Finite Group Databasebeta

← Group #10698226

Character table — Group #10698226

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666441212121212121212444488881212121212121212121224242424242424248888888844121212124444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ9222222222222-2-2-22-22222222-2-2222-2-2-2-2222-2-20000-2-22222-2-2-2-200000000000000000000000000000000
χ10222222222222-2-2-22-22222222-2-2222-2-2-2-22-2-2220000-2-2-2-2-2-2222200000000000000000000000000000000
χ11222222222-2-2-2222-222222222-2-2-2-2-22222-200000000-2-200000000000000000000000000000022-2-2000000
χ12222222222-2-2-2222-222222222-2-2-2-2-22222-200000000-2-2000000000000000000000000000000-2-222000000
χ13222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000000000002-2
χ14222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000000000-22
χ1522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ1622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ1722222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ1822222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ1922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000000000−i3−i3i3i30000000000
χ2022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000000000i3i3−i3−i30000000000
χ2122222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i30000000000i3i3−i3−i30000000000
χ2222222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i30000000000−i3−i3i3i30000000000
χ23222-22-2-2-2222-222-2-2-2-2-222-2-222-222-222-2-2-2000000002-20000000000000000000000002-22-22-20000000000
χ24222-22-2-2-2222-222-2-2-2-2-222-2-222-222-222-2-2-2000000002-2000000000000000000000000-22-22-220000000000
χ25222-22-2-2-2222-2-2-22-22-2-222-2-22-2222-2-2-222-200002i2i−2i−2i-22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ26222-22-2-2-2222-2-2-22-22-2-222-2-22-2222-2-2-222-20000−2i−2i2i2i-2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ27222-22-2-2-22-2-2222-22-2-2-222-2-22-22-2-2222-2-2200000000-2200000000000000000000000000000000002i2i−2i−2i00
χ28222-22-2-2-22-2-2222-22-2-2-222-2-22-22-2-2222-2-2200000000-220000000000000000000000000000000000−2i−2i2i2i00
χ29222-22-2-2-22-2-22-2-2222-2-222-2-222-2-2-22-2-2222000000002-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000000000
χ30222-22-2-2-22-2-22-2-2222-2-222-2-222-2-2-22-2-2222000000002-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000
χ31222-22-2-2-2-122-222-2-2-211-1-111-12-2-1-11-1-111100000000-1133−3−333−3−333−3−3−3−333000000002-2-11-110000000000
χ32222-22-2-2-2-122-222-2-2-211-1-111-12-2-1-11-1-111100000000-1133−3−333−3−3−3−33333−3−300000000-221-11-10000000000
χ33222-22-2-2-2-122-222-2-2-211-1-111-12-2-1-11-1-111100000000-11−3−333−3−33333−3−3−3−33300000000-221-11-10000000000
χ34222-22-2-2-2-122-222-2-2-211-1-111-12-2-1-11-1-111100000000-11−3−333−3−333−3−33333−3−3000000002-2-11-110000000000
χ35222-22-2-2-2-122-2-2-22-2211-1-111-1-22-1-1111-1-1100002i2i−2i−2i1-133−3−3−3−333−i−iii−i−iii0000000000−i3i3i3−i30000000000
χ36222-22-2-2-2-122-2-2-22-2211-1-111-1-22-1-1111-1-1100002i2i−2i−2i1-1−3−33333−3−3−i−iii−i−iii0000000000i3−i3−i3i30000000000
χ37222-22-2-2-2-122-2-2-22-2211-1-111-1-22-1-1111-1-110000−2i−2i2i2i1-133−3−3−3−333ii−i−iii−i−i0000000000i3−i3−i3i30000000000
χ38222-22-2-2-2-122-2-2-22-2211-1-111-1-22-1-1111-1-110000−2i−2i2i2i1-1−3−33333−3−3ii−i−iii−i−i0000000000−i3i3i3−i30000000000
χ3922-22-2-2-2222-2-2000202-22-22-2-2002-2-200002002i−2i00000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i200000000002−22−200
χ4022-22-2-2-2222-2-2000202-22-22-2-2002-2-200002002i−2i00000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000000000−22−2200
χ4122-22-2-2-2222-2-2000202-22-22-2-2002-2-20000200−2i2i0000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000000000−22−2200
χ4222-22-2-2-2222-2-2000202-22-22-2-2002-2-20000200−2i2i0000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i200000000002−22−200
χ4322-2-2-222-22-22-200020-222-2-22-200-22-2000022i−2i000000002i−2i2i−2i00000000000022−2−2−2−2220000000000−i2i2i2−i200
χ4422-2-2-222-22-22-200020-222-2-22-200-22-2000022i−2i000000002i−2i2i−2i000000000000−2−22222−2−20000000000i2−i2−i2i200
χ4522-2-2-222-22-22-200020-222-2-22-200-22-200002−2i2i00000000−2i2i−2i2i00000000000022−2−2−2−2220000000000i2−i2−i2i200
