Finite Group Databasebeta

← Group #10852220

Character table — Group #10852220

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888816161616161624242424242424242424242424242424
order1222222222344666666622444446666121212122222446666666666121212121212121244121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-111111111111-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11-111-1-11-11-11-11-111-1-111-1-1
χ1011111111111-1-111111111111-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11-111-1-1-11-11-11-11-1-111-1-111
χ1111111111111-1-111111111111-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1-1111-11-11-11-1-1-111-1-111
χ1211111111111-1-111111111111-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-11-1-111-11-11-11-1111-1-111-1-1
χ1311111111111-1-11111111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-1-1111-1-111-1-1111-1-1-1-111
χ1411111111111-1-11111111-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-11-1-111-111-1-111-1-1-11111-1-1
χ1511111111111-1-11111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111-111-1-11-1-111-1-11-1-11111-1-1
χ1611111111111-1-11111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1111-111-1-1-111-1-111-111-1-1-1-111
χ172222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000000000
χ182222222222-122-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-2-2-2-222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000000000
χ192222222222-122-1-1-1-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-12222-2-211-1-1-1-1-1-1-1-11111-1-111-2-211110000000000000000
χ202222222222-122-1-1-1-1-1-1-1-2-2-2-2222-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111-1-11122-1-1-1-10000000000000000
χ212222222222-1-2-2-1-1-1-1-1-1-12222-2-2-2-1-1-1-1111122-2-2-2-2-1-1-1-1-1-11111-1-11111112-2-1-1110000000000000000
χ222222222222-1-2-2-1-1-1-1-1-1-12222-2-2-2-1-1-1-11111-2-222-2-2-1-11111-1-1-1-1-1-1111111-2211-1-10000000000000000
χ232222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-1111122-2-22211-1-1-1-1111111-1-111-1-1-2211-1-10000000000000000
χ242222222222-1-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-1-11111-2-22222111111-1-1-1-111-1-111-1-12-2-1-1110000000000000000
χ25222222-2-2-2-2222222222222-2-22-2-2-2-2-2-222220000-222200000000-2-2-2-2-2-2220000000000000000000000
χ26222222-2-2-2-22222222222-2-2222-2-2-2-2-2-2222200002-2-2-2000000002222-2-2-2-20000000000000000000000
χ27222222-2-2-2-22-2-2222222222-2-2-222-2-2-2-2-2-2-2-200002-22200000000-2-22222-2-20000000000000000000000
χ28222222-2-2-2-22-2-22222222-2-222-222-2-2-2-2-2-2-2-20000-22-2-20000000022-2-222220000000000000000000000
χ29222222-2-2-2-2-122-1-1-1-1-1-1-122-2-22-2-21111-1-1-1-10000-22-1-1−i3−i3i3i3−i3−i3i3i3111111-1-100−i3i3−i3i30000000000000000
χ30222222-2-2-2-2-122-1-1-1-1-1-1-122-2-22-2-21111-1-1-1-10000-22-1-1i3i3−i3−i3i3i3−i3−i3111111-1-100i3−i3i3−i30000000000000000
χ31222222-2-2-2-2-122-1-1-1-1-1-1-1-2-2222-2-21111-1-1-1-100002-211−i3−i3i3i3−i3−i3i3i3-1-1-1-1111100i3−i3i3−i30000000000000000
χ32222222-2-2-2-2-122-1-1-1-1-1-1-1-2-2222-2-21111-1-1-1-100002-211i3i3−i3−i3i3i3−i3−i3-1-1-1-1111100−i3i3−i3i30000000000000000
χ33222222-2-2-2-2-1-2-2-1-1-1-1-1-1-122-2-2-2221111111100002-2-1-1−i3−i3i3i3i3i3−i3−i311-1-1-1-11100−i3i3i3−i30000000000000000
χ34222222-2-2-2-2-1-2-2-1-1-1-1-1-1-122-2-2-2221111111100002-2-1-1i3i3−i3−i3−i3−i3i3i311-1-1-1-11100i3−i3−i3i30000000000000000
χ35222222-2-2-2-2-1-2-2-1-1-1-1-1-1-1-2-222-222111111110000-2211−i3−i3i3i3i3i3−i3−i3-1-111-1-1-1-100i3−i3−i3i30000000000000000
χ36222222-2-2-2-2-1-2-2-1-1-1-1-1-1-1-2-222-222111111110000-2211i3i3−i3−i3−i3−i3i3i3-1-111-1-1-1-100−i3i3i3−i30000000000000000
χ372222-2-222-2-2222-2-222-2-220000-22-222-2-222-2-2000000000000000000002-200000000002200-2-200000000
χ382222-2-222-2-2222-2-222-2-220000-22-222-2-222-2-2000000000000000000002-20000000000-2-2002200000000
χ392222-2-222-2-22-2-2-2-222-2-2200002-2222-2-2-2-22200000000000000000000-2200000000002-200-2200000000
χ402222-2-222-2-22-2-2-2-222-2-2200002-2222-2-2-2-22200000000000000000000-220000000000-22002-200000000
χ412222-2-2-2-222222-2-222-2-220000-2-22-2-22222-2-200000000000000000000-22000000002200-2-20000000000
