Finite Group Databasebeta

← Group #10830663

Character table — Group #10830663

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12222222344444444666666622224412121212121212124466668888121212121212242424242424242422448888888844121212122224444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111
χ5111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ7111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1111-1-111
χ8111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-111-1-1
χ9111111111-1-1-1-1111111111111111-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-111-1-1-111111-1-1-1-1
χ10111111111-1-1-1-1111111111111111-1-1111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-111-1-11-1-1-1-1-11111
χ11111111111-1-1-1-1111111111111111-1-1111-1-1-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-111-111-1-11-1-111
χ12111111111-1-1-1-1111111111111111-1-1111-1-1-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-11-1-1111-1-111-111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-1-1-1-111111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-11-1-11111111-1-1-1-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111111-111-1-1-1-1-111111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1111111-1-1-1-11-111-1-1111-1-1-1-1-111
χ172222222222222-2-2-2-222222220000-2-2-2-2-22222-20000000000-2-2000000000000222200000000000000-20000-20000
χ182222222222222-2-2-2-222222220000-2-2-2-2-22222-20000000000-2-2000000000000-2-2-2-2000000000000002000020000
χ19222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-200000000002200000000000022-2-20000000000000020000-20000
χ20222222222-2-2-2-2-2-2-2-22222222000022-2-2-2-2-2-2-2-2000000000022000000000000-2-22200000000000000-2000020000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-111111111111100000000000022-1-1-1-10000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-1-1-1-122-2-2111111-1-1-1-111110000000000002-2-1-1110000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-12222-2-2-1-1-11111-1-2-2-1-1-1-1-2-2221111111111-1-1-1-1000000000000-2211-1-10000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-122111122-2-211-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1-11111-1221111-2-22211-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ29222-2-2-2-22200002-22-2222-2-2-2-222-2-20022-20000-20022-2-200000000000000000000002i2i−2i−2i00000000000002i−2i00000
χ30222-2-2-2-22200002-22-2222-2-2-2-222-2-20022-20000-20022-2-20000000000000000000000−2i−2i2i2i0000000000000−2i2i00000
χ31222-2-2-2-22200002-22-2222-2-2-2-2-2-2220022-20000-200-2-22200000000000000000000002i2i−2i−2i0000000000000−2i2i00000
χ32222-2-2-2-22200002-22-2222-2-2-2-2-2-2220022-20000-200-2-2220000000000000000000000−2i−2i2i2i00000000000002i−2i00000
χ3322-22-2-22-222i2i−2i−2i00002-2-222-2-20000000002i2i−2i−2i00000002−2−i2i200000022−2−2−i2−i2i2i22-22i−2i2−22−2−i2−i2i2i20000000000000000
χ3422-22-2-22-222i2i−2i−2i00002-2-222-2-20000000002i2i−2i−2i00000002−2−i2i200000022−2−2−i2−i2i2i2-22−2i2i−22−22i2i2−i2−i20000000000000000
χ3522-22-2-22-222i2i−2i−2i00002-2-222-2-20000000002i2i−2i−2i0000000−22i2−i2000000−2−222i2i2−i2−i22-22i−2i−22−22i2i2−i2−i20000000000000000
