Finite Group Databasebeta

← Group #10591138

Character table — Group #10591138

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222222224444444444444444444444441212121212121212121212121212121212121212121212121818181818181818
order122244442233446666661212121212121212366666666666121212121212121212121212444444441212121212121212121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-111-1111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-1-111-1-11-111-1111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111-1-111-1-11-111-1111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211-1-111-1-11-111-1111-1-1-1-11111-1-1-1-1111-1-1-1-111-1-1111-1-111-1-111-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-1-1-1-111-1111-1111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1411-1-1-1-111-1111-1111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1511-1-1-1-111-1111-1111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1611-1-1-1-111-1111-1111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-111-1-1-1-111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ1722222222222-1222-122-1-122-1-122-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000
χ1822222222222-1222-122-1-122-1-122-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000-2-2-2-2000000001111111100000000
χ192222222222-1222-12-1-122-1-122-1-122-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000000000000
χ202222222222-1222-12-1-122-1-122-1-122-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000000000000
χ2122222222-2-222-2-2222222222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2222222222-2-22-1-2-22-122-1-122-1-122-1-1-1-21-21-1-11111-1-21-211111-1-1-1-10000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ2322222222-2-22-1-2-22-122-1-122-1-122-1-1-1-21-21-1-11111-1-21-211111-1-1-1-10000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ2422222222-2-2-12-2-2-12-1-122-1-122-1-122-11-21-2-1-11111-11-21-21111-1-1-1-100000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2522222222-2-2-12-2-2-12-1-122-1-122-1-122-11-21-2-1-11111-11-21-21111-1-1-1-100000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ262222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ272222-2-2-2-2222-1-2-22-122-1-1-2-211-2-211-12-12-1-1-1-1-1-1-1-1-21-21111111110000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ282222-2-2-2-2222-1-2-22-122-1-1-2-211-2-211-12-12-1-1-1-1-1-1-1-1-21-21111111110000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ292222-2-2-2-222-12-2-2-12-1-12211-2-211-2-2-1-12-12-1-1-1-1-1-1-11-21-21111111100000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ302222-2-2-2-222-12-2-2-12-1-12211-2-211-2-2-1-12-12-1-1-1-1-1-1-11-21-21111111100000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ312222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-21-1-11111-12-12-1-1-1-1-11111000022-2-200000000-1-1-1-1111100000000
χ322222-2-2-2-2-2-22-1222-122-1-1-2-211-2-211-1-21-21-1-11111-12-12-1-1-1-1-111110000-2-222000000001111-1-1-1-100000000
χ332222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-21-2-1-11111-1-12-12-1-1-1-1111122-2-20000-1-1-1-111110000000000000000
