Finite Group Databasebeta

← Group #10849418

Character table — Group #10849418

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888121212121212121212121212161616161616161616162424242424244848
order12222234444444466644661212121212121212444488881212242424242424242444444444444488121212122424242422244444
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
χ5111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-111-111-1-1
χ911111111-1-1-1-1111111-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11-1-11-11-1
χ1011111111-1-1-1-1111111-1-1111-1-1-1-111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-11-111-11-11
χ1111111111-1-1-1-1111111-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1111-1-1-1-111-11-1-11-1-11
χ1211111111-1-1-1-1111111-1-1111-1-1-1-111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-111-111-1
χ1311111111-1-1-1-1111111-1-1111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-11-1-11-11
χ1411111111-1-1-1-1111111-1-1111-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-111-1-11111-111-11-1
χ1511111111-1-1-1-1111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111111-1-1-11111-1-1-1-11-1-111-1
χ1611111111-1-1-1-1111111-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-111-1-11
χ172222222-222-2-2-2-2-22222-222-222-2-2-2-2-22-22-200002-200000000000000000000002-22-2000000000000
χ182222222-222-2-2-2-2-22222-222-222-2-2-2-2-2-22-2200002-20000000000000000000000-22-22000000000000
χ192222222-2-2-222-2-2-2222-2222-2-2-222-2-2-22-2-220000-2200000000000000000000002-2-22000000000000
χ202222222-2-2-222-2-2-2222-2222-2-2-222-2-2-2-222-20000-220000000000000000000000-222-2000000000000
χ21222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-1-1-100000000
χ22222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111000000000000-2-2-1-1-1-1111100000000
χ23222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1000000000000-2-21111111100000000
χ24222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111000000000000221111-1-1-1-100000000
χ25222222-12-2-2-2-2222-1-1-1-2-2-1-1-11111-1-1-122-2-222-2-211-1-1-1-111110000000000002-2-1-111-1-11100000000
χ26222222-12-2-2-2-2222-1-1-1-2-2-1-1-11111-1-1-122-2-2-2-222111111-1-1-1-1000000000000-22-1-11111-1-100000000
χ27222222-12-2-2-2-2222-1-1-1-2-2-1-1-11111-1-1-1-2-22222-2-211-1-1-1-11111000000000000-2211-1-111-1-100000000
χ28222222-12-2-2-2-2222-1-1-1-2-2-1-1-11111-1-1-1-2-222-2-222111111-1-1-1-10000000000002-211-1-1-1-11100000000
χ29222222-1-222-2-2-2-2-2-1-1-12-2-1-11-1-1111112-22-20000-1133−3−333−3−300000000000000-11-113−33−300000000
χ30222222-1-222-2-2-2-2-2-1-1-12-2-1-11-1-1111112-22-20000-11−3−333−3−33300000000000000-11-11−33−3300000000
χ31222222-1-222-2-2-2-2-2-1-1-12-2-1-11-1-111111-22-220000-1133−3−333−3−3000000000000001-11-1−33−3300000000
χ32222222-1-222-2-2-2-2-2-1-1-12-2-1-11-1-111111-22-220000-11−3−333−3−333000000000000001-11-13−33−300000000
χ33222222-1-2-2-222-2-2-2-1-1-1-22-1-1111-1-11112-2-2200001-133−3−3−3−33300000000000000-111-13−3−3300000000
χ34222222-1-2-2-222-2-2-2-1-1-1-22-1-1111-1-11112-2-2200001-1−3−33333−3−300000000000000-111-1−333−300000000
χ35222222-1-2-2-222-2-2-2-1-1-1-22-1-1111-1-1111-222-200001-133−3−3−3−333000000000000001-1-11−333−300000000
χ36222222-1-2-2-222-2-2-2-1-1-1-22-1-1111-1-1111-222-200001-1−3−33333−3−3000000000000001-1-113−3−3300000000
χ372222-2-22222-2-2-2-22222-22-2-2222-2-2-2-2200000000-220000000022-2-2000000000000000000200-20000
χ382222-2-22222-2-2-2-22222-22-2-2222-2-2-2-2200000000-2200000000-2-222000000000000000000-20020000
χ392222-2-222-2-222-2-222222-2-2-22-2-222-2-22000000002-20000000022-2-2000000000000000000-20020000
χ402222-2-222-2-222-2-222222-2-2-22-2-222-2-22000000002-200000000-2-222000000000000000000200-20000
χ412222-2-22-2222222-2222-2-2-2-2-2222222-200000000-2-200000000000000000000000000000002-20-2200
