Finite Group Databasebeta

← Group #11715159

Character table — Group #11715159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222226666666666668888888812121212121212121212121212121212121212121212161616161616161616161616242424242424
order122244444444444444444444888888883666121212122224444444888888888888121212121212121212121212222444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1
χ4111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-111
χ511111111-1-1-1-11111-1-1-1-111111111111111111111-11-11111-11-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-1
χ611111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-11
χ711111111-1-1-1-1-1-1-1-1111111111111111111111111-1-111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-11
χ811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1
χ91111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-111-1-1-1-1111-1-111-1-111-1-111-1-111-1-111-1-111-1-1-11
χ101111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-111-1-11-1-111-1-111-1-11111-1-111-1-111-1-1-1-1111-1
χ111111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-1-1-11-1111-1-1-11-111-1-1-1-111-1-11111-1-1-1-111-1-1111-11-11-1
χ121111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-11-11-1-111-11-1-1-11111-1-111-1-111-1-1-1-111-1-111-11-11-11
χ131111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-11111-1-11-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1111-1-1
χ141111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111
χ151111-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1111
χ161111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-111-1-111-1-11111-1-1111-1-1-1
χ1722222222222222222222222200000000-1-1-1-1-1-1-1-12220000222000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000
χ18222222222222-2-2-2-2-2-2-2-2222200000000-1-1-1-1-1-1-1-12-2-200002-2-2000000000000-1-1-1-111111111000000
χ1922222222-2-2-2-22222-2-2-2-2222200000000-1-1-1-1-1-1-1-1-22-20000-22-20000000000001111-1-1-1-11111000000
χ2022222222-2-2-2-2-2-2-2-22222222200000000-1-1-1-1-1-1-1-1-2-220000-2-2200000000000011111111-1-1-1-1000000
χ212222-2-2-2-222-2-222-2-222-2-2-2-22200000000-1-1-1-1111122-20000-2-22000000000000-1-111-1-111-1-111000000
χ222222-2-2-2-222-2-2-2-222-2-222-2-22200000000-1-1-1-111112-220000-22-2000000000000-1-11111-1-111-1-1000000
χ232222-2-2-2-2-2-22222-2-2-2-222-2-22200000000-1-1-1-11111-22200002-2-200000000000011-1-1-1-11111-1-1000000
χ242222-2-2-2-2-2-222-2-22222-2-2-2-22200000000-1-1-1-11111-2-2-2000022200000000000011-1-111-1-1-1-111000000
χ2522-2-22i2i−2i−2i0000000000002i−2i2-222-2-22i2i−2i−2i2-22-22i2i−2i−2i0002-22i−2i000000000000000000000000000000000
χ2622-2-22i2i−2i−2i0000000000002i−2i2-2-2-222−2i−2i2i2i2-22-22i2i−2i−2i000-22−2i2i000000000000000000000000000000000
χ2722-2-2−2i−2i2i2i000000000000−2i2i2-222-2-2−2i−2i2i2i2-22-2−2i−2i2i2i0002-2−2i2i000000000000000000000000000000000
χ2822-2-2−2i−2i2i2i000000000000−2i2i2-2-2-2222i2i−2i−2i2-22-2−2i−2i2i2i000-222i−2i000000000000000000000000000000000
