Finite Group Databasebeta

← Group #10858787

Character table — Group #10858787

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222222222222222244444444448888888888888888888888888888881212121212121212121212121212121216161616242424244848
order12222222344444444666666622121212121212121222444444668888121212121212121224242424242424244444444488888888661212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ911111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-111-11
χ1011111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111111-1-1-11-1-11-1
χ1111111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11-1111-1
χ1211111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111111111-1-1-1-111-1-1-11-1-1-11
χ1311111111111-1-1-1-1111111111-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1111-1-1-1-11
χ1411111111111-1-1-1-1111111111-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-11111-1
χ1511111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-1-11-1
χ1611111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1111-11
χ17222222222-2-22222-2-22222222-2-2-2-22222-2-200000000-2-20000000000000000000022220000000000000000-2-20000
χ18222222222-2-22222-2-22222222-2-2-2-22222-2-200000000-2-200000000000000000000-2-2-2-20000000000000000220000
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
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-2-2-2-211111111111111110000000000000000-1-1-1-1000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000001111000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1222211111111-1-1-1-1-1-1-1-100000000000000001111000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-222-2-211-2-222-1-1-1-11111-1-1-1-111110000000000000000-1-111000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-2-2-2221122-2-21111-1-1-1-11111-1-1-1-10000000000000000-1-111000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22222-2-21122-2-2-1-1-1-111111111-1-1-1-1000000000000000011-1-1000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222-2-22211-2-2221111-1-1-1-1-1-1-1-11111000000000000000011-1-1000000
χ292222-2-2-2-222222-2-2-2-22-2-222-2-22-22222-2-2-2-22-22-200002-20000000000000000000000000000000000002-22-2000000
χ302222-2-2-2-222222-2-2-2-22-2-222-2-22-22222-2-2-2-2-22-2200002-2000000000000000000000000000000000000-22-22000000
χ312222-2-2-2-2222-2-222-2-22-2-222-2-2-2222-2-222-2-22-2-220000-220000000000000000000000000000000000002-2-22000000
χ322222-2-2-2-2222-2-222-2-22-2-222-2-2-2222-2-222-2-2-222-20000-22000000000000000000000000000000000000-222-2000000
χ332222-2-2-2-22-2-222-2-2222-2-222-2-2-22-2-222-2-22200000000-220000000000000000000000002i2i−2i−2i000000000000002i−2i00
χ342222-2-2-2-22-2-222-2-2222-2-222-2-2-22-2-222-2-22200000000-22000000000000000000000000−2i−2i2i2i00000000000000−2i2i00
χ352222-2-2-2-22-2-2-2-222222-2-222-2-22-2-2-2-2-22222000000002-20000000000000000000000002i2i−2i−2i00000000000000−2i2i00
χ362222-2-2-2-22-2-2-2-222222-2-222-2-22-2-2-2-2-22222000000002-2000000000000000000000000−2i−2i2i2i000000000000002i−2i00
χ372222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-1-1-111112-22-20000-11000033−3−333−3−333−3−333−3−30000000000000000-11-11000000
χ382222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-1-1-111112-22-20000-110000−3−333−3−333−3−333−3−3330000000000000000-11-11000000
χ392222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-1-1-11111-22-220000-11000033−3−333−3−3−3−333−3−33300000000000000001-11-1000000
χ402222-2-2-2-2-12222-2-2-2-2-111-1-1112-2-1-1-1-11111-22-220000-110000−3−333−3−33333−3−333−3−300000000000000001-11-1000000
χ412222-2-2-2-2-122-2-222-2-2-111-1-111-22-1-111-1-1112-2-2200001-1000033−3−3−3−33333−3−3−3−3330000000000000000-111-1000000
χ422222-2-2-2-2-122-2-222-2-2-111-1-111-22-1-111-1-1112-2-2200001-10000−3−33333−3−3−3−33333−3−30000000000000000-111-1000000
χ432222-2-2-2-2-122-2-222-2-2-111-1-111-22-1-111-1-111-222-200001-1000033−3−3−3−333−3−33333−3−300000000000000001-1-11000000
χ442222-2-2-2-2-122-2-222-2-2-111-1-111-22-1-111-1-111-222-200001-10000−3−33333−3−333−3−3−3−33300000000000000001-1-11000000
χ4522-2-22-2-222002i−2i2i−2i0022-2-2-22-200002i−2i2i−2i000000000000−i2i22−2000000002−22−2−i2i2−i2i22-22i−2i000022−2−2−i2−i2i2i20000000000
χ4622-2-22-2-222002i−2i2i−2i0022-2-2-22-200002i−2i2i−2i000000000000−i2i22−2000000002−22−2−i2i2−i2i2-22−2i2i0000−2−222i2i2−i2−i20000000000
χ4722-2-22-2-222002i−2i2i−2i0022-2-2-22-200002i−2i2i−2i000000000000i2−i2−2200000000−22−22i2−i2i2−i22-22i−2i0000−2−222i2i2−i2−i20000000000
χ4822-2-22-2-222002i−2i2i−2i0022-2-2-22-200002i−2i2i−2i000000000000i2−i2−2200000000−22−22i2−i2i2−i2-22−2i2i000022−2−2−i2−i2i2i20000000000
χ4922-2-22-2-22200−2i2i−2i2i0022-2-2-22-20000−2i2i−2i2i000000000000−i2i2−2200000000−22−22−i2i2−i2i22-2−2i2i0000−2−222−i2−i2i2i20000000000
