Finite Group Databasebeta

← Group #10594701

Character table — Group #10594701

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222224444444444444499121212121818182424242411222222244444444444444991212121218181824242424
order1233466883612121212242424242424242444224428866121222664668866121212122424242424242424442244288661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1111-1-1-1-11111111111111111111111111-1-1-1-1111-1-1-1-1
χ311111111111111111111111-1-111-1-1-1-1-111-1-111111111111111111111111-1-111-1-1-1-1-111-1-1
χ411111111111111111111111-1-1-1-111-1-1-1-1-11111111111111111111111111-1-1-1-111-1-1-1-1-111
χ51111111-1-1111111-1-1-1-1-1-1-1-1111-11-11-1-11-11-11111111-1-1111111-1-1-1-1-1-1-1-1111-11-11-1-11-11-1
χ61111111-1-1111111-1-1-1-1-1-1-1-111-11-111-1-1-11-111111111-1-1111111-1-1-1-1-1-1-1-111-11-111-1-1-11-11
χ71111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-11
χ81111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111-111-11111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ92222-2220022-2-2-2-200000000220000-20000002222-2220022-2-2-2-200000000220000-2000000
χ102222-2220022-2-2-2-200000000-2-2000020000002222-2220022-2-2-2-200000000-2-200002000000
χ11222-12-1222-1-1-12-1-122-1-1-1-1-1-1002200000-1-100222-12-1222-1-1-12-1-122-1-1-1-1-1-1002200000-1-100
χ12222-12-1222-1-1-12-1-122-1-1-1-1-1-100-2-2000001100222-12-1222-1-1-12-1-122-1-1-1-1-1-100-2-2000001100
χ13222-12-12-2-2-1-1-12-1-1-2-2111111002-200000-1100222-12-12-2-2-1-1-12-1-1-2-2111111002-200000-1100
χ14222-12-12-2-2-1-1-12-1-1-2-211111100-22000001-100222-12-12-2-2-1-1-12-1-1-2-211111100-22000001-100
χ1522-1222-122-1-12-1-1-1-1-122-1-1-1-100002200000-1-122-1222-122-1-12-1-1-1-1-122-1-1-1-100002200000-1-1
χ1622-1222-122-1-12-1-1-1-1-122-1-1-1-10000-2-2000001122-1222-122-1-12-1-1-1-1-122-1-1-1-10000-2-20000011
χ1722-1222-1-2-2-1-12-1-1-111-2-2111100002-200000-1122-1222-1-2-2-1-12-1-1-111-2-2111100002-200000-11
χ1822-1222-1-2-2-1-12-1-1-111-2-211110000-22000001-122-1222-1-2-2-1-12-1-1-111-2-211110000-22000001-1
χ192-2220-2-22−22-200002−22−222−2−22i−2i00000i2−i200002-2220-2-22−22-200002−22−222−2−22i−2i00000i2−i20000
χ202-2220-2-22−22-200002−22−222−2−2−2i2i00000−i2i200002-2220-2-22−22-200002−22−222−2−2−2i2i00000−i2i20000
χ212-2220-2-2−222-20000−22−22−2−2222i−2i00000−i2i200002-2220-2-2−222-20000−22−22−2−2222i−2i00000−i2i20000
χ222-2220-2-2−222-20000−22−22−2−222−2i2i00000i2−i200002-2220-2-2−222-20000−22−22−2−222−2i2i00000i2−i20000
χ23444-2-4-2400-2-22-422000000000000000000000444-2-4-2400-2-22-422000000000000000000000
χ2444-24-44-200-2-2-422200000000000000000000044-24-44-200-2-2-4222000000000000000000000
χ2544-2-24-2-24411-2-211-2-2-2-21111000000000000044-2-24-2-24411-2-211-2-2-2-211110000000000000
χ2644-2-24-2-2-4-411-2-2112222-1-1-1-1000000000000044-2-24-2-2-4-411-2-2112222-1-1-1-10000000000000
χ2744-2-2-4-2-2001122-1-100003i−3i3i−3i000000000000044-2-2-4-2-2001122-1-100003i−3i3i−3i0000000000000
χ2844-2-2-4-2-2001122-1-10000−3i3i−3i3i000000000000044-2-2-4-2-2001122-1-10000−3i3i−3i3i0000000000000
χ294-44-202-422−22-22000022−22−22−2−22200000000000004-44-202-422−22-22000022−22−22−2−2220000000000000
χ304-44-202-4−2222-220000−22222−222−2−200000000000004-44-202-4−2222-220000−22222−222−2−20000000000000
χ314-4-240-4222−22-220000−2222−22−2−22200000000000004-4-240-4222−22-220000−2222−22−2−2220000000000000
χ324-4-240-42−2222-2200002−2−222222−2−200000000000004-4-240-42−2222-2200002−2−222222−2−20000000000000
χ334-4-2-202222−221-1003i−3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000004-4-2-202222−221-1003i−3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000
χ344-4-2-202222−221-100−3i3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000004-4-2-202222−221-100−3i3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000
χ354-4-2-2022−22221-1003i−3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000004-4-2-2022−22221-1003i−3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000