χ4622-2-2-222-22-22-200020-222-2-22-200-22-200002−2i2i00000000−2i2i−2i2i000000000000−2−22222−2−20000000000−i2i2i2−i200
χ472-2-222-22-220002-220-2-2-2-2-2222000002-22-2000002−22−200000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000002i−2i00000000
χ482-2-222-22-220002-220-2-2-2-2-2222000002-22-2000002−22−200000000002−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000−2i2i00000000
χ492-2-222-22-220002-220-2-2-2-2-2222000002-22-200000−22−220000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000−2i2i00000000
χ502-2-222-22-220002-220-2-2-2-2-2222000002-22-200000−22−220000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i20000002i−2i00000000
χ512-2-2-222-222000-2220-222-2-2-2-2200000-222-200000−i2i2i2−i20000000000−i2i2i2−i2−i2i2i2−i22−22−2−22−22000000002i−2i000000
χ522-2-2-222-222000-2220-222-2-2-2-2200000-222-200000−i2i2i2−i20000000000−i2i2i2−i2−i2i2i2−i2−22−222−22−200000000−2i2i000000
χ532-2-2-222-222000-2220-222-2-2-2-2200000-222-200000i2−i2−i2i20000000000i2−i2−i2i2i2−i2−i2i22−22−2−22−2200000000−2i2i000000
χ542-2-2-222-222000-2220-222-2-2-2-2200000-222-200000i2−i2−i2i20000000000i2−i2−i2i2i2−i2−i2i2−22−222−22−2000000002i−2i000000
χ5544444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5644444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ57444-44-4-4-4-2-4-4444-44-422-2-222-2-4422-2-2-222-2000000002-20000000000000000000000000000000000000000
χ58444-44-4-4-4-2-4-44-4-444422-2-222-24-422-222-2-2-200000000-220000000000000000000000000000000000000000
χ5944-44-4-4-444-444000-404-44-44-4-400-4440000-400000000000000000000000000000000000000000000000000
χ6044-44-4-4-44-24-4-400040-22-22-22200-2220000-2004i−4i0000000000−2i2i−2i2i00000000000000000000000000000000
χ6144-44-4-4-44-24-4-400040-22-22-22200-2220000-200−4i4i00000000002i−2i2i−2i00000000000000000000000000000000
χ6244-44-4-4-44-2-444000-40-22-22-222002-2-2000020000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ6344-44-4-4-44-2-444000-40-22-22-222002-2-20000200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ6444-4-4-444-444-44000-40-444-4-44-4004-440000-400000000000000000000000000000000000000000000000000
χ6544-4-4-444-4-24-44000-402-2-222-2200-22-20000200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ6644-4-4-444-4-24-44000-402-2-222-2200-22-200002000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ6744-4-4-444-4-2-44-4000402-2-222-22002-220000-24i−4i00000000−2i2i−2i2i000000000000000000000000000000000000
χ6844-4-4-444-4-2-44-4000402-2-222-22002-220000-2−4i4i000000002i−2i2i−2i000000000000000000000000000000000000
χ694-444-44-4-4400000000-44-444-4-40000000000000000000000000000000000002-2-222-2-220000000000000000
χ704-444-44-4-4400000000-44-444-4-4000000000000000000000000000000000000-222-2-222-20000000000000000
χ714-44-4-4-4444000000004-4-44-44-40000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ724-44-4-4-4444000000004-4-44-44-4000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ734-4-444-44-44000-44-404-4-4-4-444400000-44-44000000000000000000000000000000000000000000000000000
χ744-4-444-44-4-20004-440-42222-2-2-200000-22-220000022−2222−220000000000−22−22−22−22000000000000000000000000
χ754-4-444-44-4-20004-440-42222-2-2-200000-22-2200000−2222−222200000000002−22−22−22−2000000000000000000000000
χ764-4-444-44-4-2000-44-4042222-2-2-2000002-22-20000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ774-4-444-44-4-2000-44-4042222-2-2-2000002-22-20000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ784-4-4-444-4440004-4-40444-4-4-4-44000004-4-44000000000000000000000000000000000000000000000000000
χ794-4-4-444-44-20004-4-404-2-22222-200000-222-200000000000000000006−6−66−666−6000000000000000000000000
χ804-4-4-444-44-20004-4-404-2-22222-200000-222-20000000000000000000−666−66−6−66000000000000000000000000
χ814-4-4-444-44-2000-4440-4-2-22222-2000002-2-2200000−2i22i22i2−2i20000000000i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ824-4-4-444-44-2000-4440-4-2-22222-2000002-2-22000002i2−2i2−2i22i20000000000−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ838-888-88-8-8-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000
χ848-88-8-8-888-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000

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