χ5022-2-22-2-22200−2i2i−2i2i0022-2-2-22-20000−2i2i−2i2i000000000000−i2i2−2200000000−22−22−i2i2−i2i2-222i−2i000022−2−2i2i2−i2−i20000000000
χ5122-2-22-2-22200−2i2i−2i2i0022-2-2-22-20000−2i2i−2i2i000000000000i2−i22−2000000002−22−2i2−i2i2−i22-2−2i2i000022−2−2i2i2−i2−i20000000000
χ5222-2-22-2-22200−2i2i−2i2i0022-2-2-22-20000−2i2i−2i2i000000000000i2−i22−2000000002−22−2i2−i2i2−i2-222i−2i0000−2−222−i2−i2i2i20000000000
χ532-22-22-22-222-200002-2-2-2-22-222002-200002-20000002-200000000002-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ542-22-22-22-222-200002-2-2-2-22-222002-200002-20000002-200000000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ552-22-22-22-222-200002-2-2-2-22-222002-200002-2000000-220000000000-22-220000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ562-22-22-22-222-200002-2-2-2-22-222002-200002-2000000-220000000000-22-22000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ572-22-2-22-222-2200002-2-2222-2-2-200-2200002-200002i−2i000000002i−2i2i−2i00000000000000002-2-2200002i−2i2i−2i0000000000
χ582-22-2-22-222-2200002-2-2222-2-2-200-2200002-200002i−2i000000002i−2i2i−2i0000000000000000-222-20000−2i2i−2i2i0000000000
χ592-22-2-22-222-2200002-2-2222-2-2-200-2200002-20000−2i2i00000000−2i2i−2i2i00000000000000002-2-220000−2i2i−2i2i0000000000
χ602-22-2-22-222-2200002-2-2222-2-2-200-2200002-20000−2i2i00000000−2i2i−2i2i0000000000000000-222-200002i−2i2i−2i0000000000
χ6144444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200000000220000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000000000
χ634444-4-4-4-4-2-4-444-4-444-222-2-222-4422-2-222-2-2000000002-20000000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-4-4-44444-222-2-2224-42222-2-2-2-200000000-220000000000000000000000000000000000000000000000
χ6544-4-44-4-44-2004i−4i4i−4i00-2-2222-220000−2i2i−2i2i000000000000−2i22i222−2200000000−22−22i2−i2i2−i200000000000000000000000000
χ6644-4-44-4-44-2004i−4i4i−4i00-2-2222-220000−2i2i−2i2i0000000000002i2−2i2−2222000000002−22−2−i2i2−i2i200000000000000000000000000
χ6744-4-44-4-44-200−4i4i−4i4i00-2-2222-2200002i−2i2i−2i000000000000−2i22i2−2222000000002−22−2i2−i2i2−i200000000000000000000000000
χ6844-4-44-4-44-200−4i4i−4i4i00-2-2222-2200002i−2i2i−2i0000000000002i2−2i222−2200000000−22−22−i2i2−i2i200000000000000000000000000
χ6944-4-4-444-44004i−4i−4i4i004-44-4-4-4400004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ7044-4-4-444-4400−4i4i4i−4i004-44-4-4-440000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ7144-4-4-444-4-2004i−4i−4i4i00-22-2222-20000−2i2i2i−2i0000000000000000000000006−6−66−i6i6i6−i600000000000000000000000000
χ7244-4-4-444-4-2004i−4i−4i4i00-22-2222-20000−2i2i2i−2i000000000000000000000000−666−6i6−i6−i6i600000000000000000000000000
χ7344-4-4-444-4-200−4i4i4i−4i00-22-2222-200002i−2i−2i2i0000000000000000000000006−6−66i6−i6−i6i600000000000000000000000000
χ7444-4-4-444-4-200−4i4i4i−4i00-22-2222-200002i−2i−2i2i000000000000000000000000−666−6−i6i6i6−i600000000000000000000000000
χ754-44-44-44-44-440000-44-4-4-44-44400-440000-4400000000000000000000000000000000000000000000000000000000
χ764-44-44-44-4-24-400004-4222-22-2-200-220000-220000004-40000000000-22-220000000000000000000000000000000000
χ774-44-44-44-4-24-400004-4222-22-2-200-220000-22000000-4400000000002-22-20000000000000000000000000000000000
χ784-44-44-44-4-2-440000-44222-22-2-2002-200002-200000000000000−2i32i32i3−2i300000000000000000000000000000000000000
χ794-44-44-44-4-2-440000-44222-22-2-2002-200002-2000000000000002i3−2i3−2i32i300000000000000000000000000000000000000
χ804-44-4-44-4444-40000-44-4444-4-4-4004-40000-4400000000000000000000000000000000000000000000000000000000
χ814-44-4-44-44-24-40000-442-2-2-222200-2200002-200000000000000000023−23−23230000000000000000000000000000000000
χ824-44-4-44-44-24-40000-442-2-2-222200-2200002-2000000000000000000−232323−230000000000000000000000000000000000
χ834-44-4-44-44-2-4400004-42-2-2-2222002-20000-2200004i−4i00000000−2i2i−2i2i00000000000000000000000000000000000000
χ844-44-4-44-44-2-4400004-42-2-2-2222002-20000-220000−4i4i000000002i−2i2i−2i00000000000000000000000000000000000000
χ854-4-4444-4-4400000000-4-44-444-4000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ864-4-4444-4-4400000000-4-44-444-40000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ874-4-44-4-444400000000-44-4-44-44000000000000000000000000000000000000000000000000000022−22−22220000000000
χ884-4-44-4-444400000000-44-4-44-440000000000000000000000000000000000000000000000000000−222222−220000000000
χ898-8-8888-8-8-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88-8-888-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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