Finite Group Databasebeta

← Group #10858305

Character table — Group #10858305

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ5111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11-1-1
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-111
χ91111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-111111-1-1-1
χ101111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11-111-1-111-1-1-1-1-1111
χ111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-11-1-11111-1-1111-1-1-1
χ121111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-11-1-111-1-111-1-1-1111
χ131111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-11-1-11111-1-11-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-111-1-111-1111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-11-111-1-1-1-1111-1-1-111
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111-111-1-111-1-1-1111-1-1
χ17222222222-22222-2-2-222222220000-2-22222-2-2-2-20000000000-2-20000000000002222000000000000000000-200-200
χ18222222222-22222-2-2-222222220000-2-22222-2-2-2-20000000000-2-2000000000000-2-2-2-2000000000000000000200200
χ19222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000000000000000-200200
χ20222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000000022000000000000-2-222000000000000000000200-200
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-222221111-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-222-2-2-1-1-1-1111111-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-222-1-1-1-11111111111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-2-2111111-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-222111111-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ292222-2-2-2-2220000-22-222-2-2-22-222-2-200000022-2-200000022-2-200000000000000000022-2-200000000002-200000000
χ302222-2-2-2-2220000-22-222-2-2-22-222-2-200000022-2-200000022-2-2000000000000000000-2-2220000000000-2200000000
χ312222-2-2-2-2220000-22-222-2-2-22-2-2-22200000022-2-2000000-2-22200000000000000000022-2-20000000000-2200000000
χ322222-2-2-2-2220000-22-222-2-2-22-2-2-22200000022-2-2000000-2-222000000000000000000-2-22200000000002-200000000
χ3322-2-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i0000002−2−i2i2000000000022−2−2−i2−i2i2i22-22i−2i−i2i2−i2i222−2−20000000000000000
χ3422-2-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i0000002−2−i2i2000000000022−2−2−i2−i2i2i2-22−2i2ii2−i2i2−i2−2−2220000000000000000
χ3522-2-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i000000−22i2−i20000000000−2−222i2i2−i2−i22-22i−2ii2−i2i2−i2−2−2220000000000000000
χ3622-2-22-2-22202i2i−2i−2i0002-22-2-2-220000002i2i−2i−2i000000−22i2−i20000000000−2−222i2i2−i2−i2-22−2i2i−i2i2−i2i222−2−20000000000000000
χ3722-2-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i0000002−2i2−i2000000000022−2−2i2i2−i2−i22-2−2i2ii2−i2i2−i222−2−20000000000000000
χ3822-2-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i0000002−2i2−i2000000000022−2−2i2i2−i2−i2-222i−2i−i2i2−i2i2−2−2220000000000000000
χ3922-2-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i000000−22−i2i20000000000−2−222−i2−i2i2i22-2−2i2i−i2i2−i2i2−2−2220000000000000000
χ4022-2-22-2-2220−2i−2i2i2i0002-22-2-2-22000000−2i−2i2i2i000000−22−i2i20000000000−2−222−i2−i2i2i2-222i−2ii2−i2i2−i222−2−20000000000000000
χ412-2-222-22-2222i−2i2i−2i-2-22-2-22-222-200002i−2i2i−2i2i−2i2-22-200000000002i−2i000000000000000000000000000000000002-202i−2i
χ422-2-222-22-2222i−2i2i−2i-2-22-2-22-222-200002i−2i2i−2i2i−2i2-22-200000000002i−2i00000000000000000000000000000000000-220−2i2i
χ432-2-222-22-222−2i2i−2i2i-2-22-2-22-222-20000−2i2i−2i2i−2i2i2-22-20000000000−2i2i000000000000000000000000000000000002-20−2i2i
χ442-2-222-22-222−2i2i−2i2i-2-22-2-22-222-20000−2i2i−2i2i−2i2i2-22-20000000000−2i2i00000000000000000000000000000000000-2202i−2i
χ452-2-222-22-22-22i−2i2i−2i22-2-2-22-222-22-22-2−2i2i2i−2i2i−2i-22-222i−2i00002-22-2−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ462-2-222-22-22-22i−2i2i−2i22-2-2-22-222-2-22-22−2i2i2i−2i2i−2i-22-22−2i2i0000-22-22−2i2i−2i−2i2i2i000000000000000000000000000000000000
χ472-2-222-22-22-2−2i2i−2i2i22-2-2-22-222-22-22-22i−2i−2i2i−2i2i-22-22−2i2i00002-22-22i−2i−2i−2i2i2i000000000000000000000000000000000000
χ482-2-222-22-22-2−2i2i−2i2i22-2-2-22-222-2-22-222i−2i−2i2i−2i2i-22-222i−2i0000-22-222i−2i2i2i−2i−2i000000000000000000000000000000000000
χ492-2-222-22-2-1-22i−2i2i−2i22-211-11-1-112-22-2−2i2i−ii−ii1-11-12i−2i0000-11-11i−i−i−iii−i3i3−i3i33−33−300000000000000−i3i33−30000000000
χ502-2-222-22-2-1-22i−2i2i−2i22-211-11-1-112-22-2−2i2i−ii−ii1-11-12i−2i0000-11-11i−i−i−iiii3−i3i3−i3−33−3300000000000000i3−i3−330000000000