χ3622-22-2-22-222i2i−2i−2i00002-2-222-2-20000000002i2i−2i−2i0000000−22i2−i2000000−2−222i2i2−i2−i2-22−2i2i2−22−2−i2−i2i2i20000000000000000
χ3722-22-2-22-22−2i−2i2i2i00002-2-222-2-2000000000−2i−2i2i2i00000002−2i2−i200000022−2−2i2i2−i2−i22-2−2i2i2−22−2i2i2−i2−i20000000000000000
χ3822-22-2-22-22−2i−2i2i2i00002-2-222-2-2000000000−2i−2i2i2i00000002−2i2−i200000022−2−2i2i2−i2−i2-222i−2i−22−22−i2−i2i2i20000000000000000
χ3922-22-2-22-22−2i−2i2i2i00002-2-222-2-2000000000−2i−2i2i2i0000000−22−i2i2000000−2−222−i2−i2i2i22-2−2i2i−22−22−i2−i2i2i20000000000000000
χ4022-22-2-22-22−2i−2i2i2i00002-2-222-2-2000000000−2i−2i2i2i0000000−22−i2i2000000−2−222−i2−i2i2i2-222i−2i2−22−2i2i2−i2−i20000000000000000
χ412-2-222-2-2220000-222-2-2-22-222-22-22-2002-2-200002002-22-2000000000000000000000000002-22-2000000000000002-2
χ422-2-222-2-2220000-222-2-2-22-222-22-22-2002-2-200002002-22-200000000000000000000000000-22-2200000000000000-22
χ432-2-222-2-2220000-222-2-2-22-222-2-22-22002-2-20000200-22-22000000000000000000000000002-22-200000000000000-22
χ442-2-222-2-2220000-222-2-2-22-222-2-22-22002-2-20000200-22-2200000000000000000000000000-22-22000000000000002-2
χ452-2-2-2-222222-22-222-2-2-2-222-2-2200002-2-22-22-22-2200000000002-200000000000000000000000000000002-20002-200
χ462-2-2-2-222222-22-222-2-2-2-222-2-2200002-2-22-22-22-2200000000002-20000000000000000000000000000000-22000-2200
χ472-2-2-2-222222-22-2-2-222-2-222-2-222-2-22-222-222-22-2-22-22-2-220000-2222-2-2000000000000000000000000000000000000
χ482-2-2-2-222222-22-2-2-222-2-222-2-22-222-2-222-222-22-2-2-22-222-20000-22-2-222000000000000000000000000000000000000
χ492-2-2-2-22222-22-2222-2-2-2-222-2-220000-22-22-2-22-2220000000000-2200000000000000000000000000000002-2000-2200
χ502-2-2-2-22222-22-2222-2-2-2-222-2-220000-22-22-2-22-2220000000000-220000000000000000000000000000000-220002-200
χ512-2-2-2-22222-22-22-2-222-2-222-2-222-2-222-22-22-22-22-2-222-2-2200002-2-2-222000000000000000000000000000000000000
χ522-2-2-2-22222-22-22-2-222-2-222-2-22-222-22-22-22-22-22-22-2-222-200002-222-2-2000000000000000000000000000000000000
χ532-2-2-2-2222-12-22-2-2-22211-1-111-12-2-22-22-11-1-11-1112-2-111-100001-1-1-1113−33−33−33−3000000000000003−33−30000000000
χ542-2-2-2-2222-12-22-2-2-22211-1-111-12-2-22-22-11-1-11-1112-2-111-100001-1-1-111−33−33−33−3300000000000000−33−330000000000
χ552-2-2-2-2222-12-22-2-2-22211-1-111-1-222-2-22-11-1-11-111-221-1-1100001-111-1-13−33−33−33−300000000000000−33−330000000000
χ562-2-2-2-2222-12-22-2-2-22211-1-111-1-222-2-22-11-1-11-111-221-1-1100001-111-1-1−33−33−33−33000000000000003−33−30000000000
χ572-2-2-2-2222-1-22-22-2-22211-1-111-12-2-222-2-11-11-11-11-22-111-10000-1111-1-13−33−3−33−33000000000000003−3−330000000000
χ582-2-2-2-2222-1-22-22-2-22211-1-111-12-2-222-2-11-11-11-11-22-111-10000-1111-1-1−33−333−33−300000000000000−333−30000000000
χ592-2-2-2-2222-1-22-22-2-22211-1-111-1-222-22-2-11-11-11-112-21-1-110000-11-1-1113−33−3−33−3300000000000000−333−30000000000
χ602-2-2-2-2222-1-22-22-2-22211-1-111-1-222-22-2-11-11-11-112-21-1-110000-11-1-111−33−333−33−3000000000000003−3−330000000000
χ6144444444-24444-4-4-4-4-2-2-2-2-2-2-20000-4-4222-2-2-2-220000000000220000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2000044222222220000000000-2-20000000000000000000000000000000000000000
