Finite Group Databasebeta

← Group #10768700

Character table — Group #10768700

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order1222222234466666662444666612121212222222446666666688881212242424242424242466121222244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1
χ41111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ5111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-111-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1-111111-1-1
χ91111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-11111-1-11-11-11111-1-1-1-111-1-11-11111-1-1-1-11-11-11-111-11-1-111-1-11-1
χ101111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-11111-1-11-11-11111-1-1-1-111-1-11-11111-1-1-1-11-11-1-11-1-11-111-1-111-11
χ111111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-11-111111-1-1-1-1-1-1111-1-1-1-1-11111-11-111-1-1-111-1111-1-1-11
χ121111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-11111-1-1-11-111111-1-1-1-1-1-1111-1-1-1-1-11111-11-11-1111-1-11-1-1-1111-1
χ131111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-111-1-1111-11-1-1-1-1-11111-1-1111-1-1-1-1-111111-11-11-111-11-1-1-1-111-11
χ141111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-111-1-1111-11-1-1-1-1-11111-1-1111-1-1-1-1-111111-11-1-11-1-11-11111-1-11-1
χ151111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-111-1-111-11-11-1-1-1-1111111-1-11-11111-1-1-1-1-11-111-1-1-111-11-1-1111-1
χ161111-1-1111-1-11-1-1-1-111-1-11111-1-1-1-111-1-111-11-11-1-1-1-1111111-1-11-11111-1-1-1-1-11-11-1111-1-11-111-1-1-11
χ17222222222-2-222222222-2-2-22222-2-2-2-200000000000000000000-2-20000000000002-2000-220000000
χ18222222222-2-222222222-2-2-22222-2-2-2-200000000000000000000-2-2000000000000-220002-20000000
χ1922222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111111100000000000000
χ2122222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-111111111-1-1-1-100000000000000
χ2222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-1111100000000000000
χ23222222-2-22222222222-2-22-2-2-2-2-22222000022-2-2000000000000-2-20000000022-2-200000000000000
χ24222222-2-22222222222-2-22-2-2-2-2-222220000-2-222000000000000-2-200000000-2-22200000000000000
χ25222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000000000000000000022000000000000002-2-2002000000
χ26222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2000000000000000000002200000000000000-22200-2000000
χ27222222-2-2-122-1-1-1-1-1-1-1-2-22-21111-1-1-1-1000022-2-2−i3−i3i3i3−i3−i3i3i3000011−i3−i3i3i3−i3−i3i3i3-1-11100000000000000
χ28222222-2-2-122-1-1-1-1-1-1-1-2-22-21111-1-1-1-1000022-2-2i3i3−i3−i3i3i3−i3−i3000011i3i3−i3−i3i3i3−i3−i3-1-11100000000000000
χ29222222-2-2-122-1-1-1-1-1-1-1-2-22-21111-1-1-1-10000-2-222−i3−i3i3i3−i3−i3i3i3000011i3i3−i3−i3i3i3−i3−i311-1-100000000000000
χ30222222-2-2-122-1-1-1-1-1-1-1-2-22-21111-1-1-1-10000-2-222i3i3−i3−i3i3i3−i3−i3000011−i3−i3i3i3−i3−i3i3i311-1-100000000000000
χ312222-2-2222222-2-2-2-222-22-2-222-2-222-2-200000000000000000000-2200000000000022000-2-20000000
χ322222-2-2222222-2-2-2-222-22-2-222-2-222-2-200000000000000000000-22000000000000-2-2000220000000
χ332222-2-222-1-2-2-11111-1-1-2-222-1-11111-1-122-2-22-22-2-1-1-1-1111122-2-2-11-1-1-1-11111-11-1100000000000000
χ342222-2-222-1-2-2-11111-1-1-2-222-1-11111-1-122-2-2-22-22-1-1-1-11111-2-222-111111-1-1-1-11-11-100000000000000
χ352222-2-222-1-2-2-11111-1-1-2-222-1-11111-1-1-2-2222-22-21111-1-1-1-1-2-222-111111-1-1-1-1-11-1100000000000000
χ362222-2-222-1-2-2-11111-1-1-2-222-1-11111-1-1-2-222-22-221111-1-1-1-122-2-2-11-1-1-1-111111-11-100000000000000
χ372222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-2000000000000000000002-2000000000000002-2200-2000000
χ382222-2-2-2-22222-2-2-2-2222-2-22-2-22222-2-2000000000000000000002-200000000000000-22-2002000000
χ392222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-22200002-2-22000000000000-22000000002-2-2200000000000000
χ402222-2-2-2-22-2-22-2-2-2-222222-2-2-222-2-2220000-222-2000000000000-2200000000-222-200000000000000
