Finite Group Databasebeta

← Group #10896472

Character table — Group #10896472

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444666688888888888888888888888888888812121212121216161616242424242424242424242424
order122222223444444446666666441212121212121212444444444444888812121212121212121212242424242424242444444412121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-1111111111-1-1111-1-1-1-11111111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1111111111-1-1111-1-1-1-11111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1111111111111-1-1-1-1111111111-1-1111-1-1-1-111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1211111111111-1-1-1-1111111111-1-1111-1-1-1-111111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1
χ1311111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1
χ1511111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-111-1-1
χ1611111111111-1-1-1-1111111111-1-1111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ17222222222-2-22222-2-22222222-2-2-2-2-22222-2222200000000000000000000-2-200000000-2-222-2-20000000000000000
χ18222222222-2-22222-2-22222222-2-2-2-2-22222-2-2-2-2-200000000000000000000-2-20000000022-2-2220000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222000000000000000000002200000000-2-2-2-2220000000000000000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000000002222-2-20000000000000000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100002222-2-2-2-2-2-2-2-211111111-1-111111111000000-1-1-1-1000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000001111000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-10000001111000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1000022-2-222-2-222-2-2-1-1-1-1111111-1-1-1-11111000000-1-111000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-1000022-2-2-2-222-2-2221111-1-1-1-1111111-1-1-1-1000000-1-111000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-10000-2-22222-2-2-2-222-1-1-1-11111111111-1-1-1-100000011-1-1000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-1-11111-10000-2-222-2-22222-2-21111-1-1-1-111-1-1-1-1111100000011-1-1000000000000
χ29222-22-2-2-222222-2-2-2-2-2-222-2-222-222-222-2-2-200002-22-200000000000000002-2000000000000002-22-2000000000000
χ30222-22-2-2-222222-2-2-2-2-2-222-2-222-222-222-2-2-20000-22-2200000000000000002-200000000000000-22-22000000000000
χ31222-22-2-2-2222-2-222-2-2-2-222-2-22-2222-2-2-222-200002-2-220000000000000000-22000000000000002-2-22000000000000
χ32222-22-2-2-2222-2-222-2-2-2-222-2-22-2222-2-2-222-20000-222-20000000000000000-2200000000000000-222-2000000000000
χ33222-22-2-2-22-2-222-2-222-2-222-2-22-22-2-2222-2-22000000000000000000000000-2200000000000000000000002i−2i2i−2i0000
χ34222-22-2-2-22-2-222-2-222-2-222-2-22-22-2-2222-2-22000000000000000000000000-220000000000000000000000−2i2i−2i2i0000
χ35222-22-2-2-22-2-2-2-22222-2-222-2-222-2-2-22-2-22220000000000000000000000002-200000000000000000000002i−2i−2i2i0000
χ36222-22-2-2-22-2-2-2-22222-2-222-2-222-2-2-22-2-22220000000000000000000000002-20000000000000000000000−2i2i2i−2i0000
χ37222-22-2-2-2-12222-2-2-2-211-1-111-12-2-1-11-1-111100002-22-20000000033−3−333−3−3-1133−3−333−3−3000000-11-11000000000000
χ38222-22-2-2-2-12222-2-2-2-211-1-111-12-2-1-11-1-111100002-22-200000000−3−333−3−333-11−3−333−3−333000000-11-11000000000000
χ39222-22-2-2-2-12222-2-2-2-211-1-111-12-2-1-11-1-11110000-22-220000000033−3−333−3−3-11−3−333−3−3330000001-11-1000000000000
χ40222-22-2-2-2-12222-2-2-2-211-1-111-12-2-1-11-1-11110000-22-2200000000−3−333−3−333-1133−3−333−3−30000001-11-1000000000000
χ41222-22-2-2-2-122-2-222-2-211-1-111-1-22-1-1111-1-1100002-2-220000000033−3−3−3−3331-133−3−3−3−333000000-111-1000000000000
χ42222-22-2-2-2-122-2-222-2-211-1-111-1-22-1-1111-1-1100002-2-2200000000−3−33333−3−31-1−3−33333−3−3000000-111-1000000000000
χ43222-22-2-2-2-122-2-222-2-211-1-111-1-22-1-1111-1-110000-222-20000000033−3−3−3−3331-1−3−33333−3−30000001-1-11000000000000
χ44222-22-2-2-2-122-2-222-2-211-1-111-1-22-1-1111-1-110000-222-200000000−3−33333−3−31-133−3−3−3−3330000001-1-11000000000000
χ4522-2-2-222-22002-22-200-2-22-222-2000002-22-2022-2-200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2002-200000000000000−i2i2−i2i2
χ4622-2-2-222-22002-22-200-2-22-222-2000002-22-2022-2-200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2002-200000000000000i2−i2i2−i2
χ4722-2-2-222-22002-22-200-2-22-222-2000002-22-20-2-22200000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200-2200000000000000i2−i2i2−i2
χ4822-2-2-222-22002-22-200-2-22-222-2000002-22-20-2-22200000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200-2200000000000000−i2i2−i2i2
