Finite Group Databasebeta

← Group #10828765

Character table — Group #10828765

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222444444444444444444666688888888888888888888888881212121212121212161616161624242424242424242448
order12222222344446666666224444666688881212121222224444488121212121212121212122424242424242424444488884121212122244444884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11
χ71111111111111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1
χ911111111111111111111-1-11111-1-1-1-1111111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-111-1-1-1-1-11111-1-1-1
χ1011111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1-1-1111
χ1111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-111111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-11111111-1-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111111-1-11111-1-1-1-1-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-111-1-11111111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-111-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-111-1-1-1-11-1-111-1-11
χ17222222222-2-2-2-2222222222000022220000-2-2-2-22222-2000000-2-20000000000000000-2-22200000000000-20000000
χ18222222222-2-2-2-2222222222000022220000-2-2-2-2-2-2-2-2-2000000-2-2000000000000000022-2-20000000000020000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-222222000000220000000000000000-2-2-2-20000000000020000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-20000-2-2-2-2-2-2-2-22000000220000000000000000222200000000000-20000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-10000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-100002-2-222-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-211110000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-12222-1-1-1-100002-2-2-2-222-1-111111111-1-1-1-1-1-1-1-100000000-211110000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-10000222-2-2-2-2-1-11111111111111111000000002-1-1-1-10000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2222211112222-1-1-1-10000-222-2-2-2-211-1-1-1-11111-1-1-1-1111100000000-2-1-1110000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-2-2-2-2-1-1-1-10000-2-2-2-2-22211-1-1-1-111111111-1-1-1-100000000211-1-10000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-211112222-1-1-1-10000-2-2-222-2-2111111-1-1-1-1-1-1-1-1111100000000211-1-10000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-2-2-2-2-1-1-1-10000-2222222111111-1-1-1-11111-1-1-1-100000000-2-1-1110000000000
χ29222-2-2-2-222000022-2-2-2-222-2000022-2-2−i2−i2i2i2000022-2-200000−i2i20000000000−i2−i2i2i2−i2−i2i2i2002-2−i2−i2i2i2000000000000−i2i20
χ30222-2-2-2-222000022-2-2-2-222-2000022-2-2−i2−i2i2i20000-2-22200000−i2i20000000000−i2−i2i2i2−i2−i2i2i200-22i2i2−i2−i2000000000000i2−i20
χ31222-2-2-2-222000022-2-2-2-222-2000022-2-2i2i2−i2−i2000022-2-200000i2−i20000000000i2i2−i2−i2i2i2−i2−i2002-2i2i2−i2−i2000000000000i2−i20
χ32222-2-2-2-222000022-2-2-2-222-2000022-2-2i2i2−i2−i20000-2-22200000i2−i20000000000i2i2−i2−i2i2i2−i2−i200-22−i2−i2i2i2000000000000−i2i20
χ33222-2-2-2-222000022-2-2-2-22-220000-2-222−i2−i2i2i2000022-2-200000i2−i20000000000−i2−i2i2i2i2i2−i2−i200-22−i2−i2i2i2000000000000i2−i20
χ34222-2-2-2-222000022-2-2-2-22-220000-2-222−i2−i2i2i20000-2-22200000i2−i20000000000−i2−i2i2i2i2i2−i2−i2002-2i2i2−i2−i2000000000000−i2i20
