Finite Group Databasebeta

← Group #10695380

Character table — Group #10695380

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111222222222222444444444444888888888888888888888888881616161616162424242424242424242424244848
order1222222222223666666644446666121212122222666666668888121224242424242424242466121222444444888844
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
χ232222-2-2-2-222-2-2222-2-2-22-2000022-2-2000000000000000022−2−20022−2−222−2−2000000002i−2i0000−i2−i2i2i200
χ242222-2-2-2-222-2-2222-2-2-22-2000022-2-2000000000000000022−2−20022−2−222−2−200000000−2i2i0000i2i2−i2−i200
χ252222-2-2-2-222-2-2222-2-2-22-2000022-2-20000000000000000−2−22200−2−222−2−222000000002i−2i0000i2i2−i2−i200
χ262222-2-2-2-222-2-2222-2-2-22-2000022-2-20000000000000000−2−22200−2−222−2−22200000000−2i2i0000−i2−i2i2i200
χ272-2-2222-2-22-22-22-2-22-2-22222-2-22-22-222-2-200000000000000002-200000000000000000000002i−2i2i−2i00
χ282-2-2222-2-22-22-22-2-22-2-22222-2-22-22-222-2-200000000000000002-20000000000000000000000−2i2i−2i2i00
χ292-2-2222-2-22-22-22-2-22-2-222-2-2222-22-2-2-2220000000000002-22-2-222-22-22-22-200000000000000000000
χ302-2-2222-2-22-22-22-2-22-2-222-2-2222-22-2-2-222000000000000-22-22-22-22-22-22-2200000000000000000000
χ312-2-2222-2-22-22-2-111-111-1-1-2-222-11-1111-1-10000−i3−i3i3i3−i3−i3i3i32-22-21-1-11-11-11-1100−i3i3−i3i300000000000000
χ322-2-2222-2-22-22-2-111-111-1-1-2-222-11-1111-1-10000−i3−i3i3i3−i3−i3i3i3-22-221-11-11-11-11-100i3−i3i3−i300000000000000
χ332-2-2222-2-22-22-2-111-111-1-1-2-222-11-1111-1-10000i3i3−i3−i3i3i3−i3−i32-22-21-1-11-11-11-1100i3−i3i3−i300000000000000
χ342-2-2222-2-22-22-2-111-111-1-1-2-222-11-1111-1-10000i3i3−i3−i3i3i3−i3−i3-22-221-11-11-11-11-100−i3i3−i3i300000000000000
χ352-2-2222-2-2-22-222-2-22-2-2222-2-22-22-2222-2-20000000000000000-2200000000000000000022-2-2000000
χ362-2-2222-2-2-22-222-2-22-2-2222-2-22-22-2222-2-20000000000000000-22000000000000000000-2-222000000
χ372-2-2222-2-2-22-222-2-22-2-222-222-2-22-22-2-22222-2-222-2-2-2-22200002-20000000000000000000000000000
χ382-2-2222-2-2-22-222-2-22-2-222-222-2-22-22-2-222-2-222-2-22222-2-200002-20000000000000000000000000000
χ392-2-2222-2-2-22-22-111-111-1-1-222-21-11-111-1-122-2-2-1-11111-1-10000-11−i3i3−i3i3i3−i3i3−i300−i3i3i3−i300000000000000
χ402-2-2222-2-2-22-22-111-111-1-1-222-21-11-111-1-122-2-2-1-11111-1-10000-11i3−i3i3−i3−i3i3−i3i300i3−i3−i3i300000000000000
χ412-2-2222-2-2-22-22-111-111-1-1-222-21-11-111-1-1-2-22211-1-1-1-1110000-11−i3i3−i3i3i3−i3i3−i300i3−i3−i3i300000000000000
χ422-2-2222-2-2-22-22-111-111-1-1-222-21-11-111-1-1-2-22211-1-1-1-1110000-11i3−i3i3−i3−i3i3−i3i300−i3i3i3−i300000000000000
χ432-2-22-2-2222-2-222-2-2-2222-200002-2-2200000000000000002−2−22002−2−222−2−220000002-20000002−2−2200
χ442-2-22-2-2222-2-222-2-2-2222-200002-2-2200000000000000002−2−22002−2−222−2−22000000-22000000−222−200
χ452-2-22-2-2222-2-222-2-2-2222-200002-2-220000000000000000−222−200−222−2−222−20000002-2000000−222−200
χ462-2-22-2-2222-2-222-2-2-2222-200002-2-220000000000000000−222−200−222−2−222−2000000-220000002−2−2200
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