χ4922-2-2-222-2200-22-2200-2-22-222-200000-22-22022-2-200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i200-2200000000000000−i2i2i2−i2
χ5022-2-2-222-2200-22-2200-2-22-222-200000-22-22022-2-200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i200-2200000000000000i2−i2−i2i2
χ5122-2-2-222-2200-22-2200-2-22-222-200000-22-220-2-22200000000−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2002-200000000000000i2−i2−i2i2
χ5222-2-2-222-2200-22-2200-2-22-222-200000-22-220-2-22200000000i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2002-200000000000000−i2i2i2−i2
χ532-22-2-22-2222-200002-22-2-222-2-2002-2-2000022i−2i2i−2i0000002i−2i000000002i−2i2i−2i00000000002i−2i00000000002-200000000
χ542-22-2-22-2222-200002-22-2-222-2-2002-2-2000022i−2i2i−2i000000−2i2i00000000−2i2i−2i2i00000000002i−2i0000000000-2200000000
χ552-22-2-22-2222-200002-22-2-222-2-2002-2-200002−2i2i−2i2i0000002i−2i000000002i−2i2i−2i0000000000−2i2i0000000000-2200000000
χ562-22-2-22-2222-200002-22-2-222-2-2002-2-200002−2i2i−2i2i000000−2i2i00000000−2i2i−2i2i0000000000−2i2i00000000002-200000000
χ572-22-2-22-222-220000-222-2-222-2-200-2220000-22i−2i2i−2i00002-20000002-22-200000000000000−2i2i000000002i−2i0000000000
χ582-22-2-22-222-220000-222-2-222-2-200-2220000-22i−2i2i−2i0000-22000000-22-2200000000000000−2i2i00000000−2i2i0000000000
χ592-22-2-22-222-220000-222-2-222-2-200-2220000-2−2i2i−2i2i00002-20000002-22-2000000000000002i−2i00000000−2i2i0000000000
χ602-22-2-22-222-220000-222-2-222-2-200-2220000-2−2i2i−2i2i0000-22000000-22-22000000000000002i−2i000000002i−2i0000000000
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000000000000000000022000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222000000000000000000000000-2-2000000000000000000000000000000
χ63444-44-4-4-4-2-4-444-4-44422-2-222-2-4422-2-2-222-20000000000000000000000002-2000000000000000000000000000000
χ64444-44-4-4-4-2-4-4-4-4444422-2-222-24-422-222-2-2-2000000000000000000000000-22000000000000000000000000000000
χ6544-44-4-4-444004-4-4400444-4-4-4-4000004-4-44000000000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44400-444-400444-4-4-4-400000-444-4000000000000000000000000000000000000000000000000000000000
χ6744-44-4-4-44-2004-4-4400-2-2-2222200000-222-2000000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ6844-44-4-4-44-2004-4-4400-2-2-2222200000-222-2000000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ6944-44-4-4-44-200-444-400-2-2-22222000002-2-22000000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ7044-44-4-4-44-200-444-400-2-2-22222000002-2-22000000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ7144-4-4-444-4-2004-44-40022-22-2-2200000-22-220000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ7244-4-4-444-4-2004-44-40022-22-2-2200000-22-2200000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ7344-4-4-444-4-200-44-440022-22-2-22000002-22-20000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000000000
χ7444-4-4-444-4-200-44-440022-22-2-22000002-22-200000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000000000
χ754-444-4-44-444-40000-44-44-44-44-4004-440000-400000000000000000000000000000000000000000000000000000000
χ764-444-4-44-44-4400004-4-44-44-44-400-44-40000400000000000000000000000000000000000000000000000000000000
χ774-444-4-44-4-24-40000-442-22-22-2200-22-20000200000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ784-444-4-44-4-24-40000-442-22-22-2200-22-200002000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ794-444-4-44-4-2-4400004-42-22-22-22002-220000-2000000000000000023−23−2323000000000000000000000000000000000000
χ804-444-4-44-4-2-4400004-42-22-22-22002-220000-20000000000000000−232323−23000000000000000000000000000000000000
χ814-44-4-44-44-24-400004-4-222-2-22200-2220000-200000000004i−4i00000000−2i2i−2i2i00000000000000000000000000000000
χ824-44-4-44-44-24-400004-4-222-2-22200-2220000-20000000000−4i4i000000002i−2i2i−2i00000000000000000000000000000000
χ834-44-4-44-44-2-440000-44-222-2-222002-2-200002000000004-4000000-22-22000000000000000000000000000000000000
χ844-44-4-44-44-2-440000-44-222-2-222002-2-20000200000000-440000002-22-2000000000000000000000000000000000000
χ854-4-4444-4-4400000000-44-4-44-4400000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ864-4-4444-4-4400000000-44-4-44-440000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ874-4-4-44-4444000000004-4-4-4-4440000000000000000000000000000000000000000000000004-40000000000000000
χ884-4-4-44-4444000000004-4-4-4-444000000000000000000000000000000000000000000000000-440000000000000000
χ898-8-8888-8-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-88-888-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000

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