χ63444-4-4-4-4440000-44-44444-4-4-4-4000000-4-44000040000000000000000000000000000000000000000000000000000
χ64444-4-4-4-44-200004-44-4-2-2-2222244-4-400-2-220000200-2-2220000000000000000000000000000000000000000000000
χ65444-4-4-4-44-200004-44-4-2-2-22222-4-44400-2-22000020022-2-20000000000000000000000000000000000000000000000
χ66444-4-4-4-44-20000-44-44-2-2-2222200000022-20000-200000000000023−2323−23000000000000000000000000000000000000
χ67444-4-4-4-44-20000-44-44-2-2-2222200000022-20000-2000000000000−2323−2323000000000000000000000000000000000000
χ6844-44-4-44-4-24i4i−4i−4i0000-222-2-222000000000−2i−2i2i2i000000022−22−2i22i2000000−2−222i2i2−i2−i20000000000000000000000000000
χ6944-44-4-44-4-24i4i−4i−4i0000-222-2-222000000000−2i−2i2i2i0000000−22222i2−2i200000022−2−2−i2−i2i2i20000000000000000000000000000
χ7044-44-4-44-4-2−4i−4i4i4i0000-222-2-2220000000002i2i−2i−2i000000022−222i2−2i2000000−2−222−i2−i2i2i20000000000000000000000000000
χ7144-44-4-44-4-2−4i−4i4i4i0000-222-2-2220000000002i2i−2i−2i0000000−2222−2i22i200000022−2−2i2i2−i2−i20000000000000000000000000000
χ7244-4-444-4-44000000004-4-4-4-444000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ7344-4-444-4-44000000004-4-4-4-4440000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ744-444-44-4-4400000000-44-4-44-440000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ754-444-44-4-4400000000-44-4-44-4400000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ764-44-44-44-444i−4i−4i4i0000-44-44-44-40000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000
χ774-44-44-44-44−4i4i4i−4i0000-44-44-44-4000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000
χ784-44-44-44-4-24i−4i−4i4i00002-22-22-22000000000−2i2i2i−2i000000000000000006−6−66−i6i6i6−i60000000000000000000000000000
χ794-44-44-44-4-24i−4i−4i4i00002-22-22-22000000000−2i2i2i−2i00000000000000000−666−6i6−i6−i6i60000000000000000000000000000
χ804-44-44-44-4-2−4i4i4i−4i00002-22-22-220000000002i−2i−2i2i000000000000000006−6−66i6−i6−i6i60000000000000000000000000000
χ814-44-44-44-4-2−4i4i4i−4i00002-22-22-220000000002i−2i−2i2i00000000000000000−666−6−i6i6i6−i60000000000000000000000000000
χ824-4-444-4-44400004-4-44-4-44-444-4000000-4440000-40000000000000000000000000000000000000000000000000000
χ834-4-444-4-44-200004-4-4422-22-2-220000002-2-20000200000000000023−23−2323000000000000000000000000000000000000
χ844-4-444-4-44-200004-4-4422-22-2-220000002-2-200002000000000000−232323−23000000000000000000000000000000000000
χ854-4-444-4-44-20000-444-422-22-2-224-44-400-2220000-200-22-220000000000000000000000000000000000000000000000
χ864-4-444-4-44-20000-444-422-22-2-22-44-4400-2220000-2002-22-20000000000000000000000000000000000000000000000
χ874-4-4-4-4444-24-44-444-4-422-2-222-200004-42-22-22-22-20000000000-220000000000000000000000000000000000000000
χ884-4-4-4-4444-2-44-4444-4-422-2-222-20000-442-222-22-2-200000000002-20000000000000000000000000000000000000000
χ8988-8-888-8-8-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000
χ908-888-88-8-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000

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