χ35222-2-2-2-222000022-2-2-2-22-220000-2-222i2i2−i2−i2000022-2-200000−i2i20000000000i2i2−i2−i2−i2−i2i2i200-22i2i2−i2−i2000000000000−i2i20
χ36222-2-2-2-222000022-2-2-2-22-220000-2-222i2i2−i2−i20000-2-22200000−i2i20000000000i2i2−i2−i2−i2−i2i2i2002-2−i2−i2i2i2000000000000i2−i20
χ3722-222-2-2-22-2-2222-2-222-2-2002i2i−2i−2i000000002-22-200000000000002i2i−2i−2i00000000000000002-22-2000000002i−2i00000
χ3822-222-2-2-22-2-2222-2-222-2-2002i2i−2i−2i000000002-22-200000000000002i2i−2i−2i0000000000000000-22-2200000000−2i2i00000
χ3922-222-2-2-22-2-2222-2-222-2-200−2i−2i2i2i000000002-22-20000000000000−2i−2i2i2i00000000000000002-22-200000000−2i2i00000
χ4022-222-2-2-22-2-2222-2-222-2-200−2i−2i2i2i000000002-22-20000000000000−2i−2i2i2i0000000000000000-22-22000000002i−2i00000
χ412-22-222-2-22-22-22-2222-2-2-2002i−2i2i−2i00002-22-2-2-222000002i−2i0000002i−2i2i−2i00002-22-200000000000002i−2i000000000000
χ422-22-222-2-22-22-22-2222-2-2-2002i−2i2i−2i0000-22-22-2-22200000−2i2i0000002i−2i2i−2i0000-22-220000000000000−2i2i000000000000
χ432-22-222-2-22-22-22-2222-2-2-200−2i2i−2i2i00002-22-2-2-22200000−2i2i000000−2i2i−2i2i00002-22-20000000000000−2i2i000000000000
χ442-22-222-2-22-22-22-2222-2-2-200−2i2i−2i2i0000-22-22-2-222000002i−2i000000−2i2i−2i2i0000-22-2200000000000002i−2i000000000000
χ452-22-222-2-2-1-22-221-1-1-1111002i−2i2i−2i−i3i3−i3i32-22-211-1-1000002i−2i0000−i3i3−ii−ii33−3−3-11-11−i3i3−i3i3000000000−ii3−30000000000
χ462-22-222-2-2-1-22-221-1-1-1111002i−2i2i−2i−i3i3−i3i3-22-2211-1-100000−2i2i0000−i3i3−ii−ii33−3−31-11-1i3−i3i3−i3000000000i−i−330000000000
χ472-22-222-2-2-1-22-221-1-1-1111002i−2i2i−2ii3−i3i3−i32-22-211-1-1000002i−2i0000i3−i3−ii−ii−3−333-11-11i3−i3i3−i3000000000−ii−330000000000
χ482-22-222-2-2-1-22-221-1-1-1111002i−2i2i−2ii3−i3i3−i3-22-2211-1-100000−2i2i0000i3−i3−ii−ii−3−3331-11-1−i3i3−i3i3000000000i−i3−30000000000
χ492-22-222-2-2-1-22-221-1-1-111100−2i2i−2i2i−i3i3−i3i32-22-211-1-100000−2i2i0000−i3i3i−ii−i−3−333-11-11−i3i3−i3i3000000000i−i−330000000000
χ502-22-222-2-2-1-22-221-1-1-111100−2i2i−2i2i−i3i3−i3i3-22-2211-1-1000002i−2i0000−i3i3i−ii−i−3−3331-11-1i3−i3i3−i3000000000−ii3−30000000000
χ512-22-222-2-2-1-22-221-1-1-111100−2i2i−2i2ii3−i3i3−i32-22-211-1-100000−2i2i0000i3−i3i−ii−i33−3−3-11-11i3−i3i3−i3000000000i−i3−30000000000
χ522-22-222-2-2-1-22-221-1-1-111100−2i2i−2i2ii3−i3i3−i3-22-2211-1-1000002i−2i0000i3−i3i−ii−i33−3−31-11-1−i3i3−i3i3000000000−ii−330000000000
χ532-2-2-22-22222-2-22-2-2-22-222002-2-2200000000-222-22-22-20000000002-2-220000000000002-200000000000000002-2000
χ542-2-2-22-22222-2-22-2-2-22-222002-2-2200000000-222-2-22-220000000002-2-22000000000000-220000000000000000-22000
χ552-2-2-22-22222-2-22-2-2-22-22200-222-200000000-222-22-22-2000000000-222-20000000000002-20000000000000000-22000
χ562-2-2-22-22222-2-22-2-2-22-22200-222-200000000-222-2-22-22000000000-222-2000000000000-2200000000000000002-2000
χ572-2-2-22-2222-222-2-2-2-22-222000000000000002-2-222-22-20002-2000000002-22-200000000-22000000000002-200000000
χ582-2-2-22-2222-222-2-2-2-22-222000000000000002-2-222-22-2000-2200000000-22-2200000000-2200000000000-2200000000
χ592-2-2-22-2222-222-2-2-2-22-222000000000000002-2-22-22-220002-2000000002-22-2000000002-200000000000-2200000000
χ602-2-2-22-2222-222-2-2-2-22-222000000000000002-2-22-22-22000-2200000000-22-22000000002-2000000000002-200000000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-2000022220000-400000022000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022220000222200004000000-2-2000000000000000000000000000000000000000