χ412222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-100002-2-22−i3−i3i3i3i3i3−i3−i300001-1−i3−i3i3i3i3i3−i3−i3-111-100000000000000
χ422222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-100002-2-22i3i3−i3−i3−i3−i3i3i300001-1i3i3−i3−i3−i3−i3i3i3-111-100000000000000
χ432222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-10000-222-2−i3−i3i3i3i3i3−i3−i300001-1i3i3−i3−i3−i3−i3i3i31-1-1100000000000000
χ442222-2-2-2-2-1-2-2-11111-1-1222-211-1-111-1-10000-222-2i3i3−i3−i3−i3−i3i3i300001-1−i3−i3i3i3i3i3−i3−i31-1-1100000000000000
χ4544444444-2-4-4-2-2-2-2-2-2-24-4-4-4-2-2-2-22222000000000000000000002200000000000000000000000000
χ46444444-4-4-2-4-4-2-2-2-2-2-2-2-44-442222222200000000000000000000-2-200000000000000000000000000
χ474444-4-444-244-22222-2-2-44-4-4-2-222-2-222000000000000000000002-200000000000000000000000000
χ484444-4-4-4-4-244-22222-2-24-4-4422-2-2-2-22200000000000000000000-2200000000000000000000000000
χ4944-4-4000044-4-400004-4000000004-4002-22-200002-22-22-22-200000000000000000000000000000000
χ5044-4-4000044-4-400004-4000000004-400-22-220000-22-22-22-2200000000000000000000000000000000
χ5144-4-400004-44-400004-400000000-44002-2-2200002-22-2-22-2200000000000000000000000000000000
χ5244-4-400004-44-400004-400000000-4400-222-20000-22-222-22-200000000000000000000000000000000
χ5344-4-40000-24-42−2i3−2i32i32i3-2200000000-22−2i32i32-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ5444-4-40000-24-42−2i3−2i32i32i3-2200000000-22−2i32i3-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ5544-4-40000-24-422i32i3−2i3−2i3-2200000000-222i3−2i32-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ5644-4-40000-24-422i32i3−2i3−2i3-2200000000-222i3−2i3-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ5744-4-40000-2-442−2i3−2i32i32i3-22000000002-22i3−2i32-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ5844-4-40000-2-442−2i3−2i32i32i3-22000000002-22i3−2i3-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ5944-4-40000-2-4422i32i3−2i3−2i3-22000000002-2−2i32i32-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ6044-4-40000-2-4422i32i3−2i3−2i3-22000000002-2−2i32i3-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ614-44-4004-4400-40000-4400004-400000000000000000000000022−2200000022−2222−22000000000000000000
χ624-44-4004-4400-40000-4400004-4000000000000000000000000−2222000000−2222−2222000000000000000000
χ634-44-4004-4-2002−2i32i3−2i32i32-20000-22−2i32i3000000000000000000000022−2200i6−i6i6−i6−22−22000000000000000000
χ644-44-4004-4-2002−2i32i3−2i32i32-20000-22−2i32i30000000000000000000000−222200−i6i6−i6i62−22−2000000000000000000
χ654-44-4004-4-20022i3−2i32i3−2i32-20000-222i3−2i3000000000000000000000022−2200−i6i6−i6i6−22−22000000000000000000
χ664-44-4004-4-20022i3−2i32i3−2i32-20000-222i3−2i30000000000000000000000−222200i6−i6i6−i62−22−2000000000000000000
χ674-44-400-44400-40000-440000-44000000000000000000000022−22000022−22−22220000000000000000000000
χ684-44-400-44400-40000-440000-440000000000000000000000−22220000−222222−220000000000000000000000
χ694-44-400-44-2002−2i32i3−2i32i32-200002-22i3−2i30000000000000000000022−220000−222−2i6−i6−i6i6000000000000000000
χ704-44-400-44-2002−2i32i3−2i32i32-200002-22i3−2i300000000000000000000−222200002−2−22−i6i6i6−i6000000000000000000
χ714-44-400-44-20022i3−2i32i3−2i32-200002-2−2i32i30000000000000000000022−220000−222−2−i6i6i6−i6000000000000000000
χ724-44-400-44-20022i3−2i32i3−2i32-200002-2−2i32i300000000000000000000−222200002−2−22i6−i6−i6i6000000000000000000
χ734-4-444-40040044-4-44-4-40000000000000000000000000000000000000000000000000000002-22-200
χ744-4-444-40040044-4-44-4-4000000000000000000000000000000000000000000000000000000-22-2200
χ754-4-44-44004004-444-4-4-40000000000000000000000000000000000000000000000000000002-2-2200
χ764-4-44-44004004-444-4-4-4000000000000000000000000000000000000000000000000000000-222-200
χ778-8-888-800-400-4-444-444000000000000000000000000000000000000000000000000000000000000
χ788-8-88-8800-400-44-4-4444000000000000000000000000000000000000000000000000000000000000

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