χ292-22-22i−2i2i−2i2i−2i2-22i−2i2-22-22i−2i00002−22−2i2−i2i2−i2-111-1i−ii−i0000000000i2−i22−2i2−i22−22−2i2−i2i−i1-1i−i1-11-1i−i000000
χ302-22-22i−2i2i−2i2i−2i2-22i−2i2-22-22i−2i0000−22−22−i2i2−i2i2-111-1i−ii−i0000000000−i2i2−22−i2i2−22−22−i2i2i−i1-1i−i1-11-1i−i000000
χ312-22-22i−2i2i−2i2i−2i2-2−2i2i-22-22−2i2i00002−22−2i2−i2i2−i2-111-1i−ii−i0000000000i2−i22−2−i2i2−22−22−i2i2i−i1-1−ii-11-11−ii000000
χ322-22-22i−2i2i−2i2i−2i2-2−2i2i-22-22−2i2i0000−22−22−i2i2−i2i2-111-1i−ii−i0000000000−i2i2−22i2−i22−22−2i2−i2i−i1-1−ii-11-11−ii000000
χ332-22-22i−2i2i−2i−2i2i-222i−2i2-2-22−2i2i00002−22−2i2−i2i2−i2-111-1i−ii−i0000000000−i2i2−22i2−i22−2−22−i2i2−ii-11i−i1-1-11−ii000000
χ342-22-22i−2i2i−2i−2i2i-222i−2i2-2-22−2i2i0000−22−22−i2i2−i2i2-111-1i−ii−i0000000000i2−i22−2−i2i2−222−2i2−i2−ii-11i−i1-1-11−ii000000
χ352-22-22i−2i2i−2i−2i2i-22−2i2i-222-22i−2i00002−22−2i2−i2i2−i2-111-1i−ii−i0000000000−i2i2−22−i2i2−222−2i2−i2−ii-11−ii-111-1i−i000000
χ362-22-22i−2i2i−2i−2i2i-22−2i2i-222-22i−2i0000−22−22−i2i2−i2i2-111-1i−ii−i0000000000i2−i22−2i2−i22−2−22−i2i2−ii-11−ii-111-1i−i000000
χ372-22-2−2i2i−2i2i2i−2i-222i−2i-222-2−2i2i00002−22−2−i2i2−i2i2-111-1−ii−ii0000000000i2−i2−22i2−i2−222−2−i2i2i−i-11i−i-111-1−ii000000
χ382-22-2−2i2i−2i2i2i−2i-222i−2i-222-2−2i2i0000−22−22i2−i2i2−i2-111-1−ii−ii0000000000−i2i22−2−i2i22−2−22i2−i2i−i-11i−i-111-1−ii000000
χ392-22-2−2i2i−2i2i2i−2i-22−2i2i2-2-222i−2i00002−22−2−i2i2−i2i2-111-1−ii−ii0000000000i2−i2−22−i2i22−2−22i2−i2i−i-11−ii1-1-11i−i000000
χ402-22-2−2i2i−2i2i2i−2i-22−2i2i2-2-222i−2i0000−22−22i2−i2i2−i2-111-1−ii−ii0000000000−i2i22−2i2−i2−222−2−i2i2i−i-11−ii1-1-11i−i000000
χ412-22-2−2i2i−2i2i−2i2i2-22i−2i-22-222i−2i00002−22−2−i2i2−i2i2-111-1−ii−ii0000000000−i2i22−2i2−i2−22−22i2−i2−ii1-1i−i-11-11i−i000000
χ422-22-2−2i2i−2i2i−2i2i2-22i−2i-22-222i−2i0000−22−22i2−i2i2−i2-111-1−ii−ii0000000000i2−i2−22−i2i22−22−2−i2i2−ii1-1i−i-11-11i−i000000
χ432-22-2−2i2i−2i2i−2i2i2-2−2i2i2-22-2−2i2i00002−22−2−i2i2−i2i2-111-1−ii−ii0000000000−i2i22−2−i2i22−22−2−i2i2−ii1-1−ii1-11-1−ii000000
χ442-22-2−2i2i−2i2i−2i2i2-2−2i2i2-22-2−2i2i0000−22−22i2−i2i2−i2-111-1−ii−ii0000000000i2−i2−22i2−i2−22−22i2−i2−ii1-1−ii1-11-1−ii000000
χ4533333333333333333333-1-1-1-11111111100000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000-1-1-1-1-1-1
χ4633333333333333333333-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000111111
χ47333333333333-3-3-3-3-3-3-3-3-1-1-1-11111111100000000-111-1-1-1-1-1111111-1-1-1-1-1-1-1-1000000000000-111-111
χ48333333333333-3-3-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-100000000-1111111-111-1-1-1-1111111110000000000001-1-11-1-1
χ4933333333-3-3-3-33333-3-3-3-3-1-1-1-111111111000000001-11-1-1-1-11-11-1-1-1-11111-1-1-1-10000000000001-111-11
χ5033333333-3-3-3-33333-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-1000000001-1111111-111111-1-1-1-11111000000000000-11-1-11-1
χ5133333333-3-3-3-3-3-3-3-33333-1-1-1-1111111110000000011-1-1-1-1-111-1-1-1-1-1-1-1-1-1111100000000000011-111-1
χ5233333333-3-3-3-3-3-3-3-33333-1-1-1-1-1-1-1-1-1-1-1-10000000011-1111111-111111111-1-1-1-1000000000000-1-11-1-11
