Finite Group Databasebeta

← Group #10592740

Character table — Group #10592740

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222222222222222222222244444444444444444444444488888888888888888818181818181818187272
order122222333344446666666666666666666612121212121212121212121212121212246666666612121212121212128888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-111111-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1
χ61111-1-111111-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11
χ71111-1-111111-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ81111-1-111111-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111-1
χ92222222222-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222-1-1-122222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-10000000000
χ112222222-1-1-122222-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2111111-2-21111110000000000
χ122222222-1-1-1-2-2-2-22-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-21111110000−i3−i3−i3i3i3i300−i3−i3−i3i3i3i30000000000
χ132222222-1-1-1-2-2-2-22-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-21111110000i3i3i3−i3−i3−i300i3i3i3−i3−i3−i30000000000
χ14222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-12-1-12-1-1-1-12-1-12-1-10000000000
χ15222222-12-1-12222-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-211-211-21111-211-2110000000000
χ16222222-12-1-1-2-2-2-2-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111100−i3i30−i3i30−i3i3−i3i30−i3i30−i3i30000000000
χ17222222-12-1-1-2-2-2-2-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111100i3−i30i3−i30i3−i3i3−i30i3−i30i3−i30000000000
χ18222222-1-12-12222-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-12-1-1-12-1-1-12-1-1-120000000000
χ19222222-1-12-12222-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-2-2111-2111-2111-2111-20000000000
χ20222222-1-12-1-2-2-2-2-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-21100−i3i3i30−i3−i3i30−i3i3i30−i3−i3i300000000000
χ21222222-1-12-1-2-2-2-2-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-21100i3−i3−i30i3i3−i30i3−i3−i30i3i3−i300000000000
χ22222222-1-1-122222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-12-12-1-1-1-1-12-12-10000000000
χ23222222-1-1-122222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2-21111-21-211111-21-210000000000
χ24222222-1-1-12-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-200−i3i3−i3i30i30−i3−i3i3−i3i30i30−i30000000000
χ25222222-1-1-12-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-200i3−i3i3−i30−i30i3i3−i3i3−i30−i30i30000000000
χ262222-2-22222-222-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ272222-2-22-1-1-12-2-222-1-1-122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-21111112-222-1-1-1-1-1-1-2-21111110000000000
χ282222-2-22-1-1-12-2-222-1-1-122-1-1-1-1-1-1-2-211111122-1-1-1-1-1-1-2-2111111-22-2-211111122-1-1-1-1-1-10000000000
χ292222-2-22-1-1-1-222-22-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-10000−i3−i3−i3i3i3i300i3i3i3−i3−i3−i30000000000
χ302222-2-22-1-1-1-222-22-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-10000i3i3i3−i3−i3−i300−i3−i3−i3i3i3i30000000000
χ312222-2-2-12-1-12-2-22-12-1-1-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-211112-2-1-12-1-12-1-111-211-2110000000000
χ322222-2-2-12-1-12-2-22-12-1-1-1-122-1-1-1-111-2-21111-1-122-1-1-1-111-2-21111-2211-211-211-1-12-1-12-1-10000000000
χ332222-2-2-12-1-1-222-2-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-100−i3i30−i3i30−i3i3i3−i30i3−i30i3−i30000000000
χ342222-2-2-12-1-1-222-2-12-1-1-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-100i3−i30i3−i30i3−i3−i3i30−i3i30−i3i30000000000
χ352222-2-2-1-12-12-2-22-1-12-1-1-1-1-122-1-11111-2-211-1-1-1-122-1-11111-2-2112-2-1-1-12-1-1-12111-2111-20000000000
χ362222-2-2-1-12-12-2-22-1-12-1-1-1-1-122-1-11111-2-211-1-1-1-122-1-11111-2-211-22111-2111-2-1-1-12-1-1-120000000000
χ372222-2-2-1-12-1-222-2-1-12-1-1-1-1-122-1-11111-2-2111111-2-211-1-1-1-122-1-100−i3i3i30−i3−i3i30i3−i3−i30i3i3−i300000000000
χ382222-2-2-1-12-1-222-2-1-12-1-1-1-1-122-1-11111-2-2111111-2-211-1-1-1-122-1-100i3−i3−i30i3i3−i30−i3i3i30−i3−i3i300000000000
χ392222-2-2-1-1-122-2-22-1-1-12-1-1-1-1-1-122111111-2-2-1-1-1-1-1-122111111-2-22-2-1-1-1-12-12-11111-21-210000000000
