Finite Group Databasebeta

← Group #10772489

Character table — Group #10772489

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222234444444466644661212121212121212444488881212242424242424242422448888888888121212122424242422444424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-11-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1111-11-1-1
χ91111-1-11-1-11-1-1111111-11-1-1-1-11-1-111111-1-111-1-11-11111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-1-111-11-11-1
χ101111-1-11-1-11-1-1111111-11-1-1-1-11-1-111111-1-111-1-11-11111-1-1-1-1-1-111-1-1-1-111111-111-1-111-1-11-1-11-11-11
χ111111-1-11-1-11-1-1111111-11-1-1-1-11-1-111111-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-11111-1111-1-1-1-111-111-11-1-11
χ121111-1-11-1-11-1-1111111-11-1-1-1-11-1-111111-1-1-1-1111-1-1-1-1-11111-1-1111111-1-1-1-1-1111-1-1-1-1111-1-11-111-1
χ131111-1-11-1-11-1-1111111-11-1-1-1-11-1-1111-1-11111-1-11-11111-1-1-1-111-1-11111-1-1-1-1-11-1-111-1-111-1-1-1111-11
χ141111-1-11-1-11-1-1111111-11-1-1-1-11-1-1111-1-11111-1-11-11111-1-1-1-1-1-111-1-1-1-11111-11-1-111-1-111111-1-1-11-1
χ151111-1-11-1-11-1-1111111-11-1-1-1-11-1-1111-1-111-1-1111-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-11111-1-1-1-1-11111-1
χ161111-1-11-1-11-1-1111111-11-1-1-1-11-1-1111-1-111-1-1111-1-1-1-1-11111-1-1111111-1-1-1-11-1-1-11111-1-1111-1-1-1-11
χ17222222222-2-2-2-2-2-2222-222222-2-2-2-2-2-22-22-200002-200000000000000000000002-22-2000000000000
χ18222222222-2-2-2-2-2-2222-222222-2-2-2-2-2-2-22-2200002-20000000000000000000000-22-22000000000000
χ192222222-2-2222-2-22222-2-222-2-2222-2-2200000000-2-200000000000000000000000000000002-220-200
χ202222222-2-2222-2-22222-2-222-2-2222-2-2200000000-2-20000000000000000000000000000000-22-20200
χ212222222-2-2-2-2-222-22222-222-2-2-2-2-222-200000000-220000000022-2-20000000000000000002000-2000
χ222222222-2-2-2-2-222-22222-222-2-2-2-2-222-200000000-2200000000-2-222000000000000000000-20002000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-1-1-1-1111100000000
χ25222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ26222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000221111-1-1-1-100000000
χ27222222-122-2-2-2-2-2-2-1-1-1-22-1-1-1-11111112-22-20000-1133−3−333−3−300000000000000-11-113−33−300000000
χ28222222-122-2-2-2-2-2-2-1-1-1-22-1-1-1-11111112-22-20000-11−3−333−3−33300000000000000-11-11−33−3300000000
χ29222222-122-2-2-2-2-2-2-1-1-1-22-1-1-1-1111111-22-220000-1133−3−333−3−3000000000000001-11-1−33−3300000000
χ30222222-122-2-2-2-2-2-2-1-1-1-22-1-1-1-1111111-22-220000-11−3−333−3−333000000000000001-11-13−33−300000000
χ312222-2-22222-2-2-2-222222-2-2-2222-2-2-2-2200000000-2200000000000000000000000000000002-2-20200
χ322222-2-22222-2-2-2-222222-2-2-2222-2-2-2-2200000000-220000000000000000000000000000000-2220-200
χ332222-2-2222-22222-2222-2-2-2-222-22222-200000000-2-2000000002222000000000000000000-2000-2000
χ342222-2-2222-22222-2222-2-2-2-222-22222-200000000-2-200000000-2-2-2-200000000000000000020002000
χ352222-2-22-2-2-222-2-2-222222-2-2-2-2-222-2-2-22-2-2200002200000000000000000000002-2-22000000000000
χ362222-2-22-2-2-222-2-2-222222-2-2-2-2-222-2-2-2-222-20000220000000000000000000000-222-2000000000000
χ372222-2-2-1-2-22-2-2222-1-1-1-221111-111-1-1-122-2-222-2-2-11-1-1-1-111110000000000002-2-1-111-1-11100000000
χ382222-2-2-1-2-22-2-2222-1-1-1-221111-111-1-1-122-2-2-2-222-111111-1-1-1-1000000000000-22-1-11111-1-100000000
χ392222-2-2-1-2-22-2-2222-1-1-1-221111-111-1-1-1-2-22222-2-2-11-1-1-1-11111000000000000-2211-1-111-1-100000000
χ402222-2-2-1-2-22-2-2222-1-1-1-221111-111-1-1-1-2-222-2-222-111111-1-1-1-10000000000002-211-1-1-1-11100000000
χ412222-2-2-1-2-2-222-2-2-2-1-1-12211111-1-11112-2-220000-1-133−3−3−3−33300000000000000-111-13−3−3300000000
χ422222-2-2-1-2-2-222-2-2-2-1-1-12211111-1-11112-2-220000-1-1−3−33333−3−300000000000000-111-1−333−300000000