χ342222-2-2-2-2-2-2-1222-12-1-12211-2-211-2-2-11-21-2-1-11111-1-12-12-1-1-1-11111-2-22200001111-1-1-1-10000000000000000
χ3522-2-222-2-22-22-1-222-1-2-21122-1-1-2-211-12-1-2111-1-111-12-1-21-1-111-1-11100002i−2i2i−2i00000000−i−iii−i−iii00000000
χ3622-2-222-2-22-22-1-222-1-2-21122-1-1-2-211-12-1-2111-1-111-12-1-21-1-111-1-1110000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ3722-2-222-2-22-2-12-22-1211-2-2-1-12211-2-2-1-121-211-1-111-1-121-2-1-111-1-1112i−2i2i−2i0000−i−iii−i−iii0000000000000000
χ3822-2-222-2-22-2-12-22-1211-2-2-1-12211-2-2-1-121-211-1-111-1-121-2-1-111-1-111−2i2i−2i2i0000ii−i−iii−i−i0000000000000000
χ3922-2-222-2-2-22222-222-2-2-2-22222-2-2-2-22-2-222-2-2-2-2222-2-222-2-22222-2-200000000000000000000000000000000
χ4022-2-222-2-2-222-12-22-1-2-21122-1-1-2-211-1-212-11111-1-1-1-212-111-1-1-1-11100000000000000003−3−333−3−3300000000
χ4122-2-222-2-2-222-12-22-1-2-21122-1-1-2-211-1-212-11111-1-1-1-212-111-1-1-1-1110000000000000000−333−3−333−300000000
χ4222-2-222-2-2-22-122-2-1211-2-2-1-12211-2-2-11-2-121111-1-1-11-2-1211-1-1-1-111000000003−3−333−3−330000000000000000
χ4322-2-222-2-2-22-122-2-1211-2-2-1-12211-2-2-11-2-121111-1-1-11-2-1211-1-1-1-11100000000−333−3−333−30000000000000000
χ4422-2-2-2-2222-2222-222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-22-2-222-2-222-2-22200000000000000000000000000000000
χ4522-2-2-2-2222-22-12-22-1-2-211-2-21122-1-1-12-1-2111-1-111-1-212-111-1-111-1-100000000000000003−3−33−333−300000000
χ4622-2-2-2-2222-22-12-22-1-2-211-2-21122-1-1-12-1-2111-1-111-1-212-111-1-111-1-10000000000000000−333−33−3−3300000000
χ4722-2-2-2-2222-2-122-2-1211-2-211-2-2-1-122-1-121-211-1-111-11-2-1211-1-111-1-1000000003−3−33−333−30000000000000000
χ4822-2-2-2-2222-2-122-2-1211-2-211-2-2-1-122-1-121-211-1-111-11-2-1211-1-111-1-100000000−333−33−3−330000000000000000
χ4922-2-2-2-222-222-1-222-1-2-211-2-21122-1-1-1-212-11111-1-1-12-1-21-1-11111-1-100002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ5022-2-2-2-222-222-1-222-1-2-211-2-21122-1-1-1-212-11111-1-1-12-1-21-1-11111-1-10000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ5122-2-2-2-222-22-12-22-1211-2-211-2-2-1-122-11-2-121111-1-1-1-121-2-1-11111-1-12i−2i−2i2i0000−i−iiiii−i−i0000000000000000
χ5222-2-2-2-222-22-12-22-1211-2-211-2-2-1-122-11-2-121111-1-1-1-121-2-1-11111-1-1−2i2i2i−2i0000ii−i−i−i−iii0000000000000000
χ532-22-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i0000000000000000000000002−22−2−i2i2−i2i2
χ542-22-22i−2i2i−2i002200-2-22-22-22i−2i2i−2i2i−2i2i−2i200002-20000-2000000002i−2i2i−2i000000000000000000000000−22−22i2−i2i2−i2
χ552-22-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i0000000000000000000000002−22−2i2−i2i2−i2
χ562-22-2−2i2i−2i2i002200-2-22-22-2−2i2i−2i2i−2i2i−2i2i200002-20000-200000000−2i2i−2i2i000000000000000000000000−22−22−i2i2−i2i2
χ572-2-222i−2i−2i2i002200-2-2-22-222i−2i2i−2i−2i2i−2i2i20000-220000-2000000002i−2i−2i2i0000000000000000000000002−2−22−i2i2i2−i2
χ582-2-222i−2i−2i2i002200-2-2-22-222i−2i2i−2i−2i2i−2i2i20000-220000-2000000002i−2i−2i2i000000000000000000000000−222−2i2−i2−i2i2
