Finite Group Databasebeta

← Group #10592878

Character table — Group #10592878

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222222222222222222224444444444444444444444444888888888888888888363636367272
order12233334466666666666688812121212121212122424242424242424242424242424242444121212121212121212121212121212121616161624
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ511-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-11-1
χ611-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-11
χ711-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-11
χ811-11111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111-1
χ9222222222222222222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ102222222-2-2222222222222000-2-2-2-2-2-2-2-200000000000000000000000000000000002−22−200
χ112222222-2-2222222222222000-2-2-2-2-2-2-2-20000000000000000000000000000000000−22−2200
χ122222-1-1-12222-1-1-1-1-1-12-1-1-12222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-1000000
χ132222-1-1-12222-1-1-1-1-1-12-1-1-12222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-2111111000000
χ142222-1-1-12222-1-1-1-1-1-12-1-1-1-2-2-22-1-1-12-1-1-1-2-2111111-2-21111110000−i3−i3−i3i3i3i300−i3−i3−i3i3i3i3000000
χ152222-1-1-12222-1-1-1-1-1-12-1-1-1-2-2-22-1-1-12-1-1-1-2-2111111-2-21111110000i3i3i3−i3−i3−i300i3i3i3−i3−i3−i3000000
χ16222-12-1-122-1-122-1-1-1-1-12-1-1222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-12-1-12-1-1-1-12-1-12-1-1000000
χ17222-12-1-122-1-122-1-1-1-1-12-1-1222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-211-211-21111-211-211000000
χ18222-12-1-122-1-122-1-1-1-1-12-1-1-2-2-2-12-1-1-12-1-111-2-2111111-2-2111100−i3i30−i3i30−i3i3−i3i30−i3i30−i3i3000000
χ19222-12-1-122-1-122-1-1-1-1-12-1-1-2-2-2-12-1-1-12-1-111-2-2111111-2-2111100i3−i30i3−i30i3−i3i3−i30i3−i30i3−i3000000
χ20222-1-12-122-1-1-1-122-1-1-1-12-1222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-12-1-1-12-1-1-12-1-1-12000000
χ21222-1-12-122-1-1-1-122-1-1-1-12-1222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-2-2111-2111-2111-2111-2000000
χ22222-1-12-122-1-1-1-122-1-1-1-12-1-2-2-2-1-12-1-1-12-11111-2-2111111-2-21100−i3i3i30−i3−i3i30−i3i3i30−i3−i3i30000000
χ23222-1-12-122-1-1-1-122-1-1-1-12-1-2-2-2-1-12-1-1-12-11111-2-2111111-2-21100i3−i3−i30i3i3−i30i3−i3−i30i3i3−i30000000
χ24222-1-1-1222-1-1-1-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-12-12-1-1-1-1-12-12-1000000
χ25222-1-1-1222-1-1-1-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-2-21111-21-211111-21-21000000
χ26222-1-1-1222-1-1-1-1-1-122-1-1-12-2-2-2-1-1-12-1-1-12111111-2-2111111-2-200−i3i3−i3i30i30−i3−i3i3−i3i30i30−i3000000
χ27222-1-1-1222-1-1-1-1-1-122-1-1-12-2-2-2-1-1-12-1-1-12111111-2-2111111-2-200i3−i3i3−i30−i30i3i3−i3i3−i30−i30i3000000
χ2822-222222-2-2-2-2-2-2-2-2-222220002222-2-2-2-200000000000000000000000000000000002−2−2200
χ2922-222222-2-2-2-2-2-2-2-2-222220002222-2-2-2-20000000000000000000000000000000000−222−200
χ3022-22222-22-2-2-2-2-2-2-2-22222-2-22-2-2-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ3122-22-1-1-1-22-2-21111112-1-1-122-2-21112-1-1-122-1-1-1-1-1-1-2-21111112-222-1-1-1-1-1-1-2-2111111000000
χ3222-22-1-1-1-22-2-21111112-1-1-122-2-21112-1-1-122-1-1-1-1-1-1-2-2111111-22-2-211111122-1-1-1-1-1-1000000
χ3322-22-1-1-1-22-2-21111112-1-1-1-2-22-21112-1-1-1-2-211111122-1-1-1-1-1-10000−i3−i3−i3i3i3i300i3i3i3−i3−i3−i3000000
χ3422-22-1-1-1-22-2-21111112-1-1-1-2-22-21112-1-1-1-2-211111122-1-1-1-1-1-10000i3i3i3−i3−i3−i300−i3−i3−i3i3i3i3000000
χ3522-2-12-1-1-2211-2-21111-12-1-122-21-211-12-1-1-1-122-1-1-1-111-2-211112-2-1-12-1-12-1-111-211-211000000
χ3622-2-12-1-1-2211-2-21111-12-1-122-21-211-12-1-1-1-122-1-1-1-111-2-21111-2211-211-211-1-12-1-12-1-1000000
χ3722-2-12-1-1-2211-2-21111-12-1-1-2-221-211-12-1-111-2-21111-1-122-1-1-1-100−i3i30−i3i30−i3i3i3−i30i3−i30i3−i3000000
