Finite Group Databasebeta

← Group #10770360

Character table — Group #10770360

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888888888888888816161616242424242424242448484848
order12222234466612121212444446612121212121244444444888812121212121212121212242424242424242412121212224444442488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-111-1-1
χ611111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-11-11-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11-11-1111-1-1
χ91111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-11-11-1
χ101111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-111-1-111-1-11-11111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1111-11-11
χ111111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-111-111-1-1-1-11-11
χ121111111-1-1111-1-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-11111-11-1
χ131111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-111-1-11
χ141111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-1-111-1111-1-11-1-111-1
χ151111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-111-11-111-1
χ161111111-1-1111-1-1-1-1-1-1-11111-1-1-1-111-11-11-1-11111-1-11-1-1-1-1-111111111-1-1-1-1-1-111-1111-1-11-11-1-11
χ1722222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000000020-20-20200000
χ1822222222222222222-2-2-2-22222-2-2-2-2000000000000-2-200000000000000000000-202020-200000
χ192222222-2-2222-2-2-2-2-222-2-222-2-222-2-2000000000000-22000000000000000000002020-20-200000
χ202222222-2-2222-2-2-2-2-222-2-222-2-222-2-2000000000000-2200000000000000000000-20-2020200000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-11111111111111111-1-1-1-1000000000000
χ23222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ24222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-11111000000000000
χ25222222-1-2-2-1-1-11111-2-2-222-1-11111-1-12-22-222-2-222-2-2-11-1-1-1-11111-1-1-1-11111-1-111000000000000
χ26222222-1-2-2-1-1-11111-2-2-222-1-11111-1-12-22-2-2-222-2-222-111111-1-1-1-11111-1-1-1-1-1-111000000000000
χ27222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-22-2222-2-2-2-222-11-1-1-1-111111111-1-1-1-111-1-1000000000000
χ28222222-1-2-2-1-1-11111-2-2-222-1-11111-1-1-22-22-2-22222-2-2-111111-1-1-1-1-1-1-1-1111111-1-1000000000000
χ292222-2-22222222222-22-22-2-2-2-2-22222000000000000-2-200000000000000000000020-20-2020000
χ302222-2-22222222222-22-22-2-2-2-2-22222000000000000-2-2000000000000000000000-202020-20000
χ312222-2-22222222222-2-22-22-2-2-2-2-2-2-2-22-2-22000000002200000000000000002-22-2000000000000
χ322222-2-22222222222-2-22-22-2-2-2-2-2-2-2-2-222-200000000220000000000000000-22-22000000000000
χ332222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-222-2-2000000002-200000000000000002-2-22000000000000
χ342222-2-22-2-2222-2-2-2-222-2-22-2-22222-2-2-2-222000000002-20000000000000000-222-2000000000000
χ352222-2-22-2-2222-2-2-2-22-222-2-2-222-2-222000000000000-2200000000000000000000020-2020-20000
χ362222-2-22-2-2222-2-2-2-22-222-2-2-222-2-222000000000000-22000000000000000000000-2020-2020000
χ372222-2-2-122-1-1-1-1-1-1-1-2-22-22111111112-2-2200000000-1-133−3−333−3−333−3−333−3−3-11-11000000000000
χ382222-2-2-122-1-1-1-1-1-1-1-2-22-22111111112-2-2200000000-1-1−3−333−3−333−3−333−3−333-11-11000000000000
χ392222-2-2-122-1-1-1-1-1-1-1-2-22-2211111111-222-200000000-1-133−3−333−3−3−3−333−3−3331-11-1000000000000
χ402222-2-2-122-1-1-1-1-1-1-1-2-22-2211111111-222-200000000-1-1−3−333−3−33333−3−333−3−31-11-1000000000000
χ412222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-11122-2-200000000-1133−3−3−3−33333−3−3−3−333-111-1000000000000
χ422222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-11122-2-200000000-11−3−33333−3−3−3−33333−3−3-111-1000000000000
