Finite Group Databasebeta

← Group #10827358

Character table — Group #10827358

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order1222222234444444466666662212121212121212122222444466666688881212121224242424242424242244444488888888661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ4111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ91111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-1111-1
χ101111111111-1-1-1-11111111111-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-11-1-1-11
χ111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1111-1-1-11-1
χ121111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1111-11
χ131111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11-111-11
χ141111111111-1-1-1-11111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111111111-1-1-1-111-1-1-11-1-11-1
χ151111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-1-1-11
χ161111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11111-1
χ17222222222-22222-2-2-22222222-2-2-2-22222-2-200000000-2-20000000000000000000022220000000000000000-2-20000
χ18222222222-22222-2-2-22222222-2-2-2-22222-2-200000000-2-200000000000000000000-2-2-2-20000000000000000220000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000022-2-20000000000000000-220000
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000-2-22200000000000000002-20000
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111100000000000000001111000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-222-2-222-1-11111-2-2-2-21111111111110000000000000000-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111122221111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-12222-2-2-2-211-1-1-1-122-2-21111-1-1-1-111110000000000000000-1-111000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-22211-1-1-1-1-2-22211111111-1-1-1-1000000000000000011-1-1000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-2111111-2-222-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-2-2-2222211111122-2-2-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ2922-22-22-2-22200002-2-222-2-2-2-22002-200002-200002-200000000000022-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ3022-22-22-2-22200002-2-222-2-2-2-22002-200002-200002-200000000000022-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ3122-22-22-2-22200002-2-222-2-2-2-22002-200002-20000-22000000000000-2-2220000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ3222-22-22-2-22200002-2-222-2-2-2-22002-200002-20000-22000000000000-2-222000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ3322-2-22-22-2202i2i−2i−2i0002-222-2-2-200002i2i−2i−2i00000000000000002−2−i2i2000022−2−2−i2−i2i2i22-22i−2i00002−22−2−i2−i2i2i20000000000
χ3422-2-22-22-2202i2i−2i−2i0002-222-2-2-200002i2i−2i−2i00000000000000002−2−i2i2000022−2−2−i2−i2i2i2-22−2i2i0000−22−22i2i2−i2−i20000000000
χ3522-2-22-22-2202i2i−2i−2i0002-222-2-2-200002i2i−2i−2i0000000000000000−22i2−i20000−2−222i2i2−i2−i22-22i−2i0000−22−22i2i2−i2−i20000000000
χ3622-2-22-22-2202i2i−2i−2i0002-222-2-2-200002i2i−2i−2i0000000000000000−22i2−i20000−2−222i2i2−i2−i2-22−2i2i00002−22−2−i2−i2i2i20000000000
χ3722-2-22-22-220−2i−2i2i2i0002-222-2-2-20000−2i−2i2i2i00000000000000002−2i2−i2000022−2−2i2i2−i2−i22-2−2i2i00002−22−2i2i2−i2−i20000000000
χ3822-2-22-22-220−2i−2i2i2i0002-222-2-2-20000−2i−2i2i2i00000000000000002−2i2−i2000022−2−2i2i2−i2−i2-222i−2i0000−22−22−i2−i2i2i20000000000
χ3922-2-22-22-220−2i−2i2i2i0002-222-2-2-20000−2i−2i2i2i0000000000000000−22−i2i20000−2−222−i2−i2i2i22-2−2i2i0000−22−22−i2−i2i2i20000000000
χ4022-2-22-22-220−2i−2i2i2i0002-222-2-2-20000−2i−2i2i2i0000000000000000−22−i2i20000−2−222−i2−i2i2i2-222i−2i00002−22−2i2i2−i2−i20000000000
χ412-22-222-2-2220000-22-2-2-22-22-22002-20000-222-20000000022-2-2000000000000000000002i−2i2i−2i00002i−2i2i−2i0000000000
χ422-22-222-2-2220000-22-2-2-22-22-22002-20000-222-20000000022-2-200000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000000000
χ432-22-222-2-2220000-22-2-2-22-22-22002-20000-22-2200000000-2-222000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000000000
χ442-22-222-2-2220000-22-2-2-22-22-22002-20000-22-2200000000-2-22200000000000000000000−2i2i−2i2i00002i−2i2i−2i0000000000
χ452-2-2-2-2222222-22-2-2-22-2-2-22-2222-2222-22-2-2-2000000002-20000000000000000000000002-2-22000000000000002-200
χ462-2-2-2-2222222-22-2-2-22-2-2-22-2222-2222-22-2-2-2000000002-2000000000000000000000000-222-200000000000000-2200
χ472-2-2-2-222222-22-22-2-22-2-2-22-222-2222-22-22-2-200000000-220000000000000000000000002-2-2200000000000000-2200
χ482-2-2-2-222222-22-22-2-22-2-2-22-222-2222-22-22-2-200000000-22000000000000000000000000-222-2000000000000002-200
χ492-2-2-2-22222-22-22-222-2-2-2-22-222-22-2-22-22-222002-2002-2-220000000000000000000000000000000000002-22-2000000