χ422222-2-22-2222222-2222-2-2-2-2-2222222-200000000-2-20000000000000000000000000000000-2202-200
χ432222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-222-200000000220000000000000000000000000000000220-2-200
χ442222-2-22-2-2-2-2-222-222222-2-2-2-2-2-2-222-200000000220000000000000000000000000000000-2-202200
χ4522-2-22-22-200002-222-2-2002-2-200002-220000002i−2i0000002i−2i2i−2i2i−2i2i−2i000022-2-2000000000000000000
χ4622-2-22-22-200002-222-2-2002-2-200002-220000002i−2i0000002i−2i2i−2i−2i2i−2i2i0000-2-222000000000000000000
χ4722-2-22-22-200002-222-2-2002-2-200002-22000000−2i2i000000−2i2i−2i2i2i−2i2i−2i0000-2-222000000000000000000
χ4822-2-22-22-200002-222-2-2002-2-200002-22000000−2i2i000000−2i2i−2i2i−2i2i−2i2i000022-2-2000000000000000000
χ4922-2-2-222-20000-2222-2-200-22-20000-22200002i−2i00002i−2i2i−2i00002i−2i−2i2i22-2-20000000000000000000000
χ5022-2-2-222-20000-2222-2-200-22-20000-22200002i−2i00002i−2i2i−2i0000−2i2i2i−2i-2-2220000000000000000000000
χ5122-2-2-222-20000-2222-2-200-22-20000-2220000−2i2i0000−2i2i−2i2i00002i−2i−2i2i-2-2220000000000000000000000
χ5222-2-2-222-20000-2222-2-200-22-20000-2220000−2i2i0000−2i2i−2i2i0000−2i2i2i−2i22-2-20000000000000000000000
χ534444-4-4-2444-4-4-4-44-2-2-2-4422-2-2-22222-2000000002-200000000000000000000000000000000000000
χ544444-4-4-24-4-444-4-44-2-2-24-422-222-2-222-200000000-2200000000000000000000000000000000000000
χ554444-4-4-2-4444444-4-2-2-2-4-4222-2-2-2-2-2-22000000002200000000000000000000000000000000000000
χ564444-4-4-2-4-4-4-4-444-4-2-2-2442222222-2-2200000000-2-200000000000000000000000000000000000000
χ5744-4-44-4440000-44-44-4-4004-440000-44-4000000000000000000000000000000000000000000000000
χ5844-4-44-4-240000-44-4-22200-22-200002-2200000000000000−2i32i32i3−2i3000000000000000000000000000000
χ5944-4-44-4-240000-44-4-22200-22-200002-22000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ6044-4-44-4-2-400004-44-22200-2220000-22-20000004i−4i000000−2i2i−2i2i000000000000000000000000000000
χ6144-4-44-4-2-400004-44-22200-2220000-22-2000000−4i4i0000002i−2i2i−2i000000000000000000000000000000
χ6244-4-4-444400004-4-44-4-400-44400004-4-4000000000000000000000000000000000000000000000000
χ6344-4-4-44-2400004-4-4-222002-2-20000-2220000000000−2i32i32i3−2i30000000000000000000000000000000000
χ6444-4-4-44-2400004-4-4-222002-2-20000-22200000000002i3−2i3−2i32i30000000000000000000000000000000000
χ6544-4-4-44-2-40000-444-222002-2200002-2-200004i−4i0000−2i2i−2i2i0000000000000000000000000000000000
χ6644-4-4-44-2-40000-444-222002-2200002-2-20000−4i4i00002i−2i2i−2i0000000000000000000000000000000000
χ674-44-40040004i−4i000-44-400000004i−4i00000000000000000000000002-22-22i−2i2i−2i000000000000000000
χ684-44-40040004i−4i000-44-400000004i−4i0000000000000000000000000-22-22−2i2i−2i2i000000000000000000
χ694-44-4004000−4i4i000-44-40000000−4i4i00000000000000000000000002-22-2−2i2i−2i2i000000000000000000
χ704-44-4004000−4i4i000-44-40000000−4i4i0000000000000000000000000-22-222i−2i2i−2i000000000000000000
χ714-4-4400404i−4i00000-4-44000004i−4i0000000000000000000000000002-2-222i−2i−2i2i000000000000000000
χ724-4-4400404i−4i00000-4-44000004i−4i000000000000000000000000000-222-2−2i2i2i−2i000000000000000000
χ734-4-440040−4i4i00000-4-4400000−4i4i0000000000000000000000000002-2-22−2i2i2i−2i000000000000000000
χ744-4-440040−4i4i00000-4-4400000−4i4i000000000000000000000000000-222-22i−2i−2i2i000000000000000000
χ758-88-800-40008i−8i0004-440000000−4i4i000000000000000000000000000000000000000000000000000
χ768-88-800-4000−8i8i0004-4400000004i−4i000000000000000000000000000000000000000000000000000
χ778-8-8800-408i−8i0000044-400000−4i4i00000000000000000000000000000000000000000000000000000
χ788-8-8800-40−8i8i0000044-4000004i−4i00000000000000000000000000000000000000000000000000000

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