Finite Group Databasebeta

← Group #10695724

Character table — Group #10695724

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order1222222222223666666644446666121212122222666666668888121224242424242424242466121244444444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-20000000000000000-2-20000000000000022-2-20000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-20000000000000000-2-200000000000000-2-2220000000000
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2111100000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-1-2-2111100000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2-1-11111111122-1-1-1-100000000000000
χ1522222222-2-2-2-2222222222-22-2-2-2-2-222220000000000000000-2-2000000002-222-2-200000000000000
χ1622222222-2-2-2-2222222222-22-2-2-2-2-222220000000000000000-2-200000000-22-2-22200000000000000
χ1722222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000000000000022000000000000000000000000002-2
χ1822222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000000000002200000000000000000000000000-22
χ1922222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000011−i3−i3−i3−i3i3i3i3i32-2-1-11100000000000000
χ2022222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000−i3−i3−i3−i3i3i3i3i3000011i3i3i3i3−i3−i3−i3−i3-2211-1-100000000000000
χ2122222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000011−i3−i3−i3−i3i3i3i3i3-2211-1-100000000000000
χ2222222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000i3i3i3i3−i3−i3−i3−i3000011i3i3i3i3−i3−i3−i3−i32-2-1-11100000000000000
χ2322-222-2-2-222-2-2222-2-2-22-2000022-2-2000000000000000022−2−20022−2−222−2−2000000002i−2i0000−i2−i2i2i200
χ2422-222-2-2-222-2-2222-2-2-22-2000022-2-2000000000000000022−2−20022−2−222−2−200000000−2i2i0000i2i2−i2−i200
χ2522-222-2-2-222-2-2222-2-2-22-2000022-2-20000000000000000−2−22200−2−222−2−222000000002i−2i0000i2i2−i2−i200
χ2622-222-2-2-222-2-2222-2-2-22-2000022-2-20000000000000000−2−22200−2−222−2−22200000000−2i2i0000−i2−i2i2i200
χ272-222-22-2-22-22-22-2-222-22-200002-22-200000000000000002−22−2002−22−22−22−20000002i−2i000000−i2i2−i2i200
χ282-222-22-2-22-22-22-2-222-22-200002-22-200000000000000002−22−2002−22−22−22−2000000−2i2i000000i2−i2i2−i200
χ292-222-22-2-22-22-22-2-222-22-200002-22-20000000000000000−22−2200−22−22−22−220000002i−2i000000i2−i2i2−i200
χ302-222-22-2-22-22-22-2-222-22-200002-22-20000000000000000−22−2200−22−22−22−22000000−2i2i000000−i2i2−i2i200
χ312-2-22-2-2222-2-222-2-2-2-22222-2-222-2-2222-2-200000000000000002-200000000000000000000002-2-2200
χ322-2-22-2-2222-2-222-2-2-2-22222-2-222-2-2222-2-200000000000000002-20000000000000000000000-222-200
χ332-2-22-2-2222-2-222-2-2-2-2222-222-22-2-22-2-2220000000000002-2-22-222-2-222-2-2200000000000000000000
χ342-2-22-2-2222-2-222-2-2-2-2222-222-22-2-22-2-222000000000000-222-2-22-222-2-222-200000000000000000000
χ352-2-22-2-2222-2-22-11111-1-1-1-222-2-111-111-1-10000−i3−i3i3i3−i3−i3i3i32-2-221-1-111-1-111-100−i3i3−i3i300000000000000
χ362-2-22-2-2222-2-22-11111-1-1-1-222-2-111-111-1-10000−i3−i3i3i3−i3−i3i3i3-222-21-11-1-111-1-1100i3−i3i3−i300000000000000
χ372-2-22-2-2222-2-22-11111-1-1-1-222-2-111-111-1-10000i3i3−i3−i3i3i3−i3−i32-2-221-1-111-1-111-100i3−i3i3−i300000000000000
χ382-2-22-2-2222-2-22-11111-1-1-1-222-2-111-111-1-10000i3i3−i3−i3i3i3−i3−i3-222-21-11-1-111-1-1100−i3i3−i3i300000000000000
χ392-2-22-2-222-222-22-2-2-2-222222-2-2-222-222-2-20000000000000000-220000000000000000002i2i−2i−2i000000
χ402-2-22-2-222-222-22-2-2-2-222222-2-2-222-222-2-20000000000000000-22000000000000000000−2i−2i2i2i000000
χ412-2-22-2-222-222-22-2-2-2-2222-2-222-222-2-2-22222-2-222-2-2-2-22200002-20000000000000000000000000000
χ422-2-22-2-222-222-22-2-2-2-2222-2-222-222-2-2-222-2-222-2-22222-2-200002-20000000000000000000000000000