χ533333-3-3-3-333-3-333-3-333-3-311-1-11111-1-1-1-100000000-1-11-1-11111-111-1-111-1-111-1-1000000000000-1-1111-1
χ543333-3-3-3-333-3-333-3-333-3-311-1-1-1-1-1-1111100000000-1-1111-1-111-1-1-111-1-111-1-11100000000000011-1-1-11
χ553333-3-3-3-333-3-3-3-333-3-33311-1-11111-1-1-1-100000000-11-1-1-1111-1111-1-1-1-111-1-111000000000000-11-11-11
χ563333-3-3-3-333-3-3-3-333-3-33311-1-1-1-1-1-1111100000000-11-111-1-11-11-1-11111-1-111-1-10000000000001-11-11-1
χ573333-3-3-3-3-3-33333-3-3-3-33311-1-11111-1-1-1-1000000001-1-1-1-111-111-1-11111-1-1-1-1110000000000001-1-1-111
χ583333-3-3-3-3-3-33333-3-3-3-33311-1-1-1-1-1-11111000000001-1-111-1-1-11111-1-1-1-11111-1-1000000000000-1111-1-1
χ593333-3-3-3-3-3-333-3-33333-3-311-1-11111-1-1-1-100000000111-1-111-1-1-1-1-111-1-11111-1-1000000000000111-1-1-1
χ603333-3-3-3-3-3-333-3-33333-3-311-1-1-1-1-1-111110000000011111-1-1-1-1-111-1-111-1-1-1-111000000000000-1-1-1111
χ6144-4-44i4i−4i−4i0000000000004i−4i4-400000000-22-22−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-4−4i−4i4i4i000000000000−4i4i4-400000000-22-222i2i−2i−2i0000000000000000000000000000000000000000
χ634-44-44i−4i4i−4i4i−4i4-44i−4i4-44-44i−4i0000000000001-1-11−ii−ii0000000000000000000000−ii-11−ii-11-11−ii000000
χ644-44-44i−4i4i−4i4i−4i4-4−4i4i-44-44−4i4i0000000000001-1-11−ii−ii0000000000000000000000−ii-11i−i1-11-1i−i000000
χ654-44-44i−4i4i−4i−4i4i-444i−4i4-4-44−4i4i0000000000001-1-11−ii−ii0000000000000000000000i−i1-1−ii-111-1i−i000000
χ664-44-44i−4i4i−4i−4i4i-44−4i4i-444-44i−4i0000000000001-1-11−ii−ii0000000000000000000000i−i1-1i−i1-1-11−ii000000
χ674-44-4−4i4i−4i4i4i−4i-444i−4i-444-4−4i4i0000000000001-1-11i−ii−i0000000000000000000000−ii1-1−ii1-1-11i−i000000
χ684-44-4−4i4i−4i4i4i−4i-44−4i4i4-4-444i−4i0000000000001-1-11i−ii−i0000000000000000000000−ii1-1i−i-111-1−ii000000
χ694-44-4−4i4i−4i4i−4i4i4-44i−4i-44-444i−4i0000000000001-1-11i−ii−i0000000000000000000000i−i-11−ii1-11-1−ii000000
χ704-44-4−4i4i−4i4i−4i4i4-4−4i4i4-44-4−4i4i0000000000001-1-11i−ii−i0000000000000000000000i−i-11i−i-11-11i−i000000
χ714-4-444-4-44000000000000000022−22−222222−22−2222-2-2222-2-220000000000000000000000000000000000000000
χ724-4-444-4-440000000000000000−222222−22−222222−22-2-2222-2-220000000000000000000000000000000000000000
χ734-4-44-444-4000000000000000022−22−2222−222222−22-2-222-222-20000000000000000000000000000000000000000
χ744-4-44-444-40000000000000000−222222−2222−22−2222-2-222-222-20000000000000000000000000000000000000000
χ7566-6-66i6i−6i−6i000000000000−2i2i-2222-2-22i2i−2i−2i00000000000-22−2i2i000000000000000000000000000000000
χ7666-6-66i6i−6i−6i000000000000−2i2i-22-2-222−2i−2i2i2i000000000002-22i−2i000000000000000000000000000000000
χ7766-6-6−6i−6i6i6i0000000000002i−2i-2222-2-2−2i−2i2i2i00000000000-222i−2i000000000000000000000000000000000
χ7866-6-6−6i−6i6i6i0000000000002i−2i-22-2-2222i2i−2i−2i000000000002-2−2i2i000000000000000000000000000000000
χ798-8-888-8-8800000000000000000000000022-2-2-222-20000000000000000000000000000000000000000
χ808-8-88-888-800000000000000000000000022-2-22-2-220000000000000000000000000000000000000000

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