χ422222-2-2-2-222222-2-222-2-220000-2-22-2-22222-2-200000000000000000000-2200000000-2-200220000000000
χ432222-2-2-2-2222-2-2-2-222-2-22000022-2-2-222-2-222000000000000000000002-2000000002-200-220000000000
χ442222-2-2-2-2222-2-2-2-222-2-22000022-2-2-222-2-222000000000000000000002-200000000-22002-20000000000
χ4522-2-2-222-22-2200-2-22-222-22-22-20002-22-200000000002-2000000002-200000000000000000000002i−2i002i−2i
χ4622-2-2-222-22-2200-2-22-222-22-22-20002-22-200000000002-2000000002-20000000000000000000000−2i2i00−2i2i
χ4722-2-2-222-22-2200-2-22-222-2-22-220002-22-20000000000-2200000000-2200000000000000000000002i−2i00−2i2i
χ4822-2-2-222-22-2200-2-22-222-2-22-220002-22-20000000000-2200000000-220000000000000000000000−2i2i002i−2i
χ4922-2-2-22-22-22200-2-22-222-22-2-22000-22-2200000000002-200000000-22000000000000000000002i−2i002i−2i00
χ5022-2-2-22-22-22200-2-22-222-22-2-22000-22-2200000000002-200000000-2200000000000000000000−2i2i00−2i2i00
χ5122-2-2-22-22-22200-2-22-222-2-222-2000-22-220000000000-22000000002-2000000000000000000002i−2i00−2i2i00
χ5222-2-2-22-22-22200-2-22-222-2-222-2000-22-220000000000-22000000002-200000000000000000000−2i2i002i−2i00
χ534444-4-444-4-4-24422-2-222-20000-44-4-2-222-2-22200000000000000000000-22000000000000000000000000
χ544444-4-444-4-4-2-4-422-2-222-200004-44-2-22222-2-2000000000000000000002-2000000000000000000000000
χ554444-4-4-4-444-24422-2-222-20000-4-4422-2-2-2-222000000000000000000002-2000000000000000000000000
χ564444-4-4-4-444-2-4-422-2-222-2000044-422-2-222-2-200000000000000000000-22000000000000000000000000
χ5744-4-44-44-4-44400444-4-4-4-400000004-4-4400000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-44-200-2-2-222220000000-222-2000000000000000000000023−230023−230000000000000000000000
χ5944-4-44-44-4-44-200-2-2-222220000000-222-20000000000000000000000−232300−23230000000000000000000000
χ6044-4-44-4-444-4400444-4-4-4-40000000-444-400000000000000000000000000000000000000000000000000
χ6144-4-44-4-444-4-200-2-2-2222200000002-2-22000000000000000000000023−2300−23230000000000000000000000
χ6244-4-44-4-444-4-200-2-2-2222200000002-2-220000000000000000000000−23230023−230000000000000000000000
χ6344-4-4-444-44-4-20022-22-2-224-44-4000-22-220000000000-2200000000-220000000000000000000000000000
χ6444-4-4-444-44-4-20022-22-2-22-44-44000-22-2200000000002-2000000002-20000000000000000000000000000
χ6544-4-4-44-44-44-20022-22-2-224-4-440002-22-20000000000-22000000002-20000000000000000000000000000
χ6644-4-4-44-44-44-20022-22-2-22-444-40002-22-200000000002-200000000-220000000000000000000000000000
χ674-4-4400000044-400-4-4004000000000004-4002-22-200002-22-22-22-2000000000000000000000000000000
χ684-4-4400000044-400-4-4004000000000004-400-22-220000-22-22-22-22000000000000000000000000000000
χ694-4-440000004-4400-4-400400000000000-44002-2-2200002-22-2-22-22000000000000000000000000000000
χ704-4-440000004-4400-4-400400000000000-4400-222-20000-22-222-22-2000000000000000000000000000000
χ714-4-44000000-24-4−2i32i322−2i32i3-200000000000-22−2i32i32-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ724-4-44000000-24-4−2i32i322−2i32i3-200000000000-22−2i32i3-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ734-4-44000000-24-42i3−2i3222i3−2i3-200000000000-222i3−2i32-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ744-4-44000000-24-42i3−2i3222i3−2i3-200000000000-222i3−2i3-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ754-4-44000000-2-44−2i32i322−2i32i3-2000000000002-22i3−2i32-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ764-4-44000000-2-44−2i32i322−2i32i3-2000000000002-22i3−2i3-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ774-4-44000000-2-442i3−2i3222i3−2i3-2000000000002-2−2i32i32-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ784-4-44000000-2-442i3−2i3222i3−2i3-2000000000002-2−2i32i3-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ798-88-800000080000-8800-80000000000000000000000000000000000000000000000000000000000000
χ808-88-8000000-400−4i34i34-44i3−4i340000000000000000000000000000000000000000000000000000000000000
χ818-88-8000000-4004i3−4i34-4−4i34i340000000000000000000000000000000000000000000000000000000000000

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