χ402222-2-2-1-1-122-2-22-1-1-12-1-1-1-1-1-122111111-2-2-1-1-1-1-1-122111111-2-2-221111-21-21-1-1-1-12-12-10000000000
χ412222-2-2-1-1-12-222-2-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2-1-1-1-1-1-12200−i3i3−i3i30i30−i3i3−i3i3−i30−i30i30000000000
χ422222-2-2-1-1-12-222-2-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2-1-1-1-1-1-12200i3−i3i3−i30−i30i3−i3i3−i3i30i30−i30000000000
χ4322-2-22-222220000-2-2-2-22-22-22-22-22-22-22-22-20000000000000000000000000000000000−i2−i2i2i2−i2−i2i2i200
χ4422-2-22-222220000-2-2-2-22-22-22-22-22-22-22-22-20000000000000000000000000000000000i2i2−i2−i2i2i2−i2−i200
χ4522-2-2-2222220000-2-2-2-22-22-22-22-2-22-22-22-220000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i200
χ4622-2-2-2222220000-2-2-2-22-22-22-22-2-22-22-22-220000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i200
χ472-22-200222202i−2i02222-2-2-2-2-2-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000002−22−2−i2i2−i2i200
χ482-22-200222202i−2i02222-2-2-2-2-2-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000−22−22i2−i2i2−i200
χ492-22-20022220−2i2i02222-2-2-2-2-2-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000002−22−2i2−i2i2−i200
χ502-22-20022220−2i2i02222-2-2-2-2-2-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000−22−22−i2i2−i2i200
χ512-2-22002222200-2-2-2-2-2-22-22-22-22000000002-22-22-22-2000000000000000000000000002i−2i−2i2i000000
χ522-2-22002222200-2-2-2-2-2-22-22-22-22000000002-22-22-22-200000000000000000000000000−2i2i2i−2i000000
χ532-2-22002222-2002-2-2-2-2-22-22-22-2200000000-22-22-22-220000000000000000000000000000002-2-2200
χ542-2-22002222-2002-2-2-2-2-22-22-22-2200000000-22-22-22-22000000000000000000000000000000-222-200
χ5544-4-44-44-2-2-20000-42224-4-22-22-224-4-22-22-2200000000000000000000000000000000000000000000
χ5644-4-44-4-24-2-200002-422-224-4-22-22-224-4-22-2200000000000000000000000000000000000000000000
χ5744-4-44-4-2-24-2000022-42-22-224-4-22-22-224-4-2200000000000000000000000000000000000000000000
χ5844-4-44-4-2-2-240000222-4-22-22-224-4-22-22-224-400000000000000000000000000000000000000000000
χ5944-4-4-444-2-2-20000-42224-4-22-22-22-442-22-22-200000000000000000000000000000000000000000000
χ6044-4-4-44-24-2-200002-422-224-4-22-222-2-442-22-200000000000000000000000000000000000000000000
χ6144-4-4-44-2-24-2000022-42-22-224-4-222-22-2-442-200000000000000000000000000000000000000000000
χ6244-4-4-44-2-2-240000222-4-22-22-224-42-22-22-2-4400000000000000000000000000000000000000000000
χ634-44-4004-2-2-204i−4i04-2-2-2-4-422222200000000000000004i−4i−2i2i−2i2i−2i2i0000000000000000000000000000
χ644-44-4004-2-2-20−4i4i04-2-2-2-4-42222220000000000000000−4i4i2i−2i2i−2i2i−2i0000000000000000000000000000
χ654-44-400-24-2-204i−4i0-24-2-222-4-422220000000000000000−2i2i4i−4i−2i2i−2i2i0000000000000000000000000000
χ664-44-400-24-2-20−4i4i0-24-2-222-4-4222200000000000000002i−2i−4i4i2i−2i2i−2i0000000000000000000000000000
χ674-44-400-2-24-204i−4i0-2-24-22222-4-4220000000000000000−2i2i−2i2i4i−4i−2i2i0000000000000000000000000000
χ684-44-400-2-24-20−4i4i0-2-24-22222-4-42200000000000000002i−2i2i−2i−4i4i2i−2i0000000000000000000000000000
χ694-44-400-2-2-2404i−4i0-2-2-24222222-4-40000000000000000−2i2i−2i2i−2i2i4i−4i0000000000000000000000000000
χ704-44-400-2-2-240−4i4i0-2-2-24222222-4-400000000000000002i−2i2i−2i2i−2i−4i4i0000000000000000000000000000
χ714-4-44004-2-2-2400-4-4222-442-22-22-2000000004-4-22-22-22000000000000000000000000000000000000
χ724-4-44004-2-2-2-4004-4222-442-22-22-200000000-442-22-22-2000000000000000000000000000000000000
χ734-4-4400-24-2-2400-42-4222-2-442-22-200000000-224-4-22-22000000000000000000000000000000000000
χ744-4-4400-24-2-2-40042-4222-2-442-22-2000000002-2-442-22-2000000000000000000000000000000000000
χ754-4-4400-2-24-2400-422-422-22-2-442-200000000-22-224-4-22000000000000000000000000000000000000
χ764-4-4400-2-24-2-400422-422-22-2-442-2000000002-22-2-442-2000000000000000000000000000000000000
χ774-4-4400-2-2-24400-4222-42-22-22-2-4400000000-22-22-224-4000000000000000000000000000000000000
χ784-4-4400-2-2-24-4004222-42-22-22-2-44000000002-22-22-2-44000000000000000000000000000000000000

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