χ3822-2-12-1-1-2211-2-21111-12-1-1-2-221-211-12-1-111-2-21111-1-122-1-1-1-100i3−i30i3−i30i3−i3−i3i30−i3i30−i3i3000000
χ3922-2-1-12-1-221111-2-211-1-12-122-211-21-1-12-1-1-1-1-122-1-11111-2-2112-2-1-1-12-1-1-12111-2111-2000000
χ4022-2-1-12-1-221111-2-211-1-12-122-211-21-1-12-1-1-1-1-122-1-11111-2-211-22111-2111-2-1-1-12-1-1-12000000
χ4122-2-1-12-1-221111-2-211-1-12-1-2-2211-21-1-12-11111-2-211-1-1-1-122-1-100−i3i3i30−i3−i3i30i3−i3−i30i3i3−i30000000
χ4222-2-1-12-1-221111-2-211-1-12-1-2-2211-21-1-12-11111-2-211-1-1-1-122-1-100i3−i3−i30i3i3−i30−i3i3i30−i3−i3i30000000
χ4322-2-1-1-12-22111111-2-2-1-1-1222-2111-2-1-1-12-1-1-1-1-1-122111111-2-22-2-1-1-1-12-12-11111-21-21000000
χ4422-2-1-1-12-22111111-2-2-1-1-1222-2111-2-1-1-12-1-1-1-1-1-122111111-2-2-221111-21-21-1-1-1-12-12-1000000
χ4522-2-1-1-12-22111111-2-2-1-1-12-2-22111-2-1-1-12111111-2-2-1-1-1-1-1-12200−i3i3−i3i30i30−i3i3−i3i3−i30−i30i3000000
χ4622-2-1-1-12-22111111-2-2-1-1-12-2-22111-2-1-1-12111111-2-2-1-1-1-1-1-12200i3−i3i3−i30−i30i3−i3i3−i3i30i30−i3000000
χ474444-2-2-2-4-444-2-2-2-2-2-24-2-2-2000-4222-42220000000000000000000000000000000000000000
χ48444-24-2-2-4-4-2-244-2-2-2-2-24-2-20002-4222-4220000000000000000000000000000000000000000
χ49444-2-24-2-4-4-2-2-2-244-2-2-2-24-200022-4222-420000000000000000000000000000000000000000
χ50444-2-2-24-4-4-2-2-2-2-2-244-2-2-24000222-4222-40000000000000000000000000000000000000000
χ5144-44-2-2-24-4-4-42222224-2-2-20004-2-2-2-42220000000000000000000000000000000000000000
χ5244-4-24-2-24-422-4-42222-24-2-2000-24-2-22-4220000000000000000000000000000000000000000
χ5344-4-2-24-24-42222-4-422-2-24-2000-2-24-222-420000000000000000000000000000000000000000
χ5444-4-2-2-244-4222222-4-4-2-2-24000-2-2-24222-40000000000000000000000000000000000000000
χ554-4044440000000000-4-4-4-422−2200000000022−2222−2222−2222−2200000000000000000000000000000000
χ564-4044440000000000-4-4-4-4−2222000000000−2222−2222−2222−222200000000000000000000000000000000
χ574-404-2-2-20000−2i32i3−2i32i3−2i32i3-422222−2200000000022−22−22−22−2200i6−i6i6−i6i6−i6000000000000000000000000
χ584-404-2-2-20000−2i32i3−2i32i3−2i32i3-4222−2222000000000−22222−22−22−200−i6i6−i6i6−i6i6000000000000000000000000
χ594-404-2-2-200002i3−2i32i3−2i32i3−2i3-422222−2200000000022−22−22−22−2200−i6i6−i6i6−i6i6000000000000000000000000
χ604-404-2-2-200002i3−2i32i3−2i32i3−2i3-4222−2222000000000−22222−22−22−200i6−i6i6−i6i6−i6000000000000000000000000
χ614-40-24-2-200−2i32i300−2i32i32i3−2i32-42222−22000000000−2222−22−22−22i6−i600i6−i6−i6i6000000000000000000000000
χ624-40-24-2-200−2i32i300−2i32i32i3−2i32-422−22220000000002−2−22222−22−2−i6i600−i6i6i6−i6000000000000000000000000
χ634-40-24-2-2002i3−2i3002i3−2i3−2i32i32-42222−22000000000−2222−22−22−22−i6i600−i6i6i6−i6000000000000000000000000
χ644-40-24-2-2002i3−2i3002i3−2i3−2i32i32-422−22220000000002−2−22222−22−2i6−i600i6−i6−i6i6000000000000000000000000
χ654-40-2-24-200−2i32i32i3−2i300−2i32i322-4222−22000000000−22−2222−22−22i6−i6−i6i600i6−i6000000000000000000000000
χ664-40-2-24-200−2i32i32i3−2i300−2i32i322-42−22220000000002−22−2−22222−2−i6i6i6−i600−i6i6000000000000000000000000
χ674-40-2-24-2002i3−2i3−2i32i3002i3−2i322-4222−22000000000−22−2222−22−22−i6i6i6−i600−i6i6000000000000000000000000
χ684-40-2-24-2002i3−2i3−2i32i3002i3−2i322-42−22220000000002−22−2−22222−2i6−i6−i6i600i6−i6000000000000000000000000
χ694-40-2-2-2400−2i32i3−2i32i32i3−2i300222-422−22000000000−22−22−2222−22i6−i6i6−i6−i6i600000000000000000000000000
χ704-40-2-2-2400−2i32i3−2i32i32i3−2i300222-4−22220000000002−22−22−2−2222−i6i6−i6i6i6−i600000000000000000000000000
χ714-40-2-2-24002i3−2i32i3−2i3−2i32i300222-422−22000000000−22−22−2222−22−i6i6−i6i6i6−i600000000000000000000000000
χ724-40-2-2-24002i3−2i32i3−2i3−2i32i300222-4−22220000000002−22−22−2−2222i6−i6i6−i6−i6i600000000000000000000000000

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