χ512-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11-22-22−2i2i−ii−ii1-11-1−2i2i00001-11-1i−iii−i−i−i3i3−i3i33−33−300000000000000i3−i3−330000000000
χ522-2-222-22-2-1-22i−2i2i−2i22-211-11-1-11-22-22−2i2i−ii−ii1-11-1−2i2i00001-11-1i−iii−i−ii3−i3i3−i3−33−3300000000000000−i3i33−30000000000
χ532-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112-22-22i−2ii−ii−i1-11-1−2i2i0000-11-11−iiii−i−i−i3i3−i3i3−33−3300000000000000−i3i3−330000000000
χ542-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-112-22-22i−2ii−ii−i1-11-1−2i2i0000-11-11−iiii−i−ii3−i3i3−i33−33−300000000000000i3−i33−30000000000
χ552-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-11-22-222i−2ii−ii−i1-11-12i−2i00001-11-1−ii−i−iii−i3i3−i3i3−33−3300000000000000i3−i33−30000000000
χ562-2-222-22-2-1-2−2i2i−2i2i22-211-11-1-11-22-222i−2ii−ii−i1-11-12i−2i00001-11-1−ii−i−iiii3−i3i3−i33−33−300000000000000−i3i3−330000000000
χ572-2-22-22-222-20000-222-2-2-22-2222-2-22000000-222-20000002-2-2200000000000000000000002-22-2000000002-2000000
χ582-2-22-22-222-20000-222-2-2-22-2222-2-22000000-222-20000002-2-220000000000000000000000-22-2200000000-22000000
χ592-2-22-22-222-20000-222-2-2-22-222-222-2000000-222-2000000-222-200000000000000000000002-22-200000000-22000000
χ602-2-22-22-222-20000-222-2-2-22-222-222-2000000-222-2000000-222-20000000000000000000000-22-22000000002-2000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-20000-4-4-2-2-2-222220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2000044222222220000000000-2-20000000000000000000000000000000000000000
χ634444-4-4-4-44-400004-4444-4-4-44-40000000000-4-4440000000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-240000-44-4-2-2222-2244-4-4000000-2-222000000-2-222000000000000000000000000000000000000000000
χ654444-4-4-4-4-240000-44-4-2-2222-22-4-444000000-2-22200000022-2-2000000000000000000000000000000000000000000
χ664444-4-4-4-4-2-400004-44-2-2222-22000000000022-2-200000000000023−2323−23000000000000000000000000000000000000
χ674444-4-4-4-4-2-400004-44-2-2222-22000000000022-2-2000000000000−2323−2323000000000000000000000000000000000000
χ6844-4-44-4-44-204i4i−4i−4i000-22-2222-2000000−2i−2i2i2i00000022−22−2i22i20000000000−2−222i2i2−i2−i20000000000000000000000000000
χ6944-4-44-4-44-204i4i−4i−4i000-22-2222-2000000−2i−2i2i2i000000−22222i2−2i2000000000022−2−2−i2−i2i2i20000000000000000000000000000
χ7044-4-44-4-44-20−4i−4i4i4i000-22-2222-20000002i2i−2i−2i00000022−222i2−2i20000000000−2−222−i2−i2i2i20000000000000000000000000000
χ7144-4-44-4-44-20−4i−4i4i4i000-22-2222-20000002i2i−2i−2i000000−2222−2i22i2000000000022−2−2i2i2−i2−i20000000000000000000000000000
χ7244-4-4-444-44000000004-4-444-4-4000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ7344-4-4-444-44000000004-4-444-4-40000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ744-44-444-4-4404-4-44000-4444-4-4-40000004-4-4400000000000000000000000000000000000000000000000000000000
χ754-44-444-4-440-444-4000-4444-4-4-4000000-444-400000000000000000000000000000000000000000000000000000000
χ764-44-444-4-4-204-4-440002-2-2-2222000000-222-200000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ774-44-444-4-4-204-4-440002-2-2-2222000000-222-200000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ784-44-444-4-4-20-444-40002-2-2-22220000002-2-2200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ794-44-444-4-4-20-444-40002-2-2-22220000002-2-2200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ804-44-4-4-444400000000-44-4-44-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ814-44-4-4-444400000000-44-4-44-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ824-4-444-44-4-244i−4i4i−4i-4-4422-22-2-2200004i−4i−2i2i−2i2i-22-220000000000−2i2i0000000000000000000000000000000000000000
χ834-4-444-44-4-24−4i4i−4i4i-4-4422-22-2-220000−4i4i2i−2i2i−2i-22-2200000000002i−2i0000000000000000000000000000000000000000
χ844-4-44-44-444400004-4-4-4-4-44-44400000000004-4-440000000000000000000000000000000000000000000000000000
χ854-4-44-44-44-2400004-4-4222-22-2-20000000000-222-2000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ864-4-44-44-44-2400004-4-4222-22-2-20000000000-222-20000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ874-4-44-44-44-2-40000-444222-22-2-24-4-440000002-2-22000000-222-2000000000000000000000000000000000000000000
χ884-4-44-44-44-2-40000-444222-22-2-2-444-40000002-2-220000002-2-22000000000000000000000000000000000000000000
χ8988-8-8-888-8-400000000-444-4-444000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-8-888-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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