χ432222-2-2-1-2-2-222-2-2-2-1-1-12211111-1-1111-222-20000-1-133−3−3−3−333000000000000001-1-11−333−300000000
χ442222-2-2-1-2-2-222-2-2-2-1-1-12211111-1-1111-222-20000-1-1−3−33333−3−3000000000000001-1-113−3−3300000000
χ4522-2-20022i−2i02i−2i2-20-22-200002i−2i02i−2i2-2000002−2−i2i2002−22−2−i2i2−i2i22-22i−2i22−2−2−i2−i2i2i2000000000000000000
χ4622-2-20022i−2i02i−2i2-20-22-200002i−2i02i−2i2-2000002−2−i2i2002−22−2−i2i2−i2i2-22−2i2i−2−222i2i2−i2−i2000000000000000000
χ4722-2-20022i−2i02i−2i2-20-22-200002i−2i02i−2i2-200000−22i2−i200−22−22i2−i2i2−i22-22i−2i−2−222i2i2−i2−i2000000000000000000
χ4822-2-20022i−2i02i−2i2-20-22-200002i−2i02i−2i2-200000−22i2−i200−22−22i2−i2i2−i2-22−2i2i22−2−2−i2−i2i2i2000000000000000000
χ4922-2-2002−2i2i0−2i2i2-20-22-20000−2i2i0−2i2i2-2000002−2i2−i2002−22−2i2−i2i2−i22-2−2i2i22−2−2i2i2−i2−i2000000000000000000
χ5022-2-2002−2i2i0−2i2i2-20-22-20000−2i2i0−2i2i2-2000002−2i2−i2002−22−2i2−i2i2−i2-222i−2i−2−222−i2−i2i2i2000000000000000000
χ5122-2-2002−2i2i0−2i2i2-20-22-20000−2i2i0−2i2i2-200000−22−i2i200−22−22−i2i2−i2i22-2−2i2i−2−222−i2−i2i2i2000000000000000000
χ5222-2-2002−2i2i0−2i2i2-20-22-20000−2i2i0−2i2i2-200000−22−i2i200−22−22−i2i2−i2i2-222i−2i22−2−2i2i2−i2−i2000000000000000000
χ53444444-2-4-4444-4-44-2-2-2-4-4-2-222-2-2-222-2000000002200000000000000000000000000000000000000
χ54444444-2-4-4-4-4-444-4-2-2-24-4-2-222222-2-22000000002-200000000000000000000000000000000000000
χ554444-4-4-2444-4-4-4-44-2-2-24-422-2-2-22222-2000000002-200000000000000000000000000000000000000
χ564444-4-4-244-44444-4-2-2-2-4-422-2-22-2-2-2-22000000002200000000000000000000000000000000000000
χ5744-4-40044i−4i0−4i4i-440-44-400004i−4i0−4i4i-440000000000000000000000000000000000000000000000000
χ5844-4-4004−4i4i04i−4i-440-44-40000−4i4i04i−4i-440000000000000000000000000000000000000000000000000
χ5944-4-400-24i−4i04i−4i4-402-220000−2i2i0−2i2i-220000022−22−2i22i200−22−22i2−i2i2−i2000000000000000000000000000000
χ6044-4-400-24i−4i04i−4i4-402-220000−2i2i0−2i2i-2200000−22222i2−2i2002−22−2−i2i2−i2i2000000000000000000000000000000
χ6144-4-400-24i−4i0−4i4i-4402-220000−2i2i02i−2i2-2000000000006−6−66−i6i6i6−i6000000000000000000000000000000
χ6244-4-400-24i−4i0−4i4i-4402-220000−2i2i02i−2i2-200000000000−666−6i6−i6−i6i6000000000000000000000000000000
χ6344-4-400-2−4i4i04i−4i-4402-2200002i−2i0−2i2i2-2000000000006−6−66i6−i6−i6i6000000000000000000000000000000
χ6444-4-400-2−4i4i04i−4i-4402-2200002i−2i0−2i2i2-200000000000−666−6−i6i6i6−i6000000000000000000000000000000
χ6544-4-400-2−4i4i0−4i4i4-402-2200002i−2i02i−2i-220000022−222i2−2i200−22−22−i2i2−i2i2000000000000000000000000000000
χ6644-4-400-2−4i4i0−4i4i4-402-2200002i−2i02i−2i-2200000−2222−2i22i2002−22−2i2−i2i2−i2000000000000000000000000000000
χ674-44-44-44000000004-4-4004-40000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000
χ684-44-44-44000000004-4-4004-4000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000
χ694-44-4-444000000004-4-400-440000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ704-44-4-444000000004-4-400-44000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ714-4-440040040000-4-4-4400000040000-40000000000000000000000−2i22i22i2−2i20000000000000000000000
χ724-4-440040040000-4-4-4400000040000-400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ734-4-4400400-400004-4-44000000-4000040000000000000000000000000022−22−2222000000000000000000
χ744-4-4400400-400004-4-44000000-40000400000000000000000000000000−222222−22000000000000000000
χ758-88-88-8-400000000-44400-4400000000000000000000000000000000000000000000000000000000
χ768-88-8-88-400000000-444004-400000000000000000000000000000000000000000000000000000000
χ778-8-8800-40080000-844-4000000-400004000000000000000000000000000000000000000000000000
χ788-8-8800-400-80000844-400000040000-4000000000000000000000000000000000000000000000000

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