χ364-4-2-2022−22221-100−3i3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000004-4-2-2022−22221-100−3i3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ381111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111
χ3911111111111111111111111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111
χ4011111111111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1
χ411111111-1-1111111-1-1-1-1-1-1-1-1111-11-11-1-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-11-11-111-11-11
χ421111111-1-1111111-1-1-1-1-1-1-1-111-11-111-1-1-11-11-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-11-11-1-1111-11-1
χ431111111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-111-11-1-1-111-1
χ441111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111111-1-111-1-11-1-11
χ452222-2220022-2-2-2-200000000220000-2000000-2-2-2-22-2-200-2-2222200000000-2-200002000000
χ462222-2220022-2-2-2-200000000-2-200002000000-2-2-2-22-2-200-2-2222200000000220000-2000000
χ47222-12-1222-1-1-12-1-122-1-1-1-1-1-1002200000-1-100-2-2-21-21-2-2-2111-211-2-211111100-2-2000001100
χ48222-12-1222-1-1-12-1-122-1-1-1-1-1-100-2-2000001100-2-2-21-21-2-2-2111-211-2-2111111002200000-1-100
χ49222-12-12-2-2-1-1-12-1-1-2-2111111002-200000-1100-2-2-21-21-222111-21122-1-1-1-1-1-100-22000001-100
χ50222-12-12-2-2-1-1-12-1-1-2-211111100-22000001-100-2-2-21-21-222111-21122-1-1-1-1-1-1002-200000-1100
χ5122-1222-122-1-12-1-1-1-1-122-1-1-1-100002200000-1-1-2-21-2-2-21-2-211-211111-2-211110000-2-20000011
χ5222-1222-122-1-12-1-1-1-1-122-1-1-1-10000-2-20000011-2-21-2-2-21-2-211-211111-2-2111100002200000-1-1
χ5322-1222-1-2-2-1-12-1-1-111-2-2111100002-200000-11-2-21-2-2-212211-2111-1-122-1-1-1-10000-22000001-1
χ5422-1222-1-2-2-1-12-1-1-111-2-211110000-22000001-1-2-21-2-2-212211-2111-1-122-1-1-1-100002-200000-11
χ552-2220-2-22−22-200002−22−222−2−22i−2i00000i2−i20000-22-2-2022−22-220000−22−22−2−222−2i2i00000−i2i20000
χ562-2220-2-22−22-200002−22−222−2−2−2i2i00000−i2i20000-22-2-2022−22-220000−22−22−2−2222i−2i00000i2−i20000
χ572-2220-2-2−222-20000−22−22−2−2222i−2i00000−i2i20000-22-2-20222−2-2200002−22−222−2−2−2i2i00000i2−i20000
χ582-2220-2-2−222-20000−22−22−2−222−2i2i00000i2−i20000-22-2-20222−2-2200002−22−222−2−22i−2i00000−i2i20000
χ59444-2-4-2400-2-22-422000000000000000000000-4-4-4242-40022-24-2-2000000000000000000000
χ6044-24-44-200-2-2-4222000000000000000000000-4-42-44-4200224-2-2-2000000000000000000000
χ6144-2-24-2-24411-2-211-2-2-2-211110000000000000-4-422-422-4-4-1-122-1-12222-1-1-1-10000000000000
χ6244-2-24-2-2-4-411-2-2112222-1-1-1-10000000000000-4-422-42244-1-122-1-1-2-2-2-211110000000000000
χ6344-2-2-4-2-2001122-1-100003i−3i3i−3i0000000000000-4-42242200-1-1-2-2110000−3i3i−3i3i0000000000000
χ6444-2-2-4-2-2001122-1-10000−3i3i−3i3i0000000000000-4-42242200-1-1-2-21100003i−3i3i−3i0000000000000
χ654-44-202-422−22-22000022−22−22−2−2220000000000000-44-420-24−22222-20000−22222−222−2−20000000000000
χ664-44-202-4−2222-220000−22222−222−2−20000000000000-44-420-2422−222-2000022−22−22−2−2220000000000000
χ674-4-240-4222−22-220000−2222−22−2−2220000000000000-442-404-2−22222-200002−2−222222−2−20000000000000
χ684-4-240-42−2222-2200002−2−222222−2−20000000000000-442-404-222−222-20000−2222−22−2−2220000000000000
χ694-4-2-202222−221-1003i−3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000-44220-2-2−2222-1100−3i3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000
χ704-4-2-202222−221-100−3i3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000-44220-2-2−2222-11003i−3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000
χ714-4-2-2022−22221-1003i−3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000-44220-2-222−22-1100−3i3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000
χ724-4-2-2022−22221-100−3i3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000-44220-2-222−22-11003i−3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.