χ502-2-2-2-22222-22-22-222-2-2-2-22-222-22-2-22-22-22200-2200-22-22000000000000000000000000000000000000-22-22000000
χ512-2-2-2-22222-2-22-2222-2-2-2-22-2222-2-2-2-22-2222002-200-222-20000000000000000000000000000000000002-2-22000000
χ522-2-2-2-22222-2-22-2222-2-2-2-22-2222-2-2-2-22-222200-22002-22-2000000000000000000000000000000000000-222-2000000
χ532-2-2-2-2222-1-22-22-222-2111-11-1-1-2211-11-11-1-1002-2002-21-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000-11-11000000
χ542-2-2-2-2222-1-22-22-222-2111-11-1-1-2211-11-11-1-1002-2002-21-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000-11-11000000
χ552-2-2-2-2222-1-22-22-222-2111-11-1-1-2211-11-11-1-100-2200-221-1−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000001-11-1000000
χ562-2-2-2-2222-1-22-22-222-2111-11-1-1-2211-11-11-1-100-2200-221-1i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000001-11-1000000
χ572-2-2-2-2222-1-2-22-2222-2111-11-1-12-2111-11-1-1-1002-200-22-11−i3i3−i3i30000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000-111-1000000
χ582-2-2-2-2222-1-2-22-2222-2111-11-1-12-2111-11-1-1-1002-200-22-11i3−i3i3−i30000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000-111-1000000
χ592-2-2-2-2222-1-2-22-2222-2111-11-1-12-2111-11-1-1-100-22002-2-11−i3i3−i3i30000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i300000000000000001-1-11000000
χ602-2-2-2-2222-1-2-22-2222-2111-11-1-12-2111-11-1-1-100-22002-2-11i3−i3i3−i30000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i300000000000000001-1-11000000
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000220000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000000000
χ63444-4-4-4-444000000004-4-4-444-4000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ64444-4-4-4-444000000004-4-4-444-40000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ6544-44-44-4-44-40000-44444-4-4-4-4400-440000-4400000000000000000000000000000000000000000000000000000000
χ6644-44-44-4-4-2400004-4-4-2-22222-200-220000-2200004-4000000000000-2-2220000000000000000000000000000000000
χ6744-44-44-4-4-2400004-4-4-2-22222-200-220000-220000-4400000000000022-2-20000000000000000000000000000000000
χ6844-44-44-4-4-2-40000-444-2-22222-2002-200002-20000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ6944-44-44-4-4-2-40000-444-2-22222-2002-200002-200000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ7044-4-44-44-4-204i4i−4i−4i000-22-2-22220000−2i−2i2i2i000000000000000022−22−2i22i20000−2−222i2i2−i2−i200000000000000000000000000
χ7144-4-44-44-4-204i4i−4i−4i000-22-2-22220000−2i−2i2i2i0000000000000000−22222i2−2i2000022−2−2−i2−i2i2i200000000000000000000000000
χ7244-4-44-44-4-20−4i−4i4i4i000-22-2-222200002i2i−2i−2i000000000000000022−222i2−2i20000−2−222−i2−i2i2i200000000000000000000000000
χ7344-4-44-44-4-20−4i−4i4i4i000-22-2-222200002i2i−2i−2i0000000000000000−2222−2i22i2000022−2−2i2i2−i2−i200000000000000000000000000
χ744-444-4-44-4404i−4i−4i4i000-44-444-4-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ754-444-4-44-440−4i4i4i−4i000-44-444-4-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ764-444-4-44-4-204i−4i−4i4i0002-22-2-2220000−2i2i2i−2i000000000000000000000000i6−i6−i6i66−6−6600000000000000000000000000
χ774-444-4-44-4-204i−4i−4i4i0002-22-2-2220000−2i2i2i−2i000000000000000000000000−i6i6i6−i6−666−600000000000000000000000000
χ784-444-4-44-4-20−4i4i4i−4i0002-22-2-22200002i−2i−2i2i000000000000000000000000i6−i6−i6i6−666−600000000000000000000000000
χ794-444-4-44-4-20−4i4i4i−4i0002-22-2-22200002i−2i−2i2i000000000000000000000000−i6i6i6−i66−6−6600000000000000000000000000
χ804-44-444-4-44-400004-44-4-44-44-4400-4400004-400000000000000000000000000000000000000000000000000000000
χ814-44-444-4-4-240000-44-422-22-22-200-2200002-24-400000000-2-222000000000000000000000000000000000000000000
χ824-44-444-4-4-240000-44-422-22-22-200-2200002-2-440000000022-2-2000000000000000000000000000000000000000000
χ834-44-444-4-4-2-400004-4422-22-22-2002-20000-22000000000000000000−2i32i32i3−2i30000000000000000000000000000000000
χ844-44-444-4-4-2-400004-4422-22-22-2002-20000-220000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ854-4-444-4-44400000000-444-4-44-4000000000000000000000000000000000000000000000000000022−22−22220000000000
χ864-4-444-4-44400000000-444-4-44-40000000000000000000000000000000000000000000000000000−222222−220000000000
χ874-4-4-4-4444-244-44-4-4-44222-22-2-24-4-2-2-22-222200000000-220000000000000000000000000000000000000000000000
χ884-4-4-4-4444-24-44-44-4-44222-22-2-2-44-2-22-22-222000000002-20000000000000000000000000000000000000000000000
χ89888-8-8-8-88-400000000-4444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-888-8-88-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000

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