000000000
χ5922-2-22-2-222-2-2222-222-2-2-2-2222-2-22-222-2-22-2-2-222000000002i−2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ6022-2-22-2-222-2-2222-222-2-2-2-2222-2-22-222-2-22-2-2-22200000000−2i2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ6122-2-22-2-222-2-2-122-222-2-211-1-1-111-11-1-111-1111-1-1000000002i−2i−2i2i−i3i3i3−i3−i3i3i3−i333−3−3−3−333−i−iiiii−i−i0000000000000000
χ6222-2-22-2-222-2-2-122-222-2-211-1-1-111-11-1-111-1111-1-1000000002i−2i−2i2ii3−i3−i3i3i3−i3−i3i3−3−33333−3−3−i−iiiii−i−i0000000000000000
χ6322-2-22-2-222-2-2-122-222-2-211-1-1-111-11-1-111-1111-1-100000000−2i2i2i−2i−i3i3i3−i3−i3i3i3−i3−3−33333−3−3ii−i−i−i−iii0000000000000000
χ6422-2-22-2-222-2-2-122-222-2-211-1-1-111-11-1-111-1111-1-100000000−2i2i2i−2ii3−i3−i3i3i3−i3−i3i333−3−3−3−333ii−i−i−i−iii0000000000000000
χ6522-2-22-2-2-2-222-122-2-2-22211-1-1-111-1111-1-1-1-1-11112-22-222-2-222-2-2-1-111-1-111-1-1-1-11111-1-1-1-111110000000000000000
χ6622-2-22-2-2-2-222-122-2-2-22211-1-1-111-1111-1-1-1-1-11112-22-2-2-222-2-222-1-111-1-1111111-1-1-1-11111-1-1-1-10000000000000000
χ6722-2-22-2-2-2-222-122-2-2-22211-1-1-111-1111-1-1-1-1-1111-22-2222-2-2-2-22211-1-111-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ6822-2-22-2-2-2-222-122-2-2-22211-1-1-111-1111-1-1-1-1-1111-22-22-2-22222-2-211-1-111-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ6922-2-2-22-22-22-22-222-22-22222-2-2-2-2-2-22-22-22-222-220000000000000000000000000000000000002-200-220000000000
χ7022-2-2-22-22-22-22-222-22-22222-2-2-2-2-2-22-22-22-222-22000000000000000000000000000000000000-22002-20000000000
χ7122-2-2-22-2-22-222-2222-22-2222-2-2-2-2-2-2-22-2222-222-20000000000000000000000000000000000000000000000002-2-22
χ7222-2-2-22-2-22-222-2222-22-2222-2-2-2-2-2-2-22-2222-222-2000000000000000000000000000000000000000000000000-222-2
χ7322-2-2-2-222-2-2222-222-2-22-2-2222-2-2-222-2-22-2-2222-2000000000000000000000000000000000000000000002-2-220000
χ7422-2-2-2-222-2-2222-222-2-22-2-2222-2-2-222-2-22-2-2222-200000000000000000000000000000000000000000000-222-20000
χ7522-2-2-2-22-222-222-22-222-2-2-2222-2-2-22-222-2-22-22-22000000000000000000000000000000000000002200-2-200000000
χ7622-2-2-2-22-222-222-22-222-2-2-2222-2-2-22-222-2-22-22-2200000000000000000000000000000000000000-2-2002200000000
χ774444-44-44-44-4-24-4-44-44-4-2-2-2-2-2-2-222-22-222-222-220000000000000000000000000000000000000000000000000000
χ784444-44-4-44-44-24-4-4-44-44-2-2-2-2-2-2-2222-22-222-222-20000000000000000000000000000000000000000000000000000
χ794444-4-444-4-44-2-44-4-444-422-222-2-22-2-222-2-2-2222-20000000000000000000000000000000000000000000000000000
χ804444-4-44-444-4-2-44-44-4-4422-222-2-22-22-2-22-22-22-220000000000000000000000000000000000000000000000000000
χ8144-4-4-44-44-44-4-2-444-44-44-2-2-2222222-22-22-22-2-22-20000000000000000000000000000000000000000000000000000
χ8244-4-4-44-4-44-44-2-4444-44-4-2-2-22222222-22-2-2-22-2-220000000000000000000000000000000000000000000000000000
χ8344-4-4-4-444-4-44-24-444-4-4422-2-2-2222-2-222-222-2-2-220000000000000000000000000000000000000000000000000000
χ8444-4-4-4-44-444-4-24-44-444-422-2-2-2222-22-2-222-22-22-20000000000000000000000000000000000000000000000000000
χ858-88i−8i00000008000000000-8008i−8i0000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i0000000-40000000−4i34i3443−43−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i0000000-400000004i3−4i34−4343−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i00000008000000000-800−8i8i0000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i0000000-40000000−4i34i34−43434i−4i0000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i0000000-400000004i3−4i3443−434i−4i0000000000000000000000000000000000000000000000000000000000000000

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