Finite Group Databasebeta

← Group #10830932

Character table — Group #10830932

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122222223444444446666666221212121212121212224466666688881212121224242424242424248888888844121212122224444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-111-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111
χ51111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-11-1-1
χ61111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-111
χ71111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ911111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-111-1-1-11-1
χ1011111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-11-1-1111-11
χ1111111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111111-1-1-1-11-11
χ1211111111111-1-1-1-1111111111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-1-11111-11-1
χ1311111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-11111-1-11
χ1411111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-11-1-111111-1-1-1-111-1
χ1511111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-111-1-1-1-11-1-11111-1
χ1611111111111-1-1-1-1111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111111-111-1-111-111-1-1-1-11
χ17222222222-2-22222-2-22222222-2-2-2-22222-2-20000-2-200000000000000000000000000000000000022-200-200
χ18222222222-2-22222-2-22222222-2-2-2-22222-2-20000-2-2000000000000000000000000000000000000-2-2200200
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000220000000000000000000000000000000000002-2200-200
χ20222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000022000000000000000000000000000000000000-22-200200
χ2122222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111100000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1111122221111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-21111111111110000000022-1-1-1-10000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-211-1-1-1-122-2-21111-1-1-1-11111000000002-2-1-1110000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-122-2-211-1-1-1-1-2-22211111111-1-1-1-100000000-2211-1-10000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-22211111122-2-2-1-1-1-1-1-1-1-1111100000000-2211-1-10000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-1-11111-1-1-2-222111111-2-222-1-1-1-11111-1-1-1-1000000002-2-1-1110000000000
χ2922-2-2-22-2222-20000-222-2-2-22-22002-200002-2002-2000000000022-2-20000000022-2-20000000000000002-2000
χ3022-2-2-22-2222-20000-222-2-2-22-22002-200002-2002-2000000000022-2-200000000-2-222000000000000000-22000
χ3122-2-2-22-2222-20000-222-2-2-22-22002-200002-200-220000000000-2-2220000000022-2-2000000000000000-22000
χ3222-2-2-22-2222-20000-222-2-2-22-22002-200002-200-220000000000-2-22200000000-2-2220000000000000002-2000
χ332-22-2-2-2222-220000-22-22-2-2-22200-2200002-22-2000022-2-200000000000000002-22-200000000002-200000000
χ342-22-2-2-2222-220000-22-22-2-2-22200-2200002-22-2000022-2-20000000000000000-22-220000000000-2200000000
χ352-22-2-2-2222-220000-22-22-2-2-22200-2200002-2-220000-2-22200000000000000002-22-20000000000-2200000000
χ362-22-2-2-2222-220000-22-22-2-2-22200-2200002-2-220000-2-2220000000000000000-22-2200000000002-200000000
χ372-2-222-2-2222222-2-2-2-2-2-222-2-222-22222-2-2-2-200002-200002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382-2-222-2-2222222-2-2-2-2-2-222-2-222-22222-2-2-2-200002-20000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ392-2-222-2-22222-2-222-2-2-2-222-2-22-2222-2-222-2-20000-2200002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402-2-222-2-22222-2-222-2-2-2-222-2-22-2222-2-222-2-20000-220000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412-2-222-2-222-2-222-2-222-2-222-2-22-22-2-222-2-2220000-22000000000000000000002-2-2222-2-20000000000000000
χ422-2-222-2-222-2-222-2-222-2-222-2-22-22-2-222-2-2220000-2200000000000000000000-222-2-2-2220000000000000000
χ432-2-222-2-222-2-2-2-22222-2-222-2-222-2-2-2-2-2222200002-2000000000000000000002-2-22-2-2220000000000000000
χ442-2-222-2-222-2-2-2-22222-2-222-2-222-2-2-2-2-2222200002-200000000000000000000-222-222-2-20000000000000000
χ452-2-222-2-22-12222-2-2-2-211-1-111-12-2-1-1-1-111110000-11−i3i3−i3i32i−2i2i−2i−i3i3−i3i3−i−iii−i−iii00000000003−33−30000000000