χ63444-4-4-4-44-20000-2-22222-24-40000-2-222−2i2−2i22i22i20000000000000−2i22i20000000000i2i2−i2−i2i2i2−i2−i200000000000000000000000
χ64444-4-4-4-44-20000-2-22222-24-40000-2-2222i22i2−2i2−2i200000000000002i2−2i20000000000−i2−i2i2i2−i2−i2i2i200000000000000000000000
χ65444-4-4-4-44-20000-2-22222-2-44000022-2-2−2i2−2i22i22i200000000000002i2−2i20000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000
χ66444-4-4-4-44-20000-2-22222-2-44000022-2-22i22i2−2i2−2i20000000000000−2i22i20000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000
χ6744-444-4-4-4444-4-44-4-444-4-400000000000000-44-440000000000000000000000000000000000000000000000000000
χ6844-444-4-4-4-244-4-4-222-2-222000000000000002-22-20000000000000000023−23−23230000000000000000000000000000000
χ6944-444-4-4-4-244-4-4-222-2-222000000000000002-22-200000000000000000−232323−230000000000000000000000000000000
χ7044-444-4-4-4-2-4-444-222-2-222004i4i−4i−4i00000000-22-220000000000000−2i−2i2i2i00000000000000000000000000000000000
χ7144-444-4-4-4-2-4-444-222-2-22200−4i−4i4i4i00000000-22-2200000000000002i2i−2i−2i00000000000000000000000000000000000
χ7244-4-4-444-4400004-44-4-44-4000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ7344-4-4-444-4400004-44-4-44-40000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ744-444-4-44-440000-44-4-444-40000000000−2i22i22i2−2i20000000000000000000000000−2i22i22i2−2i2000000000000000000000000000
χ754-444-4-44-440000-44-4-444-400000000002i2−2i2−2i22i200000000000000000000000002i2−2i2−2i22i2000000000000000000000000000
χ764-444-4-44-4-200002-222-2-22000000−2i32i32i3−2i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i2−666−600000000000000000000000
χ774-444-4-44-4-200002-222-2-22000000−2i32i32i3−2i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i26−6−6600000000000000000000000
χ784-444-4-44-4-200002-222-2-220000002i3−2i3−2i32i3−2i22i22i2−2i20000000000000000000000000i2−i2−i2i26−6−6600000000000000000000000
χ794-444-4-44-4-200002-222-2-220000002i3−2i3−2i32i32i2−2i2−2i22i20000000000000000000000000−i2i2i2−i2−666−600000000000000000000000
χ804-44-444-4-444-44-4-4444-4-4-40000000000000044-4-40000000000000000000000000000000000000000000000000000
χ814-44-444-4-4-24-44-42-2-2-2222000000−2i32i3−2i32i30000-2-222000000000002i3−2i3000000000000000000000000000000000000000
χ824-44-444-4-4-24-44-42-2-2-22220000002i3−2i32i3−2i30000-2-22200000000000−2i32i3000000000000000000000000000000000000000
χ834-4-44-44-4440000-4-44-44-440000000000000000004-4-44000000000000000000000000000000000000000000000000
χ844-4-44-44-4440000-4-44-44-44000000000000000000-444-4000000000000000000000000000000000000000000000000
χ854-4-4-44-444-24-4-44222-22-2-2004-4-44000000002-2-220000000000000-222-200000000000000000000000000000000000
χ864-4-4-44-444-24-4-44222-22-2-200-444-4000000002-2-2200000000000002-2-2200000000000000000000000000000000000
χ874-4-4-44-444-2-444-4222-22-2-200000000000000-222-200000004-400000000-22-220000000000000000000000000000000
χ884-4-4-44-444-2-444-4222-22-2-200000000000000-222-20000000-44000000002-22-20000000000000000000000000000000
χ8988-8-8-888-8-40000-44-444-440000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-88-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000000000

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