χ432222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-111-2-22200000000-1133−3−3−3−333−3−33333−3−31-1-11000000000000
χ442222-2-2-1-2-2-1-1-1111122-2-2211-1-1-1-111-2-22200000000-11−3−33333−3−333−3−3−3−3331-1-11000000000000
χ45444444-244-2-2-2-2-2-2-24-4-4-4-4-2-2-2-222220000000000002200000000000000000000000000000000
χ46444444-2-4-4-2-2-22222-444-4-4-2-222-2-2220000000000002-200000000000000000000000000000000
χ474444-4-4-244-2-2-2-2-2-2-2-44-44-42222-2-2-2-20000000000002200000000000000000000000000000000
χ484444-4-4-2-4-4-2-2-222224-444-422-2-222-2-20000000000002-200000000000000000000000000000000
χ4944-4-44-44004-4-40000000004-40000000000000022−2200000000000022−2222−2200000000000000000000
χ5044-4-44-44004-4-40000000004-400000000000000−2222000000000000−2222−222200000000000000000000
χ5144-4-44-4-200-222−2i3−2i32i32i300000-22−2i32i300000000000022−22000000000000−22−22i6−i6i6−i60000000000000000
χ5244-4-44-4-200-222−2i3−2i32i32i300000-22−2i32i3000000000000−22220000000000002−22−2−i6i6−i6i60000000000000000
χ5344-4-44-4-200-2222i32i3−2i3−2i300000-222i3−2i300000000000022−22000000000000−22−22−i6i6−i6i60000000000000000
χ5444-4-44-4-200-2222i32i3−2i3−2i300000-222i3−2i3000000000000−22220000000000002−22−2i6−i6i6−i60000000000000000
χ5544-4-4-444004-4-4000000000-440000000000000000−2i22i200000000000000−2i22i22i2−2i20000000000000000
χ5644-4-4-444004-4-4000000000-4400000000000000002i2−2i2000000000000002i2−2i2−2i22i20000000000000000
χ5744-4-4-44-200-222−2i3−2i32i32i3000002-22i3−2i300000000000000−2i22i200000000006−6−66i2−i2−i2i20000000000000000
χ5844-4-4-44-200-222−2i3−2i32i32i3000002-22i3−2i3000000000000002i2−2i20000000000−666−6−i2i2i2−i20000000000000000
χ5944-4-4-44-200-2222i32i3−2i3−2i3000002-2−2i32i300000000000000−2i22i20000000000−666−6i2−i2−i2i20000000000000000
χ6044-4-4-44-200-2222i32i3−2i3−2i3000002-2−2i32i3000000000000002i2−2i200000000006−6−66−i2i2i2−i20000000000000000
χ614-44-40044i−4i-44-44i−4i4i−4i000000000000000002-22i−2i0000002-22-22i−2i2i−2i000000000000000000000000
χ624-44-40044i−4i-44-44i−4i4i−4i00000000000000000-22−2i2i000000-22-22−2i2i−2i2i000000000000000000000000
χ634-44-4004−4i4i-44-4−4i4i−4i4i000000000000000002-2−2i2i0000002-22-2−2i2i−2i2i000000000000000000000000
χ644-44-4004−4i4i-44-4−4i4i−4i4i00000000000000000-222i−2i000000-22-222i−2i2i−2i000000000000000000000000
χ654-44-400-24i−4i2-22−2i2i−2i2i000000000−2i32i323−2300002-22i−2i000000−1+31−3−1−31+3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ664-44-400-24i−4i2-22−2i2i−2i2i000000000−2i32i323−230000-22−2i2i0000001−3−1+31+3−1−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ674-44-400-24i−4i2-22−2i2i−2i2i0000000002i3−2i3−232300002-22i−2i000000−1−31+3−1+31−3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ684-44-400-24i−4i2-22−2i2i−2i2i0000000002i3−2i3−23230000-22−2i2i0000001+3−1−31−3−1+3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ694-44-400-2−4i4i2-222i−2i2i−2i000000000−2i32i3−232300002-2−2i2i000000−1−31+3−1+31−3ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22000000000000000000000000
χ704-44-400-2−4i4i2-222i−2i2i−2i000000000−2i32i3−23230000-222i−2i0000001+3−1−31−3−1+3−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22000000000000000000000000
χ714-44-400-2−4i4i2-222i−2i2i−2i0000000002i3−2i323−2300002-2−2i2i000000−1+31−3−1−31+3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22000000000000000000000000
χ724-44-400-2−4i4i2-222i−2i2i−2i0000000002i3−2i323−230000-222i−2i0000001−3−1+31+3−1−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22000000000000000000000000
χ738-8-8800800-8-88000000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-40044-443−43−434300000000000000000000000000000000000000000000000000000000000
χ758-8-8800-40044-4−434343−4300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.