χ494444-4-4-4-444-4-4-2-2-2222-220000-2-22200000000000000002222−22−2200−2−222−2−22200000000000000000000
χ504444-4-4-4-444-4-4-2-2-2222-220000-2-2220000000000000000−22−2222220022−2−222−2−200000000000000000000
χ514444-4-4-4-4-4-444444-4-4-44-40000-4-44400000000000000000000000000000000000000000000000000
χ524444-4-4-4-4-4-444-2-2-2222-22000022-2-20000000000000000000000i6i6−i6−i6−i6−i6i6i600000000000000000000
χ534444-4-4-4-4-4-444-2-2-2222-22000022-2-20000000000000000000000−i6−i6i6i6i6i6−i6−i600000000000000000000
χ5444-4-44-44-4000044-4-44-4-440000000000002-22-22-22-22-22-20000000000000000000000000000000000
χ5544-4-44-44-4000044-4-44-4-44000000000000-22-22-22-22-22-220000000000000000000000000000000000
χ5644-4-44-44-40000-2-222-222-200000000−2i32i3−2i32i32-22-2−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000000000000000000000
χ5744-4-44-44-40000-2-222-222-200000000−2i32i3−2i32i3-22-221+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000000000000000000000
χ5844-4-44-44-40000-2-222-222-2000000002i3−2i32i3−2i32-22-2−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000000000000000000000
χ5944-4-44-44-40000-2-222-222-2000000002i3−2i32i3−2i3-22-221−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000000000000000000000
χ6044-4-4-44-44000044-44-44-4-40000000000000000000000000000000000000000000000002-22-2000000
χ6144-4-4-44-44000044-44-44-4-4000000000000000000000000000000000000000000000000-22-22000000
χ624-44-44-4-4400004-44-4-44-440000000000002-2-222-2-22-222-20000000000000000000000000000000000
χ634-44-44-4-4400004-44-4-44-44000000000000-222-2-222-22-2-220000000000000000000000000000000000
χ644-44-44-4-440000-22-222-22-200000000−2i32i32i3−2i32-2-22−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ654-44-44-4-440000-22-222-22-200000000−2i32i32i3−2i3-222-21−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ664-44-44-4-440000-22-222-22-2000000002i3−2i3−2i32i32-2-22−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ674-44-44-4-440000-22-222-22-2000000002i3−2i3−2i32i3-222-21+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ684-44-4-444-400004-4444-4-4-40000000000000000000000000000000000000000000000002-2-22000000
χ694-44-4-444-400004-4444-4-4-4000000000000000000000000000000000000000000000000-222-2000000
χ704-4-4444-4-44-44-4-222-222-2-244-4-4-22-22-2-2220000000000000000-220000000000000000000000000000
χ714-4-4444-4-4-44-44-222-222-2-24-4-442-22-2-2-22200000000000000002-20000000000000000000000000000
χ724-4-44-4-4444-4-44-2222-2-2-220000-222-2000000000000000022−22−222200−222−2−222−200000000000000000000
χ734-4-44-4-4444-4-44-2222-2-2-220000-222-20000000000000000−222222−22002−2−222−2−2200000000000000000000
χ744-4-44-4-444-444-44-4-4-4444-40000-444-400000000000000000000000000000000000000000000000000
χ754-4-44-4-444-444-4-2222-2-2-2200002-2-220000000000000000000000i6−i6−i6i6−i6i6i6−i600000000000000000000
χ764-4-44-4-444-444-4-2222-2-2-2200002-2-220000000000000000000000−i6i6i6−i6i6−i6−i6i600000000000000000000
χ7788-8-8-88-880000-4-44-44-4440000000000000000000000000000000000000000000000000000000000
χ788-88-8-888-80000-44-4-4-44440000000000000000000000000000000000000000000000000000000000

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