χ432-2-22-2-222-222-2-11111-1-1-1-2-2221-1-1111-1-122-2-2-1-11111-1-10000-11−i3i3i3−i3i3−i3−i3i300−i3i3i3−i300000000000000
χ442-2-22-2-222-222-2-11111-1-1-1-2-2221-1-1111-1-122-2-2-1-11111-1-10000-11i3−i3−i3i3−i3i3i3−i300i3−i3−i3i300000000000000
χ452-2-22-2-222-222-2-11111-1-1-1-2-2221-1-1111-1-1-2-22211-1-1-1-1110000-11−i3i3i3−i3i3−i3−i3i300i3−i3−i3i300000000000000
χ462-2-22-2-222-222-2-11111-1-1-1-2-2221-1-1111-1-1-2-22211-1-1-1-1110000-11i3−i3−i3i3−i3i3i3−i300−i3i3i3−i300000000000000
χ47444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000000000000220000000000000000000000000000
χ4844444444-4-4-4-4-2-2-2-2-2-2-2-2-44-44222222220000000000000000-2-20000000000000000000000000000
χ49444-4-4-44-4000044-44-44-4-40000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ50444-4-4-44-4000044-44-44-4-4000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ5144-444-4-4-444-4-4-2-2-2222-220000-2-22200000000000000002222−22−2200−2−222−2−22200000000000000000000
χ5244-444-4-4-444-4-4-2-2-2222-220000-2-2220000000000000000−22−2222220022−2−222−2−200000000000000000000
χ5344-444-4-4-4-4-444444-4-4-44-40000-4-44400000000000000000000000000000000000000000000000000
χ5444-444-4-4-4-4-444-2-2-2222-22000022-2-20000000000000000000000i6i6−i6−i6−i6−i6i6i600000000000000000000
χ5544-444-4-4-4-4-444-2-2-2222-22000022-2-20000000000000000000000−i6−i6i6i6i6i6−i6−i600000000000000000000
χ5644-4-4-44-44000044-4-44-4-440000000000002-22-22-22-22-22-20000000000000000000000000000000000
χ5744-4-4-44-44000044-4-44-4-44000000000000-22-22-22-22-22-220000000000000000000000000000000000
χ5844-4-4-44-440000-2-222-222-200000000−2i32i3−2i32i32-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000000000000000
χ5944-4-4-44-440000-2-222-222-200000000−2i32i3−2i32i3-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000000000000000
χ6044-4-4-44-440000-2-222-222-2000000002i3−2i32i3−2i32-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000000000000000
χ6144-4-4-44-440000-2-222-222-2000000002i3−2i32i3−2i3-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000000000000000
χ624-444-44-4-44-44-4-222-2-22-220000-22-22000000000000000022−2222−2200−22−22−22−2200000000000000000000
χ634-444-44-4-44-44-4-222-2-22-220000-22-220000000000000000−2222−2222002−22−22−22−200000000000000000000
χ644-444-44-4-4-44-444-4-444-44-40000-44-4400000000000000000000000000000000000000000000000000
χ654-444-44-4-4-44-44-222-2-22-2200002-22-20000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000
χ664-444-44-4-4-44-44-222-2-22-2200002-22-20000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000
χ674-44-44-4-4400004-444-4-4-440000000000002-2-222-2-22-222-20000000000000000000000000000000000
χ684-44-44-4-4400004-444-4-4-44000000000000-222-2-222-22-2-220000000000000000000000000000000000
χ694-44-44-4-440000-22-2-2222-200000000−2i32i32i3−2i32-2-22−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ704-44-44-4-440000-22-2-2222-200000000−2i32i32i3−2i3-222-21−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ714-44-44-4-440000-22-2-2222-2000000002i3−2i3−2i32i32-2-22−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ724-44-44-4-440000-22-2-2222-2000000002i3−2i3−2i32i3-222-21+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ734-4-44-4-4444-4-44-22222-2-2-24-4-44-222-2-2-2220000000000000000-220000000000000000000000000000
χ744-4-44-4-444-444-4-22222-2-2-244-4-42-2-22-2-22200000000000000002-20000000000000000000000000000
χ754-4-4-4444-400004-44-444-4-40000000000000000000000000000000000000000000000002-2-22000000
χ764-4-4-4444-400004-44-444-4-4000000000000000000000000000000000000000000000000-222-2000000
χ77888-8-8-88-80000-4-44-44-4440000000000000000000000000000000000000000000000000000000000
χ788-8-8-8888-80000-44-44-4-4440000000000000000000000000000000000000000000000000000000000

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