χ592-2-22−2i2i2i−2i002200-2-2-22-22−2i2i−2i2i2i−2i2i−2i20000-220000-200000000−2i2i2i−2i0000000000000000000000002−2−22i2−i2−i2i2
χ602-2-22−2i2i2i−2i002200-2-2-22-22−2i2i−2i2i2i−2i2i−2i20000-220000-200000000−2i2i2i−2i000000000000000000000000−222−2−i2i2i2−i2
χ614444444444-2-244-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-21111111100000000000000000000000000000000
χ6244444444-4-4-2-2-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-112222-1-1-1-1111100000000000000000000000000000000
χ634444-4-4-4-444-2-2-4-4-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-244-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-21111-1-1-1-100000000000000000000000000000000
χ6544-4-444-4-44-4-2-2-44-2-22222-2-2-2-222221-2-222-1-111-1-11-2-22211-1-111-1-100000000000000000000000000000000
χ6644-4-444-4-4-44-2-24-4-2-22222-2-2-2-22222122-2-2-1-1-1-111122-2-2-1-11111-1-100000000000000000000000000000000
χ6744-4-4-4-4444-4-2-24-4-2-222222222-2-2-2-21-2-222-1-111-1-1122-2-2-1-111-1-11100000000000000000000000000000000
χ6844-4-4-4-444-44-2-2-44-2-222222222-2-2-2-2122-2-2-1-1-1-1111-2-22211-1-1-1-11100000000000000000000000000000000
χ694-44-44i−4i4i−4i004-200-424-4-224i−4i−2i2i4i−4i−2i2i-20000-220000200000000−2i2i−2i2i00000000000000000000000000000000
χ704-44-44i−4i4i−4i00-24002-4-224-4−2i2i4i−4i−2i2i4i−4i-20000-220000200000000−2i2i−2i2i00000000000000000000000000000000
χ714-44-44i−4i4i−4i00-2-20022-22-22−2i2i−2i2i−2i2i−2i2i100001-13-33-3-100003i−3i3i−3ii−ii−i00000000000000000000000000000000
χ724-44-44i−4i4i−4i00-2-20022-22-22−2i2i−2i2i−2i2i−2i2i100001-1-33-33-10000−3i3i−3i3ii−ii−i00000000000000000000000000000000
χ734-44-4−4i4i−4i4i004-200-424-4-22−4i4i2i−2i−4i4i2i−2i-20000-2200002000000002i−2i2i−2i00000000000000000000000000000000
χ744-44-4−4i4i−4i4i00-24002-4-224-42i−2i−4i4i2i−2i−4i4i-20000-2200002000000002i−2i2i−2i00000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-2-20022-22-222i−2i2i−2i2i−2i2i−2i100001-13-33-3-10000−3i3i−3i3i−ii−ii00000000000000000000000000000000
χ764-44-4−4i4i−4i4i00-2-20022-22-222i−2i2i−2i2i−2i2i−2i100001-1-33-33-100003i−3i3i−3i−ii−ii00000000000000000000000000000000
χ774-4-444i−4i−4i4i004-200-42-442-24i−4i−2i2i−4i4i2i−2i-200002-20000200000000−2i2i2i−2i00000000000000000000000000000000
χ784-4-444i−4i−4i4i00-24002-42-2-44−2i2i4i−4i2i−2i−4i4i-200002-20000200000000−2i2i2i−2i00000000000000000000000000000000
χ794-4-444i−4i−4i4i00-2-200222-22-2−2i2i−2i2i2i−2i2i−2i10000-113-3-33-100003i−3i−3i3ii−i−ii00000000000000000000000000000000
χ804-4-444i−4i−4i4i00-2-200222-22-2−2i2i−2i2i2i−2i2i−2i10000-11-333-3-10000−3i3i3i−3ii−i−ii00000000000000000000000000000000
χ814-4-44−4i4i4i−4i004-200-42-442-2−4i4i2i−2i4i−4i−2i2i-200002-200002000000002i−2i−2i2i00000000000000000000000000000000
χ824-4-44−4i4i4i−4i00-24002-42-2-442i−2i−4i4i−2i2i4i−4i-200002-200002000000002i−2i−2i2i00000000000000000000000000000000
χ834-4-44−4i4i4i−4i00-2-200222-22-22i−2i2i−2i−2i2i−2i2i10000-113-3-33-10000−3i3i3i−3i−iii−i00000000000000000000000000000000
χ844-4-44−4i4i4i−4i00-2-200222-22-22i−2i2i−2i−2i2i−2i2i10000-11-333-3-100003i−3i−3i3i−iii−i00000000000000000000000000000000

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