χ462-2-222-2-22-12222-2-2-2-211-1-111-12-2-1-1-1-111110000-11−i3i3−i3i3−2i2i−2i2i−i3i3−i3i3ii−i−iii−i−i0000000000−33−330000000000
χ472-2-222-2-22-12222-2-2-2-211-1-111-12-2-1-1-1-111110000-11i3−i3i3−i32i−2i2i−2ii3−i3i3−i3−i−iii−i−iii0000000000−33−330000000000
χ482-2-222-2-22-12222-2-2-2-211-1-111-12-2-1-1-1-111110000-11i3−i3i3−i3−2i2i−2i2ii3−i3i3−i3ii−i−iii−i−i00000000003−33−30000000000
χ492-2-222-2-22-122-2-222-2-211-1-111-1-22-1-111-1-11100001-1−i3i3−i3i32i−2i−2i2ii3−i3i3−i3−i−iiiii−i−i00000000003−3−330000000000
χ502-2-222-2-22-122-2-222-2-211-1-111-1-22-1-111-1-11100001-1−i3i3−i3i3−2i2i2i−2ii3−i3i3−i3ii−i−i−i−iii0000000000−333−30000000000
χ512-2-222-2-22-122-2-222-2-211-1-111-1-22-1-111-1-11100001-1i3−i3i3−i32i−2i−2i2i−i3i3−i3i3−i−iiiii−i−i0000000000−333−30000000000
χ522-2-222-2-22-122-2-222-2-211-1-111-1-22-1-111-1-11100001-1i3−i3i3−i3−2i2i2i−2i−i3i3−i3i3ii−i−i−i−iii00000000003−3−330000000000
χ5344444444-2-4-44444-4-4-2-2-2-2-2-2-2-4-422-2-2-2-22200002200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000-2-200000000000000000000000000000000000000000000
χ554444-4-4-4-4400000000-4-44-444-40000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ564444-4-4-4-4400000000-4-44-444-400000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5744-4-44-44-44004i−4i4i−4i00-44-444-4-400004i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ5844-4-44-44-4400−4i4i−4i4i00-44-444-4-40000−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ5944-4-44-44-4-2004i−4i4i−4i002-22-2-2220000−2i2i−2i2i00000000000000000000i6−i6i6−i66−66−6000000000000000000000000
χ6044-4-44-44-4-2004i−4i4i−4i002-22-2-2220000−2i2i−2i2i00000000000000000000−i6i6−i6i6−66−66000000000000000000000000
χ6144-4-44-44-4-200−4i4i−4i4i002-22-2-22200002i−2i2i−2i00000000000000000000i6−i6i6−i6−66−66000000000000000000000000
χ6244-4-44-44-4-200−4i4i−4i4i002-22-2-22200002i−2i2i−2i00000000000000000000−i6i6−i6i66−66−6000000000000000000000000
χ6344-4-4-44-444-4400004-44-4-4-44-4400-440000-4400000000000000000000000000000000000000000000000000
χ6444-4-4-44-44-24-40000-44-2222-22-200-220000-22004-40000000000-2-22200000000000000000000000000000000
χ6544-4-4-44-44-24-40000-44-2222-22-200-220000-2200-44000000000022-2-200000000000000000000000000000000
χ6644-4-4-44-44-2-4400004-4-2222-22-2002-200002-2000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ6744-4-4-44-44-2-4400004-4-2222-22-2002-200002-20000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ684-44-444-4-44004i−4i−4i4i004-4-44-44-400004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ694-44-444-4-4400−4i4i4i−4i004-4-44-44-40000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ704-44-444-4-4-2004i−4i−4i4i00-222-22-220000−2i2i2i−2i000000000000000000006−6−66−i6i6i6−i6000000000000000000000000
χ714-44-444-4-4-2004i−4i−4i4i00-222-22-220000−2i2i2i−2i00000000000000000000−666−6i6−i6−i6i6000000000000000000000000
χ724-44-444-4-4-200−4i4i4i−4i00-222-22-2200002i−2i−2i2i000000000000000000006−6−66i6−i6−i6i6000000000000000000000000
χ734-44-444-4-4-200−4i4i4i−4i00-222-22-2200002i−2i−2i2i00000000000000000000−666−6−i6i6i6−i6000000000000000000000000
χ744-44-4-4-44444-400004-4-44-4-4-444004-40000-4400000000000000000000000000000000000000000000000000
χ754-44-4-4-444-24-400004-42-2222-2-200-2200002-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ764-44-4-4-444-24-400004-42-2222-2-200-2200002-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ774-44-4-4-444-2-440000-442-2222-2-2002-20000-224-40000-2-2220000000000000000000000000000000000000000
χ784-44-4-4-444-2-440000-442-2222-2-2002-20000-22-44000022-2-20000000000000000000000000000000000000000
χ794-4-444-4-44-2-4-444-4-44422-2-222-2-4422-2-222-2-200002-200000000000000000000000000000000000000000000
χ804-4-444-4-44-2-4-4-4-4444422-2-222-24-42222-2-2-2-20000-2200000000000000000000000000000000000000000000
χ814-4-44-444-4400000000444-4-4-4-40000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ824-4-44-444-4400000000444-4-4-4-400000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ838888-8-8-8-8-40000000044-44-4-44000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-400000000-4-4-44444000000000000000000